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By J. Gurland

The effects of variations of carbon content on the constitution and properties of sintered WC-Co alloys were studied. The grain growth of tungsten carbide during sintering was measured and it was shown that it takes place mainly by solution and reprecipitation of the carbide in and from the binder at the sintering temperature. It was found that the decomposition of W3C03C by carburization during sintering is responsible for the formation of very large grains. THE properties of sintered WC-Co alloys are critically dependent upon their final composition and structure. Slight changes of cobalt and carbon contents and small variations of grain size result in marked changes of mechanical properties and performance of products. Previous investigators have studied the microstructure as a function of composition' and have dealt with the influence of cobalt upon properties.' The present work is concerned with the effect of carbon content upon constitution, microstructure, and grain growth during sintering, as well as upon the physical properties of sintered compacts. Phase Boundaries at the Sintering Temperature The WC-Co section through the ternary diagram W-Co-C has been studied by Wyman and Kelley,' Takeda,V andford and Trent," and Rautala and Norton." Two phases, namely WC and a cobalt-rich solid solution (P), appear in the sintered structure if the carbon composition corresponds very nearly to the theoretical carbon content of WC (6.12 pct C). But small deviations from the ideal carbon content will bring about the occurrence of either graphite or the double carbide W,Co3C (7) . The 7 phase was long believed to be metastable, this conclusion being based mainly on the work of Takeda. More recent studies have shown that it is a stable phase of the ternary system,"5 but the actual phase boundaries have not been established and there has been some discussion as to whether or not the 7 phase occurs at some stage of sintering in the fully carburized alloys." In view of this uncertainty it was thought advisable to undertake an investigation of the phases present during the sintering of WC-Co alloys. Commercially available tungsten, cobalt, and carbon powders were used in the present study. A typical analysis of impurities in a sintered compact is reported in Table I. The desired carbon compositions were attained by varying the amount of carbon added to the tungsten during carburization and controlling the composition during sintering by packing the compacts into beds of mixed alundum-carbon powders of suitably selected ratios. The alloys were sintered in a hydrogen tube furnace at 1400°C, then brought to equilibrium at the temperature under investigation and quenched in water. The high temperature phases were identified by metallographic and X-ray diffraction techniques. The samples were etched with a 10 pct solution of alkaline potassium ferricyanide. The phase boundaries, established by metallo-graphic examination, are shown in Fig. 1, which is a vertical section through the ternary diagram at 16 pct Co. The temperatures of the invariant planes, at 1298" and 1357°C were established by Rautala and Norton. The vertical section shows that the three-phase field, WC + 7 + L, extends into the two-phase field, WC + L, but does not include the stoichiometric composition of WC. In practice this means that the 7

Jan 1, 1955

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965

By H. R. Brannon, R. J. Robinson, G. W. Kattawar

Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and .98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gulf water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. INTRODUCTION Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydro-dynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. l-3 One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice5.6 in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker 7 have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire,8 among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii,10 establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other areas as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents (1) a practical approach to computing wave profiles hat depict shapes of waves for use in force calculations, (2) a summary of relations for predicting probabilities of wave crest elevations, (3) correlations of parameters needed to apply these methods in the Gulf of Mexico and (4) examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities. These relations also identify quantities that must be related to storm

