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By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By C. G. Dunn, W. W. Martin

Various X ray diffraction techniques have been developed for determining orientations of crystals. Transmission and back-reflection Laue methods1,2,3 in particular have been found to be very useful. In many applications, however, a need still exists for a simplification of the details of analysis so that orientations can be determined more rapidly, and operators with little or no training in crystallography can be easily instructed in the necessary procedures. Filling this need in part is a system of analysis that has been in use for several years in the Metals Section of the Laboratory, General Electric Co., Pittsfield, Mass. This method is an extension of the one of Majima and Togino,4 which uses fifty-five indexed standard transmission Lauemams to cover the entire range of crystal orientations. Greater rapidity in determining the orientation of a crystal is achieved by using a slightly larger set of standard Lauegrams and by systematizing the steps followed. This system of analysis in its present form constitutes the subject matter of the present paper. Although the method uses transmission X ray Laue patterns, many of the operations are applicable to the analysis of back-reflection Lauegrams. Very briefly the method is based on the fact that Bragg and azimuthal angles for two or more identified Laue diffraction spots completely determine the orientation of a crystal, and standard Laue photographs of the Majima and Togino type provide a ready means for identifying Laue spots. After a preliminary analysis, which consists of identifying the pattern in terms of one of the standard patterns, a correctly marked Lauegram is selected to carry out the final analysis. From measured Bragg and azimuthal angles, the normals (poles) of the reflecting planes for the selected Laue spots are located on a stereographic projection and the orient.at.ion of the crystal determined (in terms of the positions of cube poles for example) by a few additional operations on a \I1ulff net. The actual procedure followed will be illustrated in detail after a brief treatment or X ray problems connected with orientation determinations and a discussion of useful principles and techniques. X Ray and Plotting Problems RELATIVE ADVANTAGES OF BACK-REFLECTION AND TRANSMISSION LAUE DIFFRACTION METHODS In the back-reflection Laue method it is easy to make a direct measurement of the tilt of a zone of Laue spots. Specimen thickness also is generally no problem. In the case of thin specimens, however, the time of exposure is less for the transmission Laue method. For example, with silicon ferrite this advantage holds up to a thickness of 0.6 mm if tungsten radiation at 40 kv peak voltage is used. Furthermore, the transmission photograph represents the entire thickness of the crystal whereas the back-reflection picture represents only a surface layer (a thickness of less than 0.05 mm for silicon ferrite), the deeper layers supplying a negligible amount to the diffraction pattern. If a crystal is distorted, the transmission Laue pattern gives more information particularly with regard to the orientation of the crystal and the overall amount of spread in orientation. Finally a 3 1/4 X 4 in. film suffices for transmission photograms; a 4 X 5 in. or 5 X 7 in. film with a central hole is needed for back-reflection patterns Not only is the manipulation of film easier because of the size of film, but

Jan 1, 1950

By J. Szekely, J. W. Evans

A formulation is given for radiant heat loss from the surface of molten steel held in a ladle and numerical solutions are presented for the resultant integrodif-ferential equations. The results are shown on plots of the net rate of heat loss against time, with the geometlry, emissivities, thermal properties of the walls, and Preheat as parameters. It was found that the rate of the vadiant heat loss from the exposed metal surface was comparable to the conductive losses from the Portion of the metal in direct contact with the walls. The radiant heat loss was markedly affected by the geometry and by the thermal properties of the walls the net radiant heat loss from the steel could be drastically reduced by providing a top cover and also by the provision of preheat. The results of this work are thought to be relevant to heat loss calculatious concerned with vacuum degassing and with operatzons in which molten metals are held in ladles. WhEN molten steel is held or transferred in ladles heat losses inevitably occur. The accurate assessment of these heat losses is of importance in process design considerations, as the temperature of the metal may have to meet rigid specifications in certain stages of the processing sequence. As shown in Fig. 1, the principal mechanisms responsible for heat loss are: i) Conduction into the walls and ii) Thermal radation from the top metal surface (possibly augmented by natural convection) The conductive heat loss may be readily calculated as much information is available in the literature on both the general theory1'' and on its particular applications to ladle heat loss calculations. Evaluation of the radiant component of the heat loss is less straight-forward. In two recent papers it has been shown that the presence of a slag layer 2 to 3 in. thick would prevent any significant heat loss for periods up to an hour,5'" however, should bare metal be exposed, constituting the radiant surface, substantial heat losses could occur. This latter case is of considerable practical interest in various degassing operations and in the vacuum processing of certain specialty steels, where the top surface of the metal is not covered by a protective slag layer. Under these conditions a substantial radiant flux is emitted by the top metal surface; part of this flux leaves the system, part of it falls in the ladle walls. The radiant flux incident on the ladle walls is in part absorbed and conducted away, and in part reflected and re radiated. The purpose of the paper is to present a general formulation of the problem, the resultant solution of which should enable computation of the net radiant heat loss from the metal surface. The principal variables, the effect of which will be investigated, include initial metal temperature, geometry, thermal and radiative properties of the wall, and various modes of preheat. FORMULATION Consider a cylindrical enclosure, shown in Fig. 2, with a diameter D, height H, and wall thickness W, the cover at the top of the cylinder having a wall thickness L. If the temperature of the base (representing the top surface of the metal) is kept constant, say, Tb, the problem is to calculate the net rate of heat loss from the base as a function of time, geometry, the initial temperature distribution, and the thermal properties of the system. As customary, the formulation will consist of the mathematical statement of the conservation of thermal energy within the system.

