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By Roswell H. Johnson

The principle of sliding or graduation in royalties is accomplished either by the block, period, cumulative, or class method. The block method calls for a very low royalty rate on all oil produced up to a certain amount. This amount would normally be that which is believed to suffice to repay the cost of the well. A higher rate would be charged after the well is making a profit. This method, common in many industries, is peculiarly inadaptable to any industry such as this where the productivity per day of the units gradually and inevitably decreases. This, for reasons given later, is because it forces an early abandonment of the well and so offends against conservation. In the period method, the royalty rate is changed by some definite amount when the well produces less than a specified quantity per day or other given unit of time. While simple to explain, it operates badly because a great deal is made to depend upon a small reduction in production, whereas the reduction as a matter of fact declines rather erratically owing to the exigency of lease management, connecting of tankage, and vagaries of the gaugers. These disadvantages are obviated by the cumulative method. In this method, all the production less than a certain amount per week has one rate of royalty, or none at all, and the oil produced in excess of that amount pays an additional rate of royalty. In the long run the calculation is probably no greater than with the period method, for simple tables will be published and printed in the oil papers that can be cut out, enabling quick readings to be made. Even without the table the calculation is easy with the few royalty rates, two or three, which would be used. In this method, the amount paid in royalty declines gradually, rather than suddenly as in the period method. The following reasons might be advanced for the adoption oi cumulative royalties: 1. To distribute the burden in accordance with the capacity to pay. This principle is a unique one in business, although familiar in taxation. This is because it does not distribute reward in proportion to efficiency.

Jan 1, 1916

By J. H. Scaff, J. E. Kunzler

The measurement of the electrical, thermal, and magnetic properties of metals at low temperatures, primarily in the range of liquid helium below 4.2°K, is a powerful tool for investigating many of the fundamental properties of the metallic state. Such measurements also have many practical applications, particularly as an analytical tool. One example of the practical utility of such measurements is illustrated by a short study we have made of the low-temperature resistance of copper used in preparing varistors. Copper-oxide varistors are prepared by the thermal oxidation of copper. This results in the

Jan 1, 1959

By P. M. Budge, William L. Fink, Kent R. Van Horn

The investigation of the phase relations of high-purity aluminum-base alloys is a part of the fundamental research program of the laboratories of the Aluminum Company of America. The results of a number of binary and ternary systems have previously been published in the Transactions of this society. The aluminum end of the binary aluminum-titanium system has been studied. This system has received relatively little attention. To the authors' knowledge, there are two previous papers on this subject. E. van Erckelensl determined the constitutional diagram reproduced in Fig. 1. According to this diagram, the liquidus represents the separation of TiA14, (Ti = 30.7 per cent.). He concluded that this is the composition of the compound, because in his work the eutectic horizontal terminated at 30.7 per cent. titanium and the metallographic examinalion of a sample of this composition revealed only one phase. According to the constitutional diagram developed by W. Manchot and A. Leber,² reproduced in Fig. 2 from data given in their article, the liquidus represents the separation of the compound TiA13 (Ti = 37.2 per cent. ). The composition of the compound was derived in a manner similar to that utilized by van Erckelens. Moreover, Manchot and Leber confirmed the composition of the compound by analysis of the constituent left as a residue after dissolving the alloys in weak sodium hydroxide solution. Although these are the only publications describing the constitution of the system, other investigators have studied the composition of the titanium compound. L. WÖhler3 says that there is a compound TiA13 which was later confirmed by W. Manchot and P. Richter4 and by

Jan 1, 1931

By William L. Lennemann

Chemistry of uranium with respect to its hydrometallurgical recovery from carnotite ores was investigated and well defined during the radium boom period between 1900 and 1920. Since that time, methods used to extract uranium from its ores have remained basically either acid leaching or sodium carbonate leaching. Until about 1950, the only practical methods known for achieving a better than 75 pct U2O3 concentrate from the leach liquors involved fundamental chemical techniques for either purifying a solution prior to the uranium precipitation, or refining a crude uranium concentrate that was produced by neutralizing a pregnant mill liquor.