By P. Ramachandraraa, T. R. Anantharaman

THE technique developed by Duwez, Willens and Kle-ment' for rapid solidification of molten alloys in small quantities by ejecting them on to a highly conducting substrate with the aid of a shock wave has come to be known as "liquid quenching" or "splat cooling" in literature and has already been applied to alloys of many binary systems.' The very high cooling rates of the order of l060 to 1080 per sec obtained in this technique and the consequent drastic undercooling of the melt have led to such striking results as formation of new amorphous and crystalline metastable phases and extension of solid-solubility limits in many alloy systems. The cooling rates in these experiments can, however, be neither accurately measured nor effectively controlled and hence the occurrence of either more than one metastable phase or appreciable differences in constitution in splat-cooled alloys of the same composition cannot be ruled out.3 In fact, workers in two laboratories have reported formation of two different cubic metastable phases in liquid-quenched Au-Si alloys containing 17 to 20 at. pct si.4,5 The present note deals with some new and interesting results obtained in a Ag-21 at. pct Ge alloy and a Au-27 at. pct Ge alloy subjected to the liquid-quenching treatment at different cooling rates. Two alloys of nearly the same composition had earlier been rapidly solidified by the standard "gun technique" in the same laboratory and shown to solidify in nonequilibrium structures, viz., an hcp phase (a = 2.987Å;c =4.718Å) in the Ag-Ge system6,7 and both hcp (a = 2.885Å; c = 4.754Å) and tetragonal (a = 11.627A; c = 22.491Å) phases in the Au-Ge system.3 Apart from different substrates (copper and stainless steel), different melt temperatures (50º to 500°C above the liquidus), and different capillary sizes (0.4 to 1.5 mm diam) in the "gun technique", slower cooling rates of the order of l050C per sec were also obtained in the present work by replacing the substrate by water at room temperature in a modification of the technique due to Olsen and Hultgren.8 No attempt was made to measure the cooling rate in any experiment. The products varied from fine powder (>40 pct by wt—200 mesh) obtained by quenching in water to thin flakes and foils (11.0 sq mm to 4.0 sq cm) produced by splat cooling. They were subjected to the Debye-Scherrer method of X-ray examination in each case. In case of the Ag-Ge alloy, in addition to the expected metastable hcp phase,6 a coexistent tetragonal phase (a = 5.093,Å; c = 7.009Å) was detected in some experiments. Eight weak X-ray reflections from this phase could be identified, two of them being the same as reported earlier.7 With increase in the cooling rate, the dominant hcp phase seems to be first accompanied by traces of silver or germanium and then either homogeneous or mixed with traces of this new tetragonal phase. The splat-cooled Au-Ge alloy showed generally the expected hcp and tetragonal phases,3 but sometimes traces of germanium were also present. Further, two new tetragonal phases with the following lattice param ters could be clearly identified in samples quenched

Jan 1, 1970

By W. R. Purcell, C. S. Brooks

The internal surfaces of rocks which are in contact with interstitial fluids are known to influence in some degree the recovery of hydrocarbons from pay zones. Despite the admitted importance of the influence of solid surfaces on hydrocarbon recovery, little information is available concerning the extent of surface of reservoir rocks. In this paper a description is given of the apparatus and procedure employed in the determination of the surface areas of sedimentary rocks, and values are reported for a variety of sandstone and limestone cores. In addition, consideration is given to the Kozeny equation, which relates surface area to porosity and permeability. A colliparison is made between the surface areas as calculated from this equation and the geometrical areas of a series of packs of spherical glass beads. Also, for a group of sandstone cores. Kozeny areas are compared with surface areas as determined by the gas adsorption method employed in this investigation. INTRODUCTION It has long been recognized that many processes which are of importance to hydrocarbon production are controlled in some degree by the extent of the surface of the reservoir rock through which the hydrocarbons move. For example, the recovery efficiency that is obtained in a given reservoir is certainly determined in part by the action of interfacial forces between the reservoir fluids and rock, and this action is influenced in turn by the extent of solid surface. Despite the admitted importance of surface effects to problems of petroleum recovery, little information is available concerning the extent of surface of reservoir rocks." It is the purpose of this paper to describe an apparatus which has been employed for the measurement of the surface areas of rock samples and to present the values which have been obtained for a variety of sandstone and limestone cores. In addition, the relationship of surface area to permeability and porosity, as given by the Kozeny equation, will be discussed. METHOD OF MEASURING SURFACE AREA The method of determining surface areas as employed in this work has previously found wide use in studies of porous solids such as catalysts. The method involves the measurement of the amount of physical adsorption of an inert gas, such as nitrogen or argon, on the bare surface of the solid at reduced pressure and constant temperature near the normal liquefaction temperature of the gas. With the aid of the theory of isothermal adsorption as developed by Brunauer, Emmett, and Teller,' it is possible to ascertain the amount of gas (and hence the number of molecules) which is required to cover the solid surface with a single layer of molecules. From a knowledge of the covering area per molecule the total surface ares of the solid can be computed. Since the Brunauer. Emmett, Teller (BET) theory has been adequately discussed elsewhere: it will suffice here merely to present their final equation as ordinarily employed for surface-area calculations. This equation relates the volume of gas, V, which is adsorbed at pressure, P, to the liquefaction pressure, Po, of the gas, and to the volume of gas, V.,, that is required to form a monomolecular layer: In this equation C is a quantity which is related to the heats of adsorption and liquefaction of the gas; for a particular solid-gas system at Constant temperature, C is considered to have a constant value. The basic adsorption data can be presented in the form of Equation (1) by plotting the quantity P/V(Po- P) as a func-