Jan 1, 1970

By Garth M. Crosby

Hugh E. McKinstry (Professor of Geology, Laboratory of Mining Geology, Harvard University, Cambridge, Mass.) Pre-Cambrian age for the Coeur d'Alene mineralization, as indicated by isotope studies and recently discussed by Silverman, Long, and Kulp' would explain some features of the mineralogy of the district that have long been a puzzle. In the Silver Belt, especially in the Sunshine mine, lead-zinc min erali zation passes downward into tetrahedrite ore. Although commercially speaking this is a rich silver zone, the silver is, quantitatively, a mere impurity amounting to a small fraction of 1 pct. In effect the zonal change is from lead-zinc down into copper mineralization—-the usual zonal change that occurs in many districts. In the Burke-Mullan portion of the district, on the other hand, lead-zinc ore does not pass downward into copper mineralization of the Sunshine type. Instead, pyrrhotite appears in depth while the tenor in lead and zinc declines. The change occurs at increasingly greater depth away from the Gem stocks, deepening irregularly by some 3000 ft within two to four miles. As noted by Crosby, biotite, grunerite, and garnet appear in the deep zone. The marked difference between this apparent zonal change and the more nomal change to a copper zone is quite explainable if already existing pre-Cambrian veins have been locally metamorphosed by a Tertiary intrusive. The chief obstacle to this explanation is the evidence that mineralization cuts Laramide intrusives, but evidence on this point is conflicting as indicated by Crosby's observations and summary. This is not the first instance of a problem in determining the time-relationship of mineralization to a spatially associated intrusive. At the Noranda mine veins of chalcopyrite extend into a diabase dike which apparently cuts the ore, although Price2 concludes that the ore is later. However, at the Normetal mine diabase of a similar dike is thought3 to intrude the orebody but is cut by stringers of chalcopyrite. In the Sullivan Mine, B. C.,4 galena follows a fracture in a larnprophyre dike which, itself, cuts the main orebody. In the Sudbury district dikes of olivine diabase are clearly younger than the nickel ore, yet where they cut the Creighton orebody they contain stringers of chalcopyrite. In the laboratory, Hawley5 has developed veinlets of sulfide (chalcopyrite) it] silicate gangue by heating specimens of ore in a stream of H2S at 410 °C. From this and other evidernce. it seems clear that sulfides can be transferred from one site to another — at least through short distances — at temperatures well below their melting points. It would seem then that even if sulfide Mineralization in the Gem stocks can be shown unequ ivocably to be later than the intrusive the possibility of "remobiliza tion" need not be more than local. Thus the zonal relationships are quite in accord with a pre-Cambrian age for original deposition of the lead, zinc, copper, silver, and uranium in the Coeur d'Alene district. REFERENCES 1. A. Silverman, A. Long, and J. L. Kulp: Discussion of: The Gem Stocks and Adjacent Orebodies, Coeur d'Alene District, Idaho. Mining Engineering, May 1960, pp. 470-471; AME Trans., 1960, vol. 217, p. 117. 2. Peter Price: Geol. & O. D. at the Home Mine, Noranda, Quebec. Can. Inst. M & M Bull 263, 1934, p. 108; also,Trans. CIMM 1939, pp. 108-140. 3. w. L. Brown Nometal Mine in structural Geology of Canadian Ore Deposits, Montreal, 1948, p. 690. 4. C. O. Swanson and H. C. Gunning: Geology of the Sullivan Mine. Can. Inst. Mining & Met. Trans. vol. 48, 1945, p. 653. 5. J. E. Hawley: Heat Effects on Sulphides and Possible Applications. Univ. Toronto Studies, Geol. Ser. No. 46, 1941, p. 34.

Jan 1, 1961

By Walter Miller

AFter a year's continued impact of war, the task of the petroleum-refining industry stands out clearly and looms up in larger aspect. This time it is not, as it was so largely in the first World War, simply a matter of increased quantity—more and more of the same petroleum products that had substantially been standard for years. In this era the emphasis is largely on newer and improved materials which had been produced, if at all, in comparatively insignificant quantities, and for which manufacturing equipment was not available on a large scale. At the beginning of 1942 four great product needs (besides a number of lesser ones) confronted the industry: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for aviation and Army equipment service, and petroleum chemicals for synthetic rubber manufacture. The difficulty in presenting a review of engineering progress in petroleum refining during 1942 is that there is so little one is free to say about so much which has been and is being accomplished. At the opening of 1942 the program was to increase the then existing capacity of 50,000 bbl. a day of aviation gasoline to over 150,000 bbl. daily by building new plants at an estimated installation cost of $150,000,000. Later in the year. after the announcement by President Roosevelt of a large increase in the program for war-plane building, additional contracts were made between the Reconstruction Finance Corporation and rehers to raise the capacity to 250,000 bbl. per day. The greatly increased scope of the war activities in all parts of the world, the obligation of the United States as the arsenal of the United Nations, and the greater importance and use of bomber, transport, and cargo planes will undoubtedly bring about plans and installations for a further increase in production of aviation gasoline over the present announced plan. In this connection, Jesse Jones, Reconstruction Finance Corporation Chairman, announced that as of Oct. 31 the R.F.C. had through its subsidiary Defense Plant Corporation entered into contracts for the construction, expansion, or equipping of 28 plants to increase 100-octane aviation gasoline production, but gave no data on 'capacity involved or completion dates. His list did not, of course, include a number of existing plants, and some installations being made by companies who are themselves financing the construction. Production from existing operating installations was materially increased in a number of instances as a result of pooling knowledge of improvements in operation and also by the exchange of Components going into 100-octane blend to enable greater quantities of aviation gasoline to be produced from the over-

