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By R. G. Knickerbocker, A. G. Starliper, H. Kenworthy, C. H. Gorski

This report describes the progress made in the research work on the development of a new method for preparing lower-cost titanium tetrachloride and preparing titanium oxide pigment. One of the requirements for the commercial production of ductile titanium in the process used by the Bureau of Mines is a source of lower-cost titanium tetrachloride. The production of ductile titanium by a modification of the Kroll1 process, recently developed by the Bureau of Mines, requires such a source of lower-cost titanium tetrachloride to make it commercially feasible. This report describes the progress of work done at the Mississippi Valley Experiment Station at Rolla, Missouri, on the development of a new method for preparing titanium tetrachloride. During the course of this research a new method for preparing pigment-grade titanium oxide was developed. At present, the price of technical-grade titanium tetrachloride is $0.32 a pound, which makes the price of the contained titanium $1.28 a pound.2 In addition, the titanium tetrachloride must be purified further before it is suitable for processing into metal, thus making its cost still higher.3 There were 8,562 tons of rutile produced in the United States in 1947, which was 900 tons in excess of that consumed. In addition there were 13,937 tons in various stocks, exclusive of the stocks in the Government strategic stock pile. No estimates of the domestic production of rutile are given for any of the prewar years. However, in 1939, 442 tons of rutile were imported as compared to 14,307 tons in 1947. One of the reasons for the large increase in the production of rutile is the working of the Florida beach sands for ilmenite, during which a considerable amount of rutile is produced as a by-product. It would be of value to determine methods for utilizing the excess production of rutile. The Arkansas titanium deposits in Hot Spring County produced commercial-grade rutile concentrates from 1933 to 1942. These were sold mainly to England, Germany, and Russia.

Jan 1, 1950

OLIVIA'S recent revolution, by hindsight, seems to have been inevitable. The misery of the majority of the people, coupled with the economic crisis engendered by the refusal of the United States to meet Bolivian demands for a higher tin price, gave the National Revolutionary Movement party all the excuse it needed for overthrowing the government. Most of the mines in Bolivia are owned by three families. Precisely what it will mean to the United States is still a moot question. Argentina, with a mixture of Marxism, Fascism, and few twists created by the Perons, is in a position to grab off much of the tin we need. Because of the contingencies of geographical location, language and a natural simpatico, Argentina may be able to continue its efforts to oust the United States from its South American markets. Point Four aid was supposed to be given to Bolivia, but only for agriculture. Even this was entirely too slow. Mining, Bolivia's other major source of income was forgotten by the Washington planners. Primary aim of the new power will be to diminish its dependence on the world tin market. At a time when the free world is fighting a battle for control of metal, it stands a chance of losing an important source of supply. With the accent placed on agriculture and other industries, mining in Bolivia is certain to suffer. Argentina will be in a position to get the available supply of tin, make a strong ally in the world order of things, and add to its power play against the United States in South America. Ten labor groups have formed the Bolivian Central Workers Union. The first item on their list for immediate action is the nationalization of the mining and railroad industries. They also came out for agrarian revolution and diversification of industry. President Victor Paz Estenssoro has promised to appoint a committee for the investigation of nationalization of the mines. At least, this is indicative of a feeling for the need for caution.

Jan 1, 1952

By M. J. Marcinkowski, R. M. Fisher

The flow stress-grain size relationship has been determined at room temperature in both a disordered and a fully ordered FeCo for plastic strains up to 30 pct. The results are in agreement with a Hall-Petch relation of the type given by Of =a,+kd-1/2 where of is the flour stress and a, increases mono-tonically with increasing strain to a maximum value which is much higher for the ordered than for the disordered alloy. The slope, k, is found to increase FOLLOWING the original work of Halll and petch relating the effect of grain size to the lower yield stress of iron and steel, it has been generally found that the yield stress oy.s. of polycrystalline metals with strain to a maximum and then decrease for both ordered and disordered alloys. However, k for the ordered alloy is in general higher than that for the disordered alloy and the critical strain for k max somewhat larger. All of these observations can be satisfactorily accounted for quantitatively and in some cases semiquantitatively by using a slip band-grain boundary intersection model, and by taking note of the fact that, in general, moss slip, while quite common in the disordered alloy, is extremely difficult in the ordered alloy. obeys a relation of the form oy.s.=a0+kd-1/2 [1] where a, and k are constants and d is the mean grain diameter. For convenience, and in accord with prevailing custom, Eq. [I] will be referred to simply as the Petch relation. Tjerkstra3 and Armstrong, Codd, Douthwaite, and petch4 showed that the flow stress af of iron or steel measured at strains of up to at least 20 pct also obeyed a relationship of the type given by Eq. (11. The latter investigators have also shown that Eq. [I] applies to fcc and hcp metals and alloys.