Jan 1, 1952

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

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

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

By Spencer S. Shannon

The lanthanide elements from lanthanum (atomic number 57) to lutetium (71) plus yttrium (39) are called the rare-earth elements; scandium (21) is chemically similar to yttrium and the lanthanides, but differs in occurrence. The rare-earth metals were divided into three categories by the chemist, Berzelius, in the early 1800s; however, modern usage defines only two groups. The cerium group is named after the most abundant -element and comprises lanthanum (57), cerium (58), praseodymium (59), neodymium (60), promethium (61), samarium (62), europium (63), and gadolinium (64). Traces of natural promethium were discovered in apatite in Finland (Erametsa, 1965). The yttrium group, also named after its most abundant representative, comprises terbium (65), dysprosium (66), holmium (67), erbium (68), thulium (69), ytterbium (70), and lutetium (71). Yttrium most closely resembles holmium in chemical properties, and occurs most commonly with the heavy lanthanides. The rare-earth minerals may be divided into cerium-group, yttrium-group, or mixed-group classes. A number of rare-earth minerals contain thorium and uranium, but these are variable in content and are not essential to the composition of the minerals. In monazite, a mineral that is a principal source of rare earths, the worldwide average content of thorium oxide is 7.2 % ; however, varieties of monazite contain as little as 0.001% and as much as 31.5% thoria. Monazite is the chief ore of thorium and, until recently, thorium has been the main product; the rare-earth metals were in fact byproducts. However, because of the great demand for rare-earth metals by the petroleum refining and the iron and steel industries since the early 1970s, the roles have been reversed so that thorium is now the byproduct. Uses A 9 to 1 mixture of yttrium and thorium oxides is used for high-intensity incandescent lamps and for high-temperature-resistant windows and lenses. Yttrium oxysulfide and orthovanadate, doped with europium oxide, are used in color television tube phosphors. Yttrium, as well as cerium, praseodymium, and samarium, is alloyed with cobalt to form strong permanent magnets. It hardens magnesium alloys and retards the oxidation of iron-chromium alloys. Yttrium-iron garnets are used for transmitting low microwave frequencies. Yttrium-aluminum garnets are used as host crystals for lasers and as artificial gems. Yttria also forms strong, stable, high-temperature refractories. Gadolinium-gallium garnets are used in substrate wafers on which bubble-memory films are deposited. Rare-earth chlorides, particularly of lanthanum, neodymium, and praseodymium, are used as catalysts for petroleum cracking. Mischmetal is used for lighter flints and to improve the ductility and impact strength of iron and steel alloys. Mischmetal also reduces the fatigue resistance of magnesium and aluminum alloys. Rare-earth oxides are used for polishing glasses and lenses. Individual or specific combinations of high-purity oxides are used as additives in glass to maintain or change its color, dispersion, or refractive index. High-purity oxide combinations are also used to color tile and to opacify porcelain enamel. Rare-earth fluorides and oxides are used in carbon-arc electrodes to provide incandescent white light. Lanthanum or gadolinium oxysulfide phosphors, activated with terbium, are used as x-ray screen intensifiers. Hydrogen can be stored by sorption on lanthanum-nickel alloys (Anon., 1979). Thorium232 is bombarded with slow neutrons in breeder reactors to create fissionable thorium233 for nuclear fuel cells. The 330-MW, high-temperature gas-cooled reactor at Fort St.