Jan 1, 1943

By Walter Miller

AFter a year's continued impact of war, the task of the petroleum-refining industry stands out clearly and looms up in larger aspect. This time it is not, as it was so largely in the first World War, simply a matter of increased quantity—more and more of the same petroleum products that had substantially been standard for years. In this era the emphasis is largely on newer and improved materials which had been produced, if at all, in comparatively insignificant quantities, and for which manufacturing equipment was not available on a large scale. At the beginning of 1942 four great product needs (besides a number of lesser ones) confronted the industry: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for aviation and Army equipment service, and petroleum chemicals for synthetic rubber manufacture. The difficulty in presenting a review of engineering progress in petroleum refining during 1942 is that there is so little one is free to say about so much which has been and is being accomplished. At the opening of 1942 the program was to increase the then existing capacity of 50,000 bbl. a day of aviation gasoline to over 150,000 bbl. daily by building new plants at an estimated installation cost of $150,000,000. Later in the year. after the announcement by President Roosevelt of a large increase in the program for war-plane building, additional contracts were made between the Reconstruction Finance Corporation and rehers to raise the capacity to 250,000 bbl. per day. The greatly increased scope of the war activities in all parts of the world, the obligation of the United States as the arsenal of the United Nations, and the greater importance and use of bomber, transport, and cargo planes will undoubtedly bring about plans and installations for a further increase in production of aviation gasoline over the present announced plan. In this connection, Jesse Jones, Reconstruction Finance Corporation Chairman, announced that as of Oct. 31 the R.F.C. had through its subsidiary Defense Plant Corporation entered into contracts for the construction, expansion, or equipping of 28 plants to increase 100-octane aviation gasoline production, but gave no data on 'capacity involved or completion dates. His list did not, of course, include a number of existing plants, and some installations being made by companies who are themselves financing the construction. Production from existing operating installations was materially increased in a number of instances as a result of pooling knowledge of improvements in operation and also by the exchange of Components going into 100-octane blend to enable greater quantities of aviation gasoline to be produced from the over-

Jan 1, 1943

By Oren C. Baptist, Carlon S. Land

Laboratory research has been conducted to evaluute the effect of clay hydration on the permeability to gas of water-sensitive reservoir sands. Samples of a .sandstone containing trace amounts of montmorillonite and a sample of montmorillonite were .studied in the laboratory to detertnine whether swelling or dispersion was the cause of permeability reduction in these samples. Heliuin, containing various amounts of water vapor, was used to hydrate the clay minerals and to determine the gas permeability at various stages of clay hydration. The amount of water adsorbed by the samples using this method is small. The nonwetting-phase permeability at higher water saturations war investigated by saturating the with water and measuring the permeability to humid helium while decreasing the water saturation, Relative-permeability curves obtained from results of these procedures were used to estimate the effect of the swelling of trace amounts of mont/tlorillonite on the permeability of the .samples. Most of the damage to the permeability when reservoir sands containing trace amounts of montmorillonite are exposed to fresh water is due to dispersion and movement of clays. Blockage of pores by the increased volume of expanded montmorillonite is believed to result in permeability damage that is small in comparison to the observed damage to the samples tested. INTRODUCTION Studies have shown that permeability is severely damaged when sands containing only small amounts of montmorillonite are contacted by fresh water.15 When samples of sands containing large amounts of montmorillonite are placed in fresh water in the laboratory, these samples may completely disintegrate, forming an unconsolidated mass of larger volume than that occupied by the dry sample." In this case, it is apparent that the swelling of montmoril-lonite has destroyed the pore structure of the sand. If only a trace of montmorillonite is present in a sand. samples may remain intact when saturated with water, although the permeability to water is a small fraction of the gas permeability of the dry sample. Many workers in the field of water sensitivity have attributed this reduction in permeability to the blocking of pores and reduction of pore size by the increased volume occupied by expanded mont- niorillonite. if the sand contains a detectable amount of montmorill'onite or mixed-layer clay containing rnontmorillonite. Logically3 the smaller amount of montmorillonite present in a sand, the smaller should he the effect of montnlorillonite swelling on permeability; however, the quantity of montmorillonite sufficient to cause severe damage by swelling is not known. Although hundreds of samples have been tested in our laboratory, no correlation has been established between the amount of montmorillonite in samples and the permeability reduction caused by fresh water. To many petroleum engineers, the phrase "clay swelling" is synonymous with "water sensitivity", or "permeability reduction" implying that any formation damage due to the hydration of clays is caused by swelling. Although all clays adsorb water on their surfaces, montmorillonite is the only clay mineral commonly found in reservoir rocks which adsorbs water between intercrystalline layers, resulting in expansion of the clay particle. As montmoril-lonite swells, the first few layers of water adsorbed between platelets are strongly held and well oriented, and the montmorillonite retains its crystalline structure, although expanded. As swelling of sodium montmorillonite continues, the platelets become farther apart and the forces orienting the platelets in the crystalline structure become weaker, resulting in a less orderly orientation of platelets. In an abundance of water, small groups of platelets may become detached from the original monl-rnorillonite particle and may be dispersed throughout the water phase. Because of its swelling properties, sodium montmorillonite is very easily dispersed in water. Particles of other clay minerals. such as illite and kaolinite may also be dispersed in water. causing water sensitivity of sands not containing montmorillonite. The presence of an immobile layer of water adsorbed on the surface of clays has been considered a possible cause of the low permeability to water of dirty sands. Grim states that the thickness of the layer of immobile water held by sodium montrnorillonite is three nlolecular layers or 7.5 A (angstroms), with some orientation of water extending to 100 A. Assuming a very thick, immobile water layer adsorbed on the surface of a pore represented by a capillary tube, the maximum effect of the water layer on permeability can be calculated. Using a pore radius of 10 ' cm and an immobile water layer of 50 A. the calculation shows the permeability to be reduced only 2 per cent. Similar calculations can be used to show that the effect of electro-osmotic counterflow is of the same order of magnitude as that of bound water. The reduction of the permeability to water by either an immobile water layer