Jun 1, 1956

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By Norman D. Fitzgerald

The purpose of this paper is to analyze the behavior of oil securities during the six-year period January 1932 through December 1937. This period was selected because of its varied character. It includes the depths of the depression, the broad and spasmodic recovery, and the recession collapse. The first part of the analysis is devoted to the correlation of a number of economic factors with an index of 13 oil stocks. The second part is a comparison of the different,ial behavior of 6 oil stocks. The relationships developed here are only a few of many that might be considered in a complete analysis. The stock market is regarded as a barometer of business confidence and as such exerts an important influence upon corporate policies, particularly upon industrial expansion. The complex and continuously changing nature of its price structure, the ebb and flow of influences and the effects of impacts require dynamic rather than static analysis. When treated in this way, many of the important fluctuations in market prices and changes in the relationships between securities appear quite logical. The market for oil securities has varied widely in recent years. The Standard Statistics index of 13 oil stocks made a bull market peak of 166.7 in September 1929. The collapse of the boom and the ensuing bear market finally carried the index down to a low of 36.4 in June 1932. From this point oil stocks made an irregular recovery; they reached a top at 139.7 in March 1937, and after maintaining this approximate level through August, declined precipitously to 93.3 in December 1937. The prices of these 13 oil stocks have gone up and down under the influence of numberless variables. These variables are of two kinds, those external to the industry, and those that are solely due to its internal condition. The external factors are political, social, and economic, both domestic and foreign. These are the influences that induce the ebb and flow of all prices in general and security prices in particular. Among the internal factors are the regulation of industry, the development of new reserves and processes, and the disequilibrium due to lack of balance between supply and demand. Some of the simpler relationships are examined in this paper.

Jan 1, 1938

Executive Committee. ROBERT H. RICHARDS, Chairman. ALBERT SAUVEUR, Vice-Chairman. TIMOTHY W. SPRAGUE. HENRY A. WENTWORTH. AUGUSTUS H. EUSTIS, Secretary, 131 State St., Boston, Mass. The twelfth meeting of the Boston Section was held at the Engineers' Club, 2 Commonwealth Ave., Boston, on Monday evening, May 5, 1913, fifteen members and three guests being present. The meeting was called to order by Vice-Chairman Albert Sauveur, who introduced the speaker of the evening, Utley Wedge, of Ardmore, Pa. Mr. Wedge read his paper on the chloridizing roasting of copper ores, which he illustrated with a stereopticon, and which will be published in full by the Institute. After Mr. Wedge had closed his paper, which was received with great interest by all the members, the following discussion took place: Professor Hofman said that iron was formerly thought to ho essential to the Henderson process, but that it is not absolutely essential. Mr.Wedge said that, as far as he. knew, the presence of some sulphates was an abso¬lute necessity, and that line ores can be worked satisfactorily, although lime has an effect on the subsequent leaching. He added that the low fuel consumption of the latest Wedge furnace is a result of direct application of the combustion gases to the ore. Ten per cent. of fuel was needed with the muffle furnace. By direct firing he has been able to reduce the fuel needed to from 2 to 4 per cent. In the latest types of furnaces the gases from the upper hearth are not used. There is doubtless some temperature at which the loss. from copper chloride volatilization becomes serious, but in practice on Rio Tinto ores troublesome losses are not experienced. The copper apparently does not become volatile at. the temperatures where we would expect that it would. There are doubtless ores in which there would be serious danger from losses from this source. The latest furnaces do not use the high temperatures that were needed in the former single-hearth Wedge furnaces.