Jan 1, 1983

DEVELOPMENT of a chemical process for the extraction of pure metals from mill concentrates or metal scrap has progressed beyond the pilot plant stage and may prove an important adjunct to present smelting and refining methods if initial commercial operations prove economically successful. Developed by the Chemical Construction Corp., the new process involves the treatment of oxide and sulphide ore concentrates by chemical methods, instead of the usual smelting and refining techniques. Several of the many applications are now scheduled for commercial use. Refiners using the new process will prepare ore concentrates by standard flotation methods, introduce the concentrate as a slurry into an autoclave along with water and an acid or ammonia. From the resulting leach solution, recovery of individual metals is made by use of suitable reducing agents. By varying conditions during treatment, different metals in the ore are produced separately as pure powders, which may be pressed into forms ready to market, or in the case of copper, extruded as rods or pipe. The reagents are generally recovered. By manipulating the variables during reduction, selective separation of nickel, and/or cobalt, and/or copper can be made simultaneously. The separation is a continuous operation. Low metal prices are not immediately in view because of the tremendous demand at this time. However, reduced metallurgical treatment costs will allow economical mining of orebodies with lower metal content, permitting increased production to meet demand. Although the practical horizon for use of the new process appears to be limitless, one factor may enter into its employment. Just how low grade a concentrate can be economically used is unknown. In addition, for present practical considerations, only metal below zinc in the electromotive series may be processed. Each commercial application requires specific technique adaptation and pilot-plant data for engineering design. A nickel-cobalt-copper process has been researched and piloted in collaboration with Sherritt Gordon Mines, Ltd., for the firm's Lynn Lake properties. In addition, processes were tailored for cobalt concentrates of Howe Sound Mining Co., and National Lead Co., in view of the urgent need for this specific metal. Major General William N. Porter, president of Chemical Construction, says of the new process, "piloting experience has shown that production cost, from ore concentrates to pure metals should be considerably below current costs." Other savings may be realized by cutting transportation and personnel costs, and by reducing the time lag between mining and pure metal from months to a matter of hours. First commercial use of the process will start sometime this summer. Chemico is slated to finish building a $2.5 million cobalt refinery for Howe Sound Mining near Salt Lake City. The plant is expected to raise world cobalt production by 40 pct. The plant will process 35 tons of 20 pct cobalt concentrates from Howe Sound's Blackbird mine near Cobalt, Idaho, daily. Yearly production is expected to reach 2000 tons of pure metal, about one half of U. S. consumption in 1950. Steps in the Howe Sound application of the process are: 1. Acid oxidation leach. 2. Filtration (residues thrown away are insoluble compounds-gangue, iron, arsenic). 3. Cementation (for Cu removal because Cu content is too low for recovery). 4. Reduction from ammoniacal solution. 5. Separation of Co and Ni as mixed metals (95 pct Co and 5 pct Ni). 6. Recovery of ammonium sulphate. Under construction at the Fredericktown, Mo., mine of National Lead is a $5 million refinery sched- [ ]

Jan 1, 1952

By Allen F. Agnew

Detailed stratigraphic studies in the Wisconsin-Illinois-Iowa district have made it possible to map the folds and faults that controlled the deposition of the zinc-lead ore. Prospecting on the basis of this mapping and prospecting in lower zones that are potentially ore-bearing have led to discoveries of ore. GEOLOGIC studies for the Federal and State governments in the Wisconsin-Illinois-Iowa zinc-lead district were begun in 1835, and subsequent surveys were made in the three states at intervals until 1916, see Table I. The current study of the district, Fig. 1, by the U. S. Geological Survey was begun in 1942 in the hope that a systematic investigation would help increase production of zinc and lead, then in extremely short supply. Major emphasis of the USGS program was on detailed mapping of the geologic structure and ore deposits. Preliminary maps and reports covering localities of intensive mining activity have been published during the course of this study, Fig. 2. By 1950 the objectives of the study by the USGS were revised; 71/2-min quadrangles of relatively unprospected localities as well as intensively mined localities are now being mapped in Wisconsin. Since 1945 the investigation in Wisconsin has been made in cooperation with the Wisconsin Geological and Natural History Survey, and since 1951 the geologic mapping of areas of particular interest in Iowa has been performed in cooperation with the Iowa Geological Survey. At intervals since 1943 the Illinois State Geological Survey has mapped the geologic structure and ore deposits of localities in the Illinois part of the mining district, see Fig. 2. Geology was applied by mining company personnel as early as 1853, but only sporadically, with periods of greater application between 1890 and 1925. Much of the so-called geologic work was in reality mining engineering. Since 1946 the major mining companies in the district have employed geologists who have successfully applied geologic techniques in the search for ore. History of Mining Occurrence of galena in the district was known as early as 1658 or 1659, when French explorers heard of lead mines that were apparently in the vicinity of Dubuque, Iowa. In 1690 a trading post was established near Dubuque to obtain galena. The first significant attempt at mining by white men took place in 1788 when the Indians granted to Julien Dubuque mining rights for 20 miles along the west side of the Mississippi River, including the vicinity of Dubuque, Iowa. By 1805 lead was being mined near Galena, Ill. In 1819 permanent settlement of the region was begun, and most of the important lead-producing areas had been found by 1830, see Fig. 3. Lead production in the Wisconsin-Illinois-Iowa district between 1830 and 1871 far exceeded that of any other district in the U. S.' Smithsonite was first mined in 1859, and sphalerite was mined as early as 1867. After 1873 the production of sphalerite exceeded that of smithsonite. In 1873 annual zinc production from the district first equaled lead production, and from then until 1893 production of zinc and lead was roughly the same. Since 1893 the ratio of zinc to lead mined has generally ranged between 5:l and 20:l. In 1942 the Wisconsin-Illinois-Iowa zinc-lead district ranked 14th among zinc-producing districts of the U. S. From 1946 until February 1953 the dis-