Jan 1, 1966

By F. Peter

I. GENERAL INTRODUCTION. TECHNICAL progress takes place in two directions: the improvement of methods, affecting the quality of the product; and increase in the economy of operations, affecting its cost. In the iron-industry, practice is pretty well settled, and. revolutionary changes of method are, for the present, not to be expected. Hence, in this industry, the principal endeavor is to reduce costs by the use of labor-saving inventions, such as the machines brought into use during the last decade. But it is not alone necessary to reduce the labor-cost; complete economy requires also a saving in raw material. Under this head we may rank the coal employed as metallurgical fuel; and it follows that progress includes the economic use of fuel, so managed as not to injure quality of product. In the present paper it will be shown how, by suitable utilization of the heat from the furnace, a large portion of it may be made available for other purposes. Such utilization of waste-gases is important in all industries which employ furnaces (especially heating- and smelting-furnaces); and in the first rank of these stand the iron-, glass-, and porcelain-manufactures. The following pages are devoted chiefly to the waste-gases of smelting-works, and especially to those reverberatory-furnace gases which are not combustible.'

Jan 12, 1913

MANY are the salts produced. by Nature in various regions and parts of the world, as Pliny shows in his History. Likewise, many are the differences among things that are salty and from which salt can be extracted, as, for instance, all the lyes from any kind of ashes and the urine of all animals. But because these are not things that give men the useful elements necessary to life, I shall omit speaking of them in detail with the exception of some of the more notable ones, and I shall tell you that I find that men proceed in only two ways in order to have a sufficiency for their needs. One is that of extracting it from the salty waters of the sea itself, or from springs, with a certain technique [34v] adapted to the places, either by congealing or by evaporation; and the other is that of mining it from the earth. The latter salt is clear and beautiful, and it is mined from mountains, already made by Nature in the form of stone without the aid of art. All these salts have more or less efficacy* according to the fineness or coarseness of their earthy elemental mixture, and according to the provinces and places where they are found generated. All are of an earthy

Jan 1, 1942

By Carl J. Christensen

This paper presents the development of diamond coring of the Weber sand section in the Rangely Field, Colorado. The description and operation of the diamond-coring equipment is included as well as the economics and results obtained by its use. Diamond coring is compared with the other methods used for drilling the Weber sand. Two types of diamond coring are discussed. The first and the one used most extensively is the regular 6 ?x 3¾-in. diamond bit and bottom hole 50-ft barrel. The second type, which has also been used successfully by Stanolind, consists of a 4 13/16 x 2 11/32-in. cutting bit and reverse circulation coring equipment. The first type will be referred to as regular or conventional diamond coring while the latter type will be referred to as reverse circulation diamond coring. Introduction Diamond coring has been used for many years in mines, quarries, surface coring at dam sites, laboratory work, and so on, but, until recently, had never been used very extensively in coring oil sands and other oil-bearing strata. It was demonstrated early in its development that hard forma-tions could be cut rapidly and that core recoveries far exceeded those obtained with conventional hard rock bits and quite often 100 pet recovery was obtained. However, the poorly constructed diamond-coring equipment and resulting high costs of early diamond coring slowed down its progress. Early in the development Of the Rangely Weber field, Rio Blanco County, Colorado, the Rangely Engineering Committee selected key wells that were to core the Weber section in its entirety. These cores were to be analyzed and various sections tested to gather sufficient information so that accurate reservoir studies could be made. The number of wells selected were kept at a minimum inasmuch as the productive Weber section, which is found at an approximate depth of 6000 ft, is thick, being as much as 600 to 700 ft on top of the structure. The Weber section is also comparatively hard to drill. For instance, one well took 60 days to core 490 ft of Weber sand with conventional coring equipment. It was noticed, however, that Core Labora-verse diamond plug cutter could quickly cut a plug from. one of these hard cores. This fact led to the serious consideration of diamond coring the Weber sand. The first diamond coring at Randy was performed by Stanolind in August 1946 andl although we experienced some difficulties, the results definitely indicated that diamond coring would be successful at Rangely for .coring the Weber sand. As more wells were cored and the equipment improved somewhat, diamond coring became less expensive than drilling the Weber sand with the conventional rock bit. In less than one Year diamond coring has definitely Proved its usefulness in oil-field drilling operations in the Rocky Mountain area where formations quite often drill very hard. The practice of spot coring in hard oil-bearing formations with conventional coring equipment is giving way diaimond coring of the entire sections, thus givng an operator the complete picture.