Jan 7, 1913

By C. R. Sandberg, C. A. Connally, N. Stein

This paper describes the results of volumetric efficiency tests on oil well pumps handling gas oil mixtures. The work was performed in a large scale, above ground unit wherein test conditions could be accurately controlled and measured. The main variables studied were gas/oil ratio (including gas from solution and free gas mixed with oil), pump compression ratio, pump stroke length, pump speed, and clearance volume between the valves at their closest approach. Results are presented for two different pumps and for oils of two viscosities. Relatively small amounts of gas entering the pump resulted in large decreases in volumetric efficiency. Under conditions where the pump was operating at reduced efficiency because of the presence of gas, it was found that variation in the clearance volume between the standing and traveling valves had a considerable effect on pump efficiency level. This effect of the valve clearance volume was found to be significantly altered by the viscosity of the oil used in the tests. The effects on pump efficiency of the other variables studied were found to be relatively small over the range of conditions utilized. INTRODUCTION The production of oil by pumping is often hampered by low volumetric efficiency. A direct increase in lifting costs results from low volumetric efficiency. An indirect increase in lifting costs, probably greater than the direct increase, results from additional wear and tear on pumping equipment and from the down-time necessary for the repairs which can be traced to low-efficiency operation. Both increases in lifting costs tend to reduce economically recoverable oil. A number of different factors can contribute to low pump efficiency. A known basic cause of low efficiency is the presence of free gas in the pumped fluid. Pump volumetric efficiency is calculated only on the basis of liquid pumped and because any free gas pumped is discounted, this volume of free gas would represent a loss of pump efficiency. However, gas also causes a reduction in pump efficiency because it is a highly compressible fluid. It is known that pumps some- times "gas lock" because of excessive gas-to-liquid ratios in the pump barrel. Little is known of the role of gas compressibility in the intermediate case where the pump is operating at low efficiency. The opinion exists, however, that oil-well pumps tend to operate at higher efficiency with long stroke lengths at low speeds, but no quantitative studies of these pumping variables have been reported. It was believed that a much better understanding of the variables which control pump volumetric efficiency could be obtained and that possibly some suggestions as to the methods for increasing efficiency might be found from a study of the operation of pumps handling gas under closely controlled conditions. Previous investigators have studied the effects on pump efficiency of such factors as oil viscosity, oil temperature, slippage of oil. past pump plungers, pump submergence, valve size and spacing, pressure above pump plunger and fluid vapor pressure. However, none of these published investigations were conducted with pumps being subjected to large amounts of gas such as might be the case in a pumping well, nor did any of the investigations study the effect of variation in stroke length or pump speed. A large-scale teat unit was therefore constructed for studying the operation of pumps handling gas and for evaluating effects of such variables as pump stroke length and pump speed. PROCEDURE AND EQUIPMENT A schematic diagram of the pump testing equipment is given in Fig. 1. A 45-ft length of 6-in. casing is mounted vertically in a 65-ft tower. Sight ports are mounted in the casing at intervals near the location of the pump intake and the liquid level in the casing. These sight ports are fitted with Lucite windows sealed by neoprene "0" rings. The Lucite windows are machined to conform to the I.D. of the casing so that no obstruction to flow is present along the casing wall. The casing is fitted with a tubing head and 2-in. tubing is hung inside the casing. Pumps are seated in a shoe attached to the 2-in. tubing. A 1-in. polish rod is attacked directly to the pump without any intervening sucker rods. The top of the polish rod is attached to the weight carrier, which contains a number of weights to be used to force the polish rod in against tubing pressure on the down-stroke. This is necessary because a long string of sucker

Jan 1, 1953

By B. M. Larsen

Jan 1, 1965

By P. Ramakrishnan, Ramjilal

Fine powders of lead zirconate titanate have been prepared by three different methods such as ball milling, conventional coprecipitation and spray drying. Different powders have also been prepared by changing the process variables in each method. These powders were analysed for particle size chemical composition and reactivity. DTA, TGA and x-ray analysis have been carried out to study the lead zirconate titanate formation with reference to calcination temperatures. The calcined powders were then consolidated by compaction and sintering. An attempt has bean made to explain the consolidation behaviour of these powders on the basis of powder characteristics.