Jan 1, 1956

By R. F. Rolsten

The preparation of pure metals by the thermal decomposition of volatile halides was developed byde boer' and van Arkel.2 This has proved to be a useful technique for the refining of columbium,the mechanical and physical properties of which are seriously altered by such interstitial contaminants as oxygen, nitrogen, hydrogen, and carbon. The conventional deposition surface of a resis-tively heated metal filament was replaced, Fig. I, with an indirectly heated clear quartz surface. The impure columbium (feed) was contained in the annular space between the Vycor deposition bulb and the perforated molybdenum retaining cylinder. The head assembly was attached to the deposition bulb by fusing the Vycor at "A". This unit was then connected to a vacuum system composed of a three-turn glass coil to eliminate fracture due to vibration or expansion, a McLeod gage, a cold trap, a two-stage mercury diffusion pump, and a mechanical pump. The entire system was cold outgassed, and the 10 to 20 g of iodine in the auxiliary bulb (reservoir) was held in dry ice to prevent excessive loss of iodine. The columbium was hot outgassed at 800" to 825oC with the pressure maintained at l0-5 to 10-6 mm Hg for 48 hr and cooled under vacuum to 200° to 240oC. Iodine was sublimed from the reservoir and collected in the deposition bulb. The feed material temperature was adjusted to give the desired iodide vapor pressure and the finger temperature of 1000" C was independently attained and measured with a platinum-platinum 10 pct Rh thermocouple located in the center of the nichrome wire helical heating element, "F." The system was attended until temperature equilibrium was established, whence it operated without attention. This is a definite ad- vantage over the conventional "hot-wire" technique which required either constant attention or automatic control. In operation, the iodine vapor originally introduced into the vessel reacted with the crude metal to form a columbium iodide. This iodide vapor diffused to the hot deposition surface where it thermally decomposed, depositing columbium and releasing iodine. This liberated iodine then diffused back to the crude columbium where iodide was formed again. Thus, by repetition of this process, the iodine carried pure columbium from the crude material to the filament, where it deposited. The success of the "iodide" process in producing ductile metals depends on preventing the transfer of oxygen, nitrogen, hydrogen, and carbon from the feed material to the deposit. In many cases relatively minor quantities of these interstitial contaminants impair the ductility of metals. The material produced by the iodide process has such exceptional ductility that it is frequently and mistakenly assumed that iodide metal is always of very high purity. This assumption is not necessarily true since a number of metallic impurities can also be transferred. In the present investigation, the temperature of the feed material was adjusted to iodinate selectively and the deposition temperature adjusted to decompose the iodides selectively. By this technique, some metals present in the feed material were prevented from codepositing with the columbium. It is quite important to have the feed material symmetrically located around the deposition surface in order to obtain a uniform deposit at the maximum rate. For example, Runnalls and pidgeon3 observed that, when the base of a titanium filament was about 1 cm from the feed material, deposition was rapid on that section close to the feed, but that the rate decreased with distance from the feed so that a