Jan 1, 1948

By Carl J. Christensen

This paper presents the development of diamond coring of the Weber sand section in the Rangely Field, Colorado. The description and operation of the diamond-coring equipment is included as well as the economics and results obtained by its use. Diamond coring is compared with the other methods used for drilling the Weber sand. Two types of diamond coring are discussed. The first and the one used most extensively is the regular 6 ?x 3¾-in. diamond bit and bottom hole 50-ft barrel. The second type, which has also been used successfully by Stanolind, consists of a 4 13/16 x 2 11/32-in. cutting bit and reverse circulation coring equipment. The first type will be referred to as regular or conventional diamond coring while the latter type will be referred to as reverse circulation diamond coring. Introduction Diamond coring has been used for many years in mines, quarries, surface coring at dam sites, laboratory work, and so on, but, until recently, had never been used very extensively in coring oil sands and other oil-bearing strata. It was demonstrated early in its development that hard forma-tions could be cut rapidly and that core recoveries far exceeded those obtained with conventional hard rock bits and quite often 100 pet recovery was obtained. However, the poorly constructed diamond-coring equipment and resulting high costs of early diamond coring slowed down its progress. Early in the development Of the Rangely Weber field, Rio Blanco County, Colorado, the Rangely Engineering Committee selected key wells that were to core the Weber section in its entirety. These cores were to be analyzed and various sections tested to gather sufficient information so that accurate reservoir studies could be made. The number of wells selected were kept at a minimum inasmuch as the productive Weber section, which is found at an approximate depth of 6000 ft, is thick, being as much as 600 to 700 ft on top of the structure. The Weber section is also comparatively hard to drill. For instance, one well took 60 days to core 490 ft of Weber sand with conventional coring equipment. It was noticed, however, that Core Labora-verse diamond plug cutter could quickly cut a plug from. one of these hard cores. This fact led to the serious consideration of diamond coring the Weber sand. The first diamond coring at Randy was performed by Stanolind in August 1946 andl although we experienced some difficulties, the results definitely indicated that diamond coring would be successful at Rangely for .coring the Weber sand. As more wells were cored and the equipment improved somewhat, diamond coring became less expensive than drilling the Weber sand with the conventional rock bit. In less than one Year diamond coring has definitely Proved its usefulness in oil-field drilling operations in the Rocky Mountain area where formations quite often drill very hard. The practice of spot coring in hard oil-bearing formations with conventional coring equipment is giving way diaimond coring of the entire sections, thus givng an operator the complete picture.