Jan 1, 1965

By George Scott

MANY requests for information as to the possibility of washing coals to some predetermined percentage of ash or sulfur have suggested that the producers aim to satisfy some degree of purity set by the user of the fuel, rather than to attain the greatest economic benefit to all concerned. This paper is written to show that the highest economic purity of washed coal can be determined from washability studies of the raw coal, costs of mining and washing coal, and data on the effect of ash and sulphur on the value of the coal for the particular use for which it is intended. COKE FOR BLAST-FURNACE USE For purposes of illustration, we take the case of coal washed for coke to be used in the iron blast furnace. The method outlined can be made general in its application by substituting for the figures used here the actual operating figures for the particular case under consideration. In general, it costs the blast-furnace operation from 8 to 25 c. per ton of pig iron to slag out each 1 per cent. of ash introduced into the blast furnace by the coke. This figure depends on which one per cent. of ash is removed, and decreases with decrease in ash: When blast furnaces and coal mines are considered as a whole, the figure decreases to zero and then becomes negative, on account of low recovery of washed coal. Various figures1 have been given by different investigators: These figures necessarily differ, not only on account of the differences in operating costs but on account of the difference in the respective fuels as well. For the purpose of this paper, which, as explained, is to point out a method of attacking a certain problem, the figures used in the exposition of the method are of secondary importance. It is apparent that no universally applicable figures can be used, because there are none. Each plant has its own coal,2 its own operating cost, and its own conditions.

Jan 1, 1929

By Howard L. Hartman

6.1-1. Introduction. Of necessity, the first of the unit operations conducted during the exploitation phase in surface mining is production drilling. It precedes blasting, with which it is associated as the two unit operations employed to break or fragment consolidated material (usually rock) in place. The purpose of production drilling is to provide the cavity for placement of the explosives. So far, no alternative to blasting has been devised for fragmenting very resistant rock in situ, although some forms of excavation (ripping, bucket wheel) are suitable without prior blasting for softer rock, such as weathered shale or mudstone, decomposed sediments, etc. For the vast majority of surface mines, however, drilling and blasting are pre- requisite to excavation and essential to the production cycle. Drilling is also used in surface mining for purposes other than providing blastholes. It finds application during exploration for obtaining samples and during development for drainage, slope stability, foundation testing, etc. Only in the exploitation phase of surface mining, however, are unique or specialized drilling methods and equipment employed; and the discussion in this Section is directed primarily to that application of drilling. Drilling is the most common means of rock penetration, the operation of placing a directed hole in rock. Closely akin to drilling for exploitation purposes is the cutting or freeing of dimension stone in quarrying. This operation, usually termed channeling or sawing, also takes the form of directional penetration of rock; but instead of producing a cylindrical hole, it yields a kerf or cut. The material thus freed from the solid is both a shaped and sized product, an objective of vital importance in the dimension stone industry. In sawing, holes are sometimes drilled to insert tools, but this drilling is a minor part of the sawing operation and employs conventional methods. Cutting, as a unit operation for freeing stone in quarrying, may be considered equivalent in purpose to drilling and blasting in other forms of surface mining.

Jan 1, 1968

By F. H. Newell

Measurements of the amount of water flowing in many of the larger rivers of the west have been made by the United States Geological Survey, and by this means the daily discharges of these rivers have been computed for a period of over two years. These measurements have been confined mainly to that part of the country commonly known as the arid region, where the rainfall is insufficient for the needs of plants most useful to man, and the supply of water, not only for agriculture, but also for mining and all other purposes, falls below the demands made upon it. In such localities flowing water has a great value, for without it many industries are impossible. Experience has shown that in the western part of the United States, over an area a little less than two-fifths of the whole extent of the country, there are great bodies of fertile land enjoying a genial climate, and in every way adapted to the support of a large population, except in the one particular of water-supply. By utilizing the water available, portions of this rich land can be rendered valnable. In other words, the laud-values rest directly upon the prospects of a continuous artificial water-supply. The same is true of many mineral lands, which require for hydraulic mining, or for the supply of concentrating-works, stanip-mills, etc., a certain water-supply, and are impaired in value if this supply is inadequate or irregular. The pressure of this need upon the mining industry is not so widespread, or in the first instance so severe as upon agriculture; but as different regions become more thickly settled, and the two industries compete for a water-supply not sufficient for both, it, is probable that the miner will suffer. But he can snspend operations with less inconvenience than the farmer. Agricuitural land, if the watersupply is not continuous, becomes a desert; on the other hand, the profit of mining is greatly enhanced by the presence of agricultural