Jan 1, 1960

By J. S. Crump, H. L. Stone

Laboratory studies have indicated that displacement of oil from a reservoir by means of a condensing gas drive results in extremely high oil recovery, approaching 100 per cent under the most favorable circumstances. A condensing gas drive is defined as a gas drive in which the gas utilized is appreciably soluble in the oil it is displacing. The laboratory studies consisted of a number of gas drive displacement experiments, all using a horizontal, sand-packed, steel tube as the laboratory reservoir. The experimental results indicate that the more soluble a gas is in the oil to he displaced, the more efficient that gar is as a displacing fluid. Experiments were conducted utilizing both a light, volatile crude and a heavy, asphalt crude as the in-place oil. In both cases, oil recovery was appreciably enhanced by solubility of the displacing gas. It is believed that the use of condensing gas drives would result in increased oil recovery from many reservoirs during either primary or secondary phases of production. INTRODUCTION Since the early days of the oil industry there has been an increasing awareness of the problems of oil recovery. During the last few decades particularly a growing recognition of the problems has led to widespread attempts on the part of the industry to increase oil recovery by improved technology. One method which has been used to increase recovery is the maintenance of reservoir pressure by injection of gas. Part of the beneficial effect resulting from this gas injection was to prevent evolution of the gas dissolved in the reservoir oil, since such evolution would cause the oil to shrink and become more viscous, thereby adversely affecting oil recovery. In most instances, the gas injected was predomillantly methane, and so the possibility of oil recovery by retrograde vaporization existed. Laboratory investigations of displacement of reservoir oils by methane, carried out at high pressure, have indicated that considerable additional recovery of light oils could be effected by vaporization, but only at the cost of a severe volumetric shrinkage of the residual oil which would cause a decrease in relative permeability to oil in the reservoir. Consequently, recovery of oil by physical displacement would be impaired. The study suggested, therefore, that recovery of oil might be enhanced by injecting into the reservoir a gas known to be appreciably soluble in the oil at reservoir conditions. Swelling of the oil due to solution of gas should result and yield a consequent increase in the relative permeability to oil. The work described in the following sections was, therefore, undertaken to investigate the possibility of increased recovery by this mechanism. Research similar to that reported in this paper has been conducted by The Atlantic Refining Co.1,2,3 In these studies, Whorton, et al, and Slobod, et al, used methane-rich gas to displace oil from model reservoirs. Solubility of the gas was achieved by keeping the reservoir pressure greater than the saturation pressure of the original oil, and the degree of this solubility was varied by operating at different reservoir pressures. Thus the Atlantic project was primarily a study of the effect of reservoir pressure upon oil recovery by gas drive. The objective of the work reported in this paper was to study the effect of gas composition upon oil recovery while holding the reservoir pressure constant. DESCRIPTION OF EXPERIMENTS The discussion of the preceding section suggests that

Jan 1, 1957

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.

By L. R. Page, J. J. Norton

EFFECTIVE methods for determining grade and reserves of pegmatites in advance of mining have been developed in recent years. When intensive work began on the economic geology of pegmatites during the early years of World War 11, it was widely believed that grade and reserves could be estimated only in a most general way. The literature indicated that not all pegmatite deposits are unpredictable, but statements emphasizing unpredictability and irregularity seem to have been more widely accepted. Many standard references reflect the prevailing opinion that minerals: are unsystematic in their occurrence in pegmatites. Pegmatites have been described as "notorious for their irregular structure," and minerals within pegmatites as "irregularly distributed." "irregularly disseminated," of "erratic occurrence," "proverbially erratic in distribution," "characterized by extreme irregularity in ... size and distribution of the essential minerals, and variety and proportion of the accessory minerals," and "spotty.'"" Over many years, however, geologic techniques have been applied with increasing success to economic analysis of pegmatites. Investigations, chiefly since 1939, have shown that mineral distribution and structure of pegmatites are largely systematic and that detailed geologic study can be used to predict the size and shape of mineral deposits in pegmatites. Because the writers are most familiar with the pegmatites of the Black Hills, S. D., examples cited are from that area." Pegmatites mined in other dis- * All examples are described more cornpletely elsewhere.: tricts are similar to those in the Black Hills," and the techniques described here have been applied by geologists and engineers working in other districts. In actual practice few pegmatite mine operators attempt to make accurate estimates of grade and reserves in advance of mining. Many deposits are too small for mining except on a very small scale; few pegmatite mines have more than ten employes. Hence there is little systematic preparation for mining, and the capital outlay may be so small that only a general knowledge of reserves is necessary. Technical personnel are rarely employed by pegmatite mine operators to make such estimates. In the future, however, as capital outlay becomes larger, estimates of grade and reserves will have to be more accurate. Geologic Aspects of Determining Grade and Reserves Estimating grade and reserves requires that the type of pegmatite, the size and shape, and the internal structure be determined by detailed geologic mapping and careful mineralogic study. The wide variations in the texture and distribution of minerals within many pegmatite deposits make a thorough geologic study of this kind necessary before it is possible to decide what sampling methods should be used to determine mineral content or grade. Types of Pegmatites: The first step in economic appraisal of a pegmatite is to determine the min-eralogical and structural type. In general, pegmatites may be classified into two groups: 1) those in which component minerals are more or less evenly distributed throughout the entire body and show relatively minor variations in texture, and 2) those in which component minerals have been segregated into units with recognizable differences in texture, mineralogy. or both. Johnston" has classified these types of pegmatites as homogeneous and heterogeneous, respectively. Cameron et al.10 have used the terms ~inzoned and zoned for similar types. The difference between the homogeneous and heterogeneous types is of great commercial importance. Homogeneous pegmatites can seldom be mined where the products are concentrated by the hand methods now commonly used, but they have been mined in a few places where a milling process has