Jan 1, 1948

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Herbert H. Kellogg

The chemistry of sulfide roasting is analyzed to show those aspects of performance which Thecan be predicted from considerations of thermodynamic equilibrium. It is concluded that equilibrium calculations can serve as a yardstick for prediction of roaster-gas composition and sulfate formation in the calcine for fluid-bed roasting practice. A method of calculation which combines the equilibrium and stoichiometric factors is outlined, and illustrated by an example from the roasting of Cu-Fe sulfides. ON first examination the roasting of sulfides would not seem to be a process to which equilibrium calculations could be applied to yield results of practical value. The burning of sulfides is an ex-tremely spontaneous reaction, excess air is always used to obtain rapid reaction, and in most traditional roaster designs (hearth roasting) the temperature and gas composition vary widely from point to point in the roaster. These are all conditions which promote a non-equilibrium state in the roasting process. However, the introduction of the fluid-bed roaster1 has brought to roasting practice new conditions of operation, so that equilibrium calculations can be used to predict certain limited aspects of practical operation. The fluid bed is characterized by uniformity of temperature, gas composition, and calcine composition from point to point throughout the bed. These relatively uniform properties of the bed make the meaningful calculation of the equilibrium state of certain reactions in roasting possible. It is the purpose of this paper to analyze roasting from an equilibrium viewpoint, to show where the method may be expected to yield valuable information, where it fails, and to outline methods of calculation. Main Roasting Reaction The reaction MS (s) + 3/2 0, = MO (s) + SO, [I] might well be called the main roasting reaction. It adequately accounts for the well known facts that metal sulfide and air are the main reactants, and metal oxide and SO, the main products. Deviations from this simple stoichiometry will be discussed under side reactions. For all metal sulfides, Reaction 1 is strongly exothermic and the equilibrium position is far to the right. Since the reaction is exothermic, the equilibrium shifts in the right-to-left direction as the temperature is raised. However, at all practical roaster temperatures (between 500" and 1200°C), the amount of this shift is small, and the equilibrium position remains far to the right. The main roasting reaction is essentially irreversible, and the application of equilibrium considerations to this reaction will not be! a fruitful field of investigation. A knowledge of the rate of this reaction. although not the proper subject of this paper, is of great importance to the roasting process. Analysis of the factors which influence this rate shows that: 1) The rate will increase rapidly with increased temperature. 2) The rate will be proportional to the partial pressure of oxygen at the surface of the reacting particle. Because of diffusion effects, the partial pressure of oxygen at the particle surface may be considerably less than in the bulk of the roaster gas. For this reason, intimate contact between gas and solid and high relative velocity between gas and solid, such as can be obtained in a fluid bed or flash roaster, will markedly increase the rate of reaction. 3) The rate will be proportional to the surface area of metal sulfide. Therefore, smaller particle size will permit a more rapid rate per unit of weight. To achieve practical rates of roasting the partial pressure of oxygen in the roaster gases must be maintained at a finite level at all times. Even where the gas-solid contact is very good, as in the fluid-bed roaster, the oxygen content of the gas must not be allowed to drop below some limiting value (perhaps 1 pct), or the rate of the main roasting reaction will become too small for practical operation. Side Reactions in the Gas Phase The gas phase during roasting of metallic sulfides contains the elements oxygen, sulfur, nitrogen, by-

Jan 1, 1957

By J. M. Flaitz, A. S. Parks

OF the various methods of sampling gas-condensate wells, a method that secures a continuous representative sample of the well stream is desirable. Such a method, consisting of a sampling tube introduced into the well tubing, has proved satisfactory. The method is sufficiently accurate for operating and engineering problems A portable testing apparatus can be used with the sampling tube to obtain data useful in studying the economic and technical aspects of the development and operation of gas-condensate properties. Introduction The recent discovery and development of gas reserves that contain hydrocarbons that condense with reduction of temperature or Pressure, or both, to form a product known as condensate, has brought many new problems to the oil and gas industries. With further discovery of deep, high-pressure fields it is presumable that many more gas fields of this type will be added to the steadily increasing number. Such gas reserves are found either associated with oil as a gas cap or in separate formations. There seems to be no positive correlation between the physical or geological nature of the reservoir, and the chemical composition or phase characteristics of its contents. Knowledge of the chemical make-up and phase behavior of gas-condensate reserves is needed to cope with many problems. A knowledge of the chemical composition and phase characteristics of the reservoir material is necessary to properly design a gasoline or recycling plant, to estimate natural gas and condensate reserves, to enable the operator to study the economic and technical aspects of various methods of operation and development, and to carry Out the plan of operating subsurface and surface lease equipment. This information is often useful in questions of mineral ownership, proration, legal position, and taxation. It is the purpose of this paper to discuss methods used by the writers to determine the chemica1 composition and phase characteristics of the fluids produced from a condensate well. The scope of the paper includes a discussion and description of the method of sampling, the results of tests on the accuracy of the sampling method, a description of a portable testing apparatus used to examine the phase characteristics, typical results of tests on wells from several condensate fields, and some of the applications of these data to production problems. References to previous work on this subject are cited at the end of the paper. The Problem At reservoir conditions of temperature and pressure, the fluids produced from a condensate well exist in a homogeneous vaporous condition. The consequent reduction of temperature and pressure that occurs as this gas enters and flows up the well tube results in condensation of some of the hydrocarbon material to form a liquid. The relative amount of liquid condensed at any point in the flowing system

Jan 1, 1942

By J. M. Flaitz, A. S. Parks

OF the various methods of sampling gas-condensate wells, a method that secures a continuous representative sample of the well stream is desirable. Such a method, consisting of a sampling tube introduced into the well tubing, has proved satisfactory. The method is sufficiently accurate for operating and engineering problems A portable testing apparatus can be used with the sampling tube to obtain data useful in studying the economic and technical aspects of the development and operation of gas-condensate properties. Introduction The recent discovery and development of gas reserves that contain hydrocarbons that condense with reduction of temperature or Pressure, or both, to form a product known as condensate, has brought many new problems to the oil and gas industries. With further discovery of deep, high-pressure fields it is presumable that many more gas fields of this type will be added to the steadily increasing number. Such gas reserves are found either associated with oil as a gas cap or in separate formations. There seems to be no positive correlation between the physical or geological nature of the reservoir, and the chemical composition or phase characteristics of its contents. Knowledge of the chemical make-up and phase behavior of gas-condensate reserves is needed to cope with many problems. A knowledge of the chemical composition and phase characteristics of the reservoir material is necessary to properly design a gasoline or recycling plant, to estimate natural gas and condensate reserves, to enable the operator to study the economic and technical aspects of various methods of operation and development, and to carry Out the plan of operating subsurface and surface lease equipment. This information is often useful in questions of mineral ownership, proration, legal position, and taxation. It is the purpose of this paper to discuss methods used by the writers to determine the chemica1 composition and phase characteristics of the fluids produced from a condensate well. The scope of the paper includes a discussion and description of the method of sampling, the results of tests on the accuracy of the sampling method, a description of a portable testing apparatus used to examine the phase characteristics, typical results of tests on wells from several condensate fields, and some of the applications of these data to production problems. References to previous work on this subject are cited at the end of the paper. The Problem At reservoir conditions of temperature and pressure, the fluids produced from a condensate well exist in a homogeneous vaporous condition. The consequent reduction of temperature and pressure that occurs as this gas enters and flows up the well tube results in condensation of some of the hydrocarbon material to form a liquid. The relative amount of liquid condensed at any point in the flowing system