Jan 1, 1980

By Charles E. Locke

IN gathering material for this review the aid of the individual members of the Milling Committee was invoked and the assistance received is hereby most grate- fully acknowledged. The replies were much alike; almost everyone stated that in 1932 his operations had been cur- tailed or stopped entirely, that the only activity and progress were in milling gold ores, and that the Hadsel mill' looked like a coming machine in the crushing and grinding field. However, further inquiry and search have shown that the year was not quite so barren of developments as the foregoing statement would indicate.

Jan 1, 1933

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed.

Jan 9, 1951

By P. A. Beck

ACCORDING to a recent hypothesis of Sully,' xY. binary CT phases are characterized by 1.7 bonding 3d electrons per atom, which completely fill the first Brillouin zone. This hypothesis appears to imply that there are no empty 3d orbitals in the u phase, and that, correspondingly, this phase must be dia-magnetic, or at most weakly paramagnetic. On the other hand, Bowen and Hoar' reported that a u phase extracted electrolytically from an alloy steel became ferromagnetic when cooled to about —113°C. In view of the fundamental interest of the problem from the point of view of the electron structure of the u phase, it seemed worthwhile to study the magnetic properties of massive u phase specimens of various known compositions. Sigma specimens of the following compositions were tested: 1—40 atomic pct Fe, 40 atomic pct Cr, and 20 atomic pct Mo 2—35 atomic pct Fe, 35 atomic pct Cr, and 30 atomic pct Mo 3—48.7 atomic pct Fe, 50.2 atomic pct Cr, and 1.1 atomic pct W 4—40.7 atomic pct Co and 59.3 atomic pct Cr All specimens were found to be strongly paramagnetic at room temperature, particularly alloy No. 1. At liquid nitrogen temperature, alloy No. 1 be- came ferromagnetic; the other u alloys remained paramagnetic. Even though apparently not all u alloys become ferromagnetic at liquid nitrogen temperature, in view of their strong paramagnetism it is probable that the electron structure proposed by Sully is not correct. Similar qualitative studies were made with the p, P, and 8 phases." A p phase specimen of 57.2 atomic pct Co and 42.8 atomic pct Mo; a P specimen of 19.9 atomic pct Cr, 37.8 atomic pct Ni, and 42.3 atomic pct Mo; and a 8 specimen of 50.4 atomic pct Ni and 49.6 atomic pct Mo were tested at room temperature, and all were found to be paramagnetic, although considerably weaker than the u phase specimens described above. A test at liquid nitrogen temperature gave similar results for all specimens; none became ferromagnetic. Thanks are due to D. K. Das for preparing several of the alloys and to Pol Duwez of California Institute of Technology for kindly loaning four specimens of cr alloys. References 1 A. H. Sully: The Sigma Phase in Binary Alloys of the Transition Elements. Journal Inst. Metals (1951) 80, p. 173. - K. W. J. Bowen and T. P. Hoar: Low Temperature Ferromagnetism of Sigma Phase in an Alloy Steel. Research (1950) 3, p. 484. 3 S. Rideout, W. D. Manly, E. L. Kamen, B. S. Lement, and P. A. Beck: Intermediate Phases in Ternary Alloy Systems of Transition Elements. Trans. AIME (1951) 191, p. 872; Journal of Metals (October 1951).

Jan 1, 1953

By W. C. Lilliendahl, H. W. Highriter

THE method developed and used in this laboratory for the production of metallic uranium of such purity that it is ductile and can be cold-worked to fine wire or thin sheet by rolling has already been described1. It consists, briefly, in the electrolysis of potassium uranous fluoride (KUF6) in a molten bath composed of equal parts of sodium and calcium chlorides. The bath is contained in a graphite crucible, electrically heated to about 775° C., the crucible serving as the anode for electrolysis. The uranium deposits in finely divided form mixed with salts upon a molybdenum cathode suspended axially in the crucible. Upon completion of the electrolysis the cathode is removed and cooled, the deposit broken and leached to remove salts. The metal powder is washed with water and dilute acetic acid and dried in vacuo to reduce oxidation. Suitable amounts are then pressed into pellets and heated in vacuo by high-frequency induction, using a thoria crucible. The uranium melts and flows away from the pellet, leaving a shell, which is largely oxide. In general, this method produced a satisfactory metal, although at times the uranium was not ductile. The investigations recorded here were made to find the cause of this embrittlement. It was known that the metal generally contained carbon, derived from disintegration of the graphite crucible in which electrolysis is conducted, in amounts dependent upon the thoroughness of washing the metal powder. Accordingly, analyses of several samples, both ductile and brittle, were made by combustion and absorption of CO2 in Ascarite, using air instead of oxygen to reduce the temperature and rate of oxidation. Several of these metals were made with special precautions to reduce carbon content. The results show no relationship between ductility and carbon content in the range investigated (Table 1).