Jan 1, 1892

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2'3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By AIME AIME

As already announced in the January Bulletin, this publication will be issued during the coming year monthly instead of bi-monthly as heretofore. Among other reasons for this change, it is desired to effect thereby the earlier transmission to members of important papers, lists of candidates for membership, and other items of timely information. Spokane Meeting and Excursions. Further details of the' 97th meeting of the Institute have been sent to members in the Circular of May 8, 1909. For, convenience of the members a summary of the additional in¬formation is here presented. A special train of Pullman cars will leave Chicago about September 15. This train will be side-tracked at all places visited, and the sleepers will be available for lodging and the dining-car for meals during the entire trip, except during the Yellowstone Park tour. The general. cost of the trip per member will be $300, which includes transportation, berth, and meals for the entire trip from Chicago back to Chicago, almost 6,000 miles, and the tour through Yellowstone Park, occupying in all about 30 days. Special accommodations on the train will be furnished at the following, rates

May 1, 1909

* A loan, perhaps as great as $100 million, from American insurance companies is about negotiated for development of Labrador iron ore properties. The program will call for a total expenditure of up to $200 million, including, as well as all mine development work, the power facilities, housing for mining personnel, and auxiliary equipment. * Mobile air compressors and a water tank, mounted on a 30-ton rubber-tired trailer and towed right up to the drilling crews, eliminates the need for expensive underground water and air pipe lines in the experimental oil shale mine operated by the Bureau of Mines near Rifle, Colo.

Jan 11, 1950

By Stuart A. Bengson

It is extremely difficult to revegetate disturbed sites and mineral wastes in an arid environment because of sporadic and undependable rainfall. Thus, irrigation is often a must for starting seed germination and vegetation. Quite aside from the harsh climate, mining disturbances by themselves cause various adverse conditions for a revegetation program. The problems of revegetating a harsh soil, for instance, are often compounded by the steep slopes of mine wastes. Since these steep slopes intensify the droughty conditions by rapidly draining away soil moisture and accelerating runoff, supplemental irrigation may be the only solution for establishing vegetative cover on the slope.

Jan 8, 1976

TENDENCIES toward nationalization grew noticeably stronger in some areas. Late last fall Bolivia took over the tin mines of four foreign operators and handed them a bill for a fabulous amount claimed for damages. In the same breath, the price Bolivia offered to pay for the mines appeared to many to be slightly ridiculous. Many engineers felt that the country would not be able to run the mines successfully. Even if they could, some thought that the Bolivian Government would gut the orebodies in an attempt to get at rich deposits for high profits, leaving the lean ores in unmineable condition.

Jan 2, 1953

By E. Northcott, F. N. Oberg

High-grade concentrates from Florida pebble phosphate deposits have long been recovered by wet methods. When work was begun in the field, only the coarse pebble (generally +1 mm) was recovered. In the 1920's a froth flotation process was developed to separate quartz from the finer phosphate fractions, but this method proved unsatisfactory for treating the intermediate fraction (-1 mm +35 mesh). Consequently various other processes were adapted, including agglomerate tabling and spiral separation of reagentized feed. Today the three processes are used-washing and screening for coarse pebble, tabling or spiraling for intermediate sizes, and flotation for -35 mesh material.

Jan 10, 1958

By D. Duffey, P. F. Wiggins, F. E. Senftle

An examination of the neutron capture gamma ray method using a 252CF neutron source indicates that this technique may be feasible for process stream analysis of ores. Simulated laboratory experiments were made on iron in taconite and magnetite, and copper and nickel in their respective ores. Satisfactory analyses were obtained for 500-1000-g samples in a combined irradiation and counting time of 100 min. For large industrial size samples this time could be shortened. Based on these experiments, a set of guidelines are given for the use of the neutron capture gamma method in an industrial mill.