Jan 1, 1942

By J. D. Alexander, W. L. Martin, J. N. Dew

This paper presents data obtained using a flood-pot technique to determine the fuel available and the corresponding theoretical air requirements for in situ combustion of crude oils. Since the technique is relatively quick and easy, it is a practical and convenient tool for evaluating reservoirs as fireflood prospects. It is also a research tool which facilitates systematic study of the variables affecting fuel availability and corresponding air requirements. The understanding of these variables is of prime importance to those concerned with the technical and economic development of in situ combustion as an oil-recovery process. The experimental results show conclusively that the fuel available for in situ combustion is not a constant but, rather, varies with crude-oil characteristics, porous-medium type, oil saturation, air flux and time-temperature relationships. Thus, the fuel availability for specified field applications should be determined using actual reservoir crude and core material and the process conditions expected during in situ combustion in the reservoir. INTRODUCTION In situ combustion is a thermal process for recovering crude oil from reservoirs. The thermal energy released during the combustion of a small amount of the oil in place aids in the displacement of the remaining oil. Numerous articles have been published describing the in situ combustion process giving detailed results of laboratory and field experiments.10 In order to engineer an in situ combustion project, a number of important factors must be considered and determined. These factors include: (1) the amount of fuel consumed per unit of reservoir volume swept by the combustion zone, (2) the composition of the fuel consumed, (3) the amount of air required to consume this fuel, (4) the portion of the reservoir swept by the combustion zone, (5) the appropriate air-injection rates and pressures, (6) the amount of oil that will be recovered, (7) the rate of oil production and (8) the operating costs. Nelson and McNiell1 recently have described a procedure which utilizes laboratory combustion-tube data as a basis for the calculation of some of these design factors. Various authors have attempted to describe the in situ combustion process mathematically, and considerable progress has been made. Analytical solutions to the problem of heat transfer from a moving combustion front have been obtained for linear and radial systems."-' All of the published results involve the assumptions that: (1) fuel concentration is constant throughout the reservoir, or that fuel concentration is inversely proportional to the velocity of the front for a given rate of oxygen consumption; and (2) the fuel reacts instantaneously with injected oxygen, while liberating a constant amount of heat per unit weight of fuel at all temperatures. It seems both desirable and reasonable to test the validity of these assumptions experimentally. This paper presents laboratory data which were obtained by means of a "fire flood-pot" method for determining fuel availability and composition, and the corresponding theoretical air requirements for in situ combustion of crude oils under variable conditions. The mechanics of the method are similar to a conventional tube-run experiment.' The important differences involve the size of the reservoir model used and the method for providing the experimental environment. The new method subjects conventionally-sized core samples or unconsolidated sands to a programmed environmental sequence similar to that experienced by a similar volume of rock during the approach and passage of a combustion front in a long tube or in an oil reservoir undergoing in situ combustion. Restored-state samples can also be used. The small samples and relatively simple techniques involved allow an experiment to be set up, run and calculated in about three 8-hour days. This is a considerable improvement over long-combustion-tube techniques which can require several days to run and several more work days to set up and calculate. All the runs presented were run at 40-psig injection pressure. Pressure was not considered as a variable for these experiments, since we previously had found that it had only a small effect on fuel availability up to 600 psig.APPARATUS AND MATERIALS APPARATUS The fire flood-pot apparatus consists of a consolidated