Jan 1, 1957

By Nicasio del Castillo

INTRODUCTION The tax structure of foreign mining investment into the United States has a significant impact on the financing and the profitability of the operation. For these reasons, it is critical for the foreign investor to develop and implement a well planned tax strategy that will enable its venture to: (1) reduce its U.S. income tax liability (2) lower U.S. withholding taxes when funds are transferred from the United States, and (3) decrease or defer home country taxation on its U.S. earnings ALTERNATIVE FORMS OF INVESTMENT A threshold business and tax consideration is the form in which the investment is to be made. The most common alternatives include: forming or acquiring a U.S. mining corporation, directly establishing a branch mining operation, or entering into a joint venture or partnership with a U.S. mining company. U.S. Corporations The most common structure through which foreign mining companies engage in business in the United States is to form a U.S. mining corporation. Forming a U.S. Corporation. If the investor decides to establish a new U.S. corporation the organization is relatively simple. No distinctions are made in the United States between "public" and "private" forms of incorporation. Minimum share capital is not usually required and share capital may consist of shares with no par value. Since corporate law is the responsibility of the individual states, the foreign investor must choose a state in which to incorporate. If appreciated mining property is transferred to a corporation solely in exchange for stock or securities in that corporation, and the transferors have control of the corporation (defined as at least 80 percent of all voting shares and at least 80 percent of all other shares) immediately after the exchange, no gain or loss will be recognized. However, if the transferors receive cash or other mining properties in addition to stock, any resulting gain may, in certain situations, be taxed to the extent of the cash and the fair market value of other property received. Acquiring an Existing U.S. Corporation. Acquiring an existing U.S. mining corporation is not as straight-forward as forming a corporation. This alternative may be accomplished through either a stock or an asset acquisition. Generally, with a stock acquisition the purchaser inherits all of the business and tax attributes of the former mining corporation. If the investor is able to acquire mining assets, however, the purchaser will usually be able to avoid any unknown or hidden liabilities that could be attached to an existing corporation. Another principal advantage in acquiring assets is that the purchase price may be directly allocated to the acquired mines or other mineral-related assets with the result that the assets' depreciable base may be increased. Assuming the domestic seller and the foreign purchaser can agree, it is generally advisable to allocate the purchase price in the sales agreement to specific individual assets. From the foreign investor's standpoint, it is preferable to allocate the purchase price to depreciable assets such as buildings and equipment versus an allocation to mineral land holdings or intangibles such as goodwill, which are generally not depreciable. It is not uncommon, however, for a seller mining company being acquired to insist for tax reasons that the investor purchase shares rather than assets. If the foreign