Jan 1, 1974

By A. F. Daily

Free World consumption of diamonds of all types closely follows the fluctuations of the business cycles in the large industrialized countries, particularly the U.S. Sustained purchasing by this country for stockpiling purposes has been a major factor in Free World demand for crushing bort and industrial diamonds, and it has been for this reason that investments in larger plants have been made by all major diamond mining companies during the past few years. For the purposes of this study, the diamonds produced in the Congo and elsewhere in the Free World are divided into three types:

Jan 5, 1961

By K. V. S. Sastry

This paper summarizes recent research on the kinetic aspects and process behavior of agglomeration in balling circuits. The physical concepts underlying agglomeration, the mechanisms responsible for size changes during agglomeration, and a generalized population balance model for agglomeration systems are summarized. Experimental techniques for investigating the batch balling behavior and for simulating the balling- circuit operations are reviewed. Further, the effect of such operating variables as feed moisture, bentonite content, and the rate of feed addition are discussed. An approach to the computer simulation of the agglomerating circuits is shown and the importance of such models in process engineering is discussed.

Jan 1, 1977

By M. H. Brady, J. G. Roscoe

Continental No. 1 This mine in Lisbon Valley has an orebody about 1200 ft long and varying from 250 to 70 ft wide. Average width is about 100 ft and stope heights average about 9 ft. It was developed by a 350-ft, 11º inclined shaft for trackless haulage, although a hoist and track are installed for auxiliary hoisting. Mining has been done from horizontal open stopes with random pillar support, using a HD5 tractor for mucking and a 4-wheel drive Gettman shuttle car for tramming. Slushers have been used to some extent in thin ore zones. Back support for stopes and haulage ways has been accomplished by rock bolts and landing mat. The most interesting feature of this mine has been pillar extraction. Mining was done under contract during the first year of operations with little regard for an orderly plan of stope layout or regularity of openings. Most of this work was done in the largest area of the orebody; consequently, pillar recovery has been accomplished under conditions which are far from ideal. However, a workable system has been developed which is competitive, both in cost and production rate, with open stoping.

Jan 7, 1958

By I. H. Warren, E. A. Devuyst

The selective dissolution of pyrolusite (MnO2) in presence of goethite (FeO•OH) in aqueous ammoniacal ammonium carbamate solution has been investigated: various reducing agents were studied, in particular sodium sulfite (Na2SO3,) and hydrazine hydrate (N2H4•H2O). Sodium sulfite was found to be an unsatisfactory reducing agent for both goethite and pyrolusite, for the leaching rate decreased steadily with time to an impractical level because of the limited solubility of the reactions products. Hydrazine hydrate was an effective reducing agent for pyrolusite even at low temperature, whereas goethite required much higher temperatures for any appreciable dissolution. A 1-hr leach at 35°C dissolved 90% of the pyrolusite but only 0.1% of the goethite. An activation energy of 17.0 Kcal per mole was found for the dissolution of pyrolusite with hydrazine. A reaction mechanism for the leaching of pyrolusite with hydrazine is proposed in which a reduction reaction on the surface of the mineral is the rate-determining step. The application of ammonium carbamate to the beneficiation of ilmenite is briefly described.

Jan 1, 1973

By David B. Brooks, William A. Wallace, James R. Dunn

As the conflict between the mineral industry and preservationists steadily increases, it becomes urgent to determine as precisely as possible the costs of developing vs. not developing our domestic mineral resources so that enlightened mineral policy decisions can be made. A simple discounted cash flow equation is suggested as an approach to assigning a public-interest dollar value to mineral resources. Present value of a piece of land underlain by a mineral resource is taken as equal to the discounted cash flow derived from the resource corrected for present and future surface land values. The equation is effective as a base for mineral aggregate resource planning for metropolitan areas if transportation cost differences are substituted into the cash flow component. Suitably modified, the equation can be fitted readily into an existing computer simulation program for aggregate mineral resource planning in metropolitan areas. However, because of the lack of accurate input, the equation is less effective for other mineral commodities such as base metals and coal. Nevertheless, within a somewhat philosophical context, the equation still has utility and is effective in defining the problem of public interest values for minerals other than mineral aggregates.

Jan 1, 1972

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