By F. H. Wilson, M. L. Kronberg

The low temperature recrystalliza-tion of very heavily rolled copper produces a fine grained structure with a high degree of preferred orientation. Additional heating to within a few hundred degrees of the melting point may induce an abrupt and pronounced increase in the grain size, with the resulting crystals having new orientations. This behavior at high temperatures is commonly termed "secondary recrystallization." Several investigations have dealt with the phenomenon arid have served to bare many features of the beha~ior.1-4 In general,observations have been made on the sizes and shapes of the grains, and data have been presented showing the existence of an induction period in isothermal experiments. Although it has been well established that the orientation before the change is statistically (100) 10011, the so-called "cubically aligned" texture, there is no such agreement on the orientation after the change. For example, Dahl and Pawlek1 describe it as being equivalent to an approximately 30" rotation about the [l00] axis of the ideal cubic texture which is parallel to the rolling direction, the resulting orientation being near (210)[001]; and Cook and Richards2 find an orientation of approximately (110)[L12]. Since the completion of most of the work to be reported in this paper, Rowles and Boas3 have published their ver] illuminating paper on "secondary recrystallization," in which they present convincing evidence for a third orientation and show that their esperiments give no evidence for either of the other two orientations. The orientation is described as equivalent to an approximately 30° rotation about a [ 111] pole of the ideal cubic orientation. The existence of a variety of reported orientations is not unique for copper, for a similar state of affairs exists for other systems that have been studied— aluminum, nickel, nickel-iron alloys, and others. It seems therefore that the existence of this variety does not necessarily constitute a contradiction, but rather indicates that different experimental conditions yield different results. The fundamental nature of the phenomenon has not been elucidated. However, it has been generally recognized that the large grains could be the end product of growth of a few select grains already existing in the sample in minor amounts—too small to allow detection—or that entirely new ones could be formed by a process of nu-cleation and growth. Existing experimental evidence does not distinguish between these two most apparent possibilities. Nevertheless, the former has been more generally favored largely because our current understanding of the state of an annealed metal has not made it seem reasonable to expect a nucleation event to occur at temperatures above those required for the primary recrystallization. Observations on the Preparation and Heating of Twin-bearing Cubically Aligned Copper The starting material used throughout. the investigation was a bar of OFHC copper, forged and annealed at 950°C. Visual inspection showed the grain size to be around 0.5 mm, and did not disclose any preferred orientation. A chemical analysis showed the following composition: Cu + Ag— 99.99 Pct S — 0.005 pct 0 — <0.005 pct For the preparation of cubically aligned copper, ¾ in. thick slabs were cut from the bar, heavily pickled in concentrated HNO3 and cold rolled to sheets about 0.012 in. thick. The reduction in thickness was approximately 98.5 pct. Standardized annealing techniques were followed. Samples to be heated were lightly dusted with alumina in order to prevent sticking and then sandwiched between 1/16 in. copper plates. The resulting sandwich was heavily wrapped with copper sheet, and then annealed in air. The protection was such that only very thin films of oxide were formed. That the associated light oxidation of the samples had no specific effect on the recrystallization behavior was shown by the similar results that could be obtained on annealing in highly purified and dried hydrogen. Two methods were used in bringing samples to temperature: (1) by placing the package directly in the furnace at temperature and (2) by placing the package in the furnace at room temperature, and then slowly increasing the temperature. The corresponding heating rates are illustrated in Fig 1, and will be referred to as "rapid" and "slow," respectively. Unless specified otherwise, all anneals will be of the former type. Metallographic examination was made on samples prepared by electrolytic polishing and etching as described in the Metals Handhook.* STRUCTURES FOUND BEFORE "SECONDARY RECRYSTALLIZATION" OCCURS Annealing the rolled material for 1 hr at 400°C produced a heavily twinned, cubically aligned structure, the grain size being of the order of 0.03

Jan 1, 1950

By L. A. Rapoport, W. J. Leas, C. W. Carpenter

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.&apos; More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" &apos; ratio.""&apos; These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By William B. Senseman

FoR reasons well known to mining engineers, wet grinding is quite universal in plants having to do with the extraction of metallic values from crude ores. In the processing of the nonmetallic and industrial minerals, dry grinding is the more common method. The crude materials usually contain less moisture than is required for wet grinding and the products usually are marketed in dry form; most of them as powders. To grind wet, therefore, would entail the addition of water and an expense for drying the product, which is not justified. Furthermore, the material would be a dried cake that would still have to be pulverized or disintegrated before use. For producing fine products, air separators have largely replaced the earlier practice of sizing with screens and bolting reels. Mills in which the air-separating feature is an integral part of the design are now commonplace. Mill designs are many and air systems have developed along various lines, but for the purpose of this discussion, only the fundamental idea need be emphasized— the idea of using air for sizing and removing pulverized material from a grinding mill. About 20 years ago, when the use of mills equipped with air separation had become common practice, heated air or gas was introduced to such a system for the removal of moisture. The purpose of this discussion is to outline the developments and trends that have followed this experiment. It is an important development, for mills equipped with air separation are now universally used for pulverizing not only nonmetallic and industrial minerals, but a great variety of other materials. All such mills are essentially the same. Dried material is pulverized, removed by an air stream, trapped in a cyclone collector, and relatively clean air from the cyclone is returned through a fan to the mill. There is no theoretical need for a vent from the system. The practical need is to vent the air that leaks into the system; and, since the cyclone is not 100 per cent efficient as a dust collector, this vented air carries some dust with it. The initial attempt at drying was made on a system like that described, by the addition of a furnace. The minus pressure within the mill draws hot gas from the furnace. Infiltration air, along with the drying gases and evaporated moisture, is vented as before. The first application was made to a mill used for pulverizing coal. The coal contained very little moisture, so very little drying effect was needed for the success of this experiment. Actually, some calculated efficiencies of over 100 per cent were obtained before due allowance was made for the conversion of mill power into useful heat. When moisture is low, the heat obtained from the conversion of milt power is an appreciable part of that required. That drying can be effected in the short time interval available in a grinding mill of this type is better understood by visual-

Jan 1, 1948