Jan 1, 1935

By Ronald D. Irving

The object of the present paper is to give an outline account of the mineral resources of the State of Wisconsin, so far as they are now known, including both metallic ores and non-metallic useful mineral substances. Tl~e only previous publication making ally attempt at such an account is one of a popular nature, prepared by the writer for Snyder and Van Vechten7s Historicccl Atlas of Wisconsin, which was published at Milwaukee in 1878. The data upon which the statements of the following pages are based are chiefly from the

Jan 1, 1880

John Eliot Allen has been made acting head, dept. of geology, New Mexico Institute of Mining and Technology, Socorro, N. Mex. He had been associate professor of geology. Robert B. Anderson has accepted a position with the U. S. Steel Co., Gary, W. Va., as assistant to the superintendent, No. 2 mine. [ ] Donald L. Archibald has joined the sales dept. of the Ellicott Machine Corp., Baltimore. He formerly had been associated with the Joy Mfg. Co., St. Louis. J. C. Boswell has been appointed manager of the Fairbanks dept., United Smelting Refining & Mining Co. J. B. Metcalfe has been appointed assistant to the president. G. Howard LeFevre was elected vice-president and general manager of metal sales and R. N. Hunt, vice-president and chief geologist was elected a director. R. B. Earling, vice-president and general manager of Alaskan operations, has retired but. will con¬tinue to serve on the board of directors. J. D. Crawford has been appointed general manager of Alaskan operations.

Jan 1, 1952

US 4,152,143-Continuous precipitation of cement copper from an aqueous ore leach solution mixed with pieces of iron as the precipitant Copper depositing on the pieces of iron is loosened and removed therefrom by means of constant but regulated oscillating movement of the pieces of iron in a horizontal elongated chamber, and the loosened copper is separated and collected from the mixture E Kausel and R Nissen, assigned to Klockner-Humboldt-Deutz A G May 1, 1979 8 pp (75-100) Filed 1-12-78 (868,981) (Drawings below) [ ] US 4,156,711-Removal of metal impurities from an acidic zinc or cadmium solution prior to electrolysis. Impurities such as manganese, cobalt, nickel, and thallium are selectively precipitated by contacting the solution with persulfuric acid or an ammonium or alkali metal salt thereof while maintaining a pH value of from 1 5 to 4 5 This patent is a continuation-in-

Jan 1, 1980

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

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

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

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

(Members are urged to send in for, this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Aug. 10 to Sept. 10, 1915: Everett L. Booth, New York, N. Y. Raymond B. Ladoo, Cambridge, Mass. T. E. Sturtevant, Dover, N. J. Henry A. Tobelman, Ajo, Ariz. C. A: Filteau, New York, N. Y. R. B.Tinsley, B. Tinsley; Venezuela. Guy C. Riddell, Helena; Mont. ; E. H. Hamilton, Norfolk, Va. Joseph Leiner, New. York; N. Y. M. Yoshimura, Tokyo, Japan. Alfred W. G. Wilson, Ottawa, Canada. Van H. Manning has been appointed Director of the U.. S., Bureau of Mines, to succeed the, late, Dr. Joseph A. Holmes. Mr. Manning was Assistant Director of the Bureau. 0. M. Lewyn, formerly Mine. Superintendent for the Braden Copper Co., has accepted the position of Assistant Mine Manager with the Union Minière de Haut Katanga of South Africa.

Jan 10, 1915