Jan 1, 1985

By Albert G. Anderson

I'm sure many of you have wondered what the term "Cross Flow Filtration" means. I shall explain it so that you more clearly understand it, and I hope you will be able to make it a useful tool for you in the future. In the simplest form of cross flow filtration contaminated fluid. or feed stream, is fed at a high velocity down the center of a porous tube, clear fluid weeps through the porous wall of the tube while the suspended solids concentrate in and are swept away by the feed stream. (See figure A). The high velocity flow of the feed stream tends to keep the inside of the tube free from a build up of contamination. By utilizing this cross flow approach to filtration, we have been able to concentrate such things as paint pigments, titanium dioxide, iron oxide, precipitated metals such as uranium yellowcake or silver, cadmium, some metal hydroxides, as well as gelatinous particles such as yeast cells. You will recognize that cross flow filtration lends itself to a recirculation loop system due to the necessity of maintaining a high velocity on the inside of the tube. This means that we generally have a storage tank from which we are recirculating, and the solids will concentrate in the storage tank. (See figure B). The storage tank design becomes an integral part of the total system and is very important to the total function of the system. The cross flow filter system requires only low pressure, and will work with centrifugal pumps, diaphram pumps or in some cases no pump at all. As an example, if we wanted to filter a 10 GPM (37.8 liters/min.) stream that contained 1% of submicronic particulate, we would flow the 10 GPM (37.8 liters/min.) into the storage tank and recirculate through the filter at a flow of anywhere from 30 GPM to 100 GPM (113.6 to 378.5 liters/min.) depending upon the filterability of the particles from the liquid. As the contaminated fluid recirculates, the solids will build up in the storage tank and loop until they reach a level, which is dependent upon the design of the tank. Then the settling rate in the tank becomes equal to the amount of the solids being fed to the tank, and as a result you reach an equilibrium in the amount of solids being presented to the inside of the porous tubing. We have in effect created a dynamic settling tank or thickener. A flow of 10 GPM (37.8 liters/min.) of clear filtrate comes off for either recycle or disposal with periodic removal of thick mud from the bottom of the tank. The thick mud can be either processed through a centrifuge, a rotary drum filter. a flat bed pressure type filter, or other means. Often the small volume of filtrate from the mud de-watering stream can be recycled back into the recirculation tank so that any fines in the feedback are again concentrated, thus closing the loop on the continuous process 100% removal system. Cross flow filtration will not do efficient molecular separation. We work primarily with discrete solids but we do separate them totally from the liquid carrier fluid. I know some of you will raise your eyebrows when I say that we remove 100% of the particulate, but in measurement tests, we have measured the filtrate cleanliness with instruments that record as low as .05 ppm and the instruments read zero, so that it is less than .05 ppm.

Jan 1, 1980

By J. S. Kasper, R. M. Waterstrat, B. F. Decker

THE existence of v phase in the Mn-Mo system was discovered in this laboratory several years ago,' but neither the conditions of its formation nor its composition were known, and preliminary attempts to reproduce the phase were unsuccessful. We wish now to specify the information appropriate to phase formation on the basis of experiments performed since that time. The starting materials were in every case electrolytic manganese and high purity molybdenum. Two methods of preparation were employed: l—arc-melting varying combinations of the elements in an inert atmosphere and subsequent heat treating, and 2—sintering compressed mixtures of finely divided powders of the elements. In the latter method, the powders were first passed through 200 mesh screen and then compressed into cylinders of % in. diameter and % in. length, which were sintered at elevated temperatures in an atmosphere of dry hydrogen. For some samples, the sintering temperature was 1200°C (for 1 hr), and these were then heat- treated at lower temperatures for times up to 24 hr. Eventually it was found, for the proper composition, that essentially pure a phase could be produced by sintering at 1125°C for 3 hr. Quenching to room temperature was effected by means of a stream of cold, dry hydrogen in a water-cooled chamber. The arc-melting procedure was found to be unsatisfactory after an investigation of many samples at different compositions and temperatures. Large quantities of manganese were vaporized during melting and none of the products were homogeneous or contained extended regions of pure phase. Nonetheless, these experiments established that no formation occurs in the Mn-Mo system below 1115oC, and indicated, at least roughly, the composition range of interest for further exploration. The more definite results obtained from samples produced by the second method are given in Table I. A portion of sample 2 heated for 16 hr at 1000°C in a Vycor tube transformed to molybdenum plus unidentified phases of complex X-ray pattern. From these few results it appears that the region of phase is quite narrow in composition. It is of interest that the composition is such as to make for difficulties in correlating this structure on an electron atom basis with other a structures of iron, cobalt, and nickel. In that respect Mn-Mo shows the same anomaly as Mn-Cr and Mn-V systems.' A second feature is that in common with the two other known molybdenum (Fe-Mo and Co-Mo), Mn-Mo v exists only at elevated temperatures. The X-ray powder pattern of the pure a phase of Mn-Mo is given in Table 11. It agrees well with the patterns established for other structures, especially with that for Fe-Mo as given by Goldschmidt.An attempt is being made to establish whether an ordering of the respective atoms occurs and such information will be reported in a future publication. Acknowledgment The authors acknowledge gratefully the assistance of Mrs. J. R. Belanger in some portions of this work. References 'J. S. Kasper, B. F. Decker, and J. R. Belanger: Journal of Applied Physics (1951) 22, p. 361. 2 A. H. Sully: Journal Inst. Metals (1951) 80, p. 173. H. J. Goldschmidt: Research (1949) 2, p. 343.

Jan 1, 1954

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l'wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown