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By Rex W. Woods, Morris Muskat

A leastmsquare analysis procedure has been developed and applied for the study of the deviations in estimations of oil in place as given by the material-balance equations. The data used were those obtained from field observations on the Jones sand in the Schuler pool, Arkansas, and the Monroe dolomite in the Reed City pool, Michigan. Possible effects of water intrusion were taken into account by expressing the cumulative water influx in terms of various functions previously proposed in the literature. Formulas were developed and values calculated for the minimum deviations and minimal percentage deviations in the calculated volumes of oil in place from the average values, as could be obtained by suitable choice of the water encroachment and initial gas-cap volume parameters. The results show that the fluctuations in these calculated volumes are very insensitive to the values chosen for the rate of water intrusion and initial gas-cap volume, and hence cannot be safely used in discriminating between spurious values for these parameters and such as actually pertain to the producing reservoirs. Moreover, the exact form of the water-intrusion function seems to have but little effect on the fluctuations in the computed oil in place. Accordingly, it is concluded that the material-balance method does not of itself provide a satisfactory criterion for determining the basic physical unknowns of producing reservoirs or in making conclusive decisions regarding the production mechanism, unless independently established geological control data are available for eliminating unreasonable values for the reservoir parameters, even though they may still satisfy the material-balance formulas. If, however, from core or logging data the initial oil in place and the gas-cap volume can be established in advance, the material-balance formulas can be inverted to find the water intrusion. Moreover, by determining by such calculations the water-intrusion coefficient, the iuture production performance can then be predicted by the aid of the materiaI-balance formulas for specified operating conditions. This type of application may be of particular value in predicting the results of Pressure-maintenance operations. Introduction The evaluation of the forces acting upon an oil reservoir is a problem of considerable interest to the operator as an aid in determining the proper method of operation for the reservoir to obtain an optimum recovery of oil. In many pools, the nature and magnitude of the forces acting upon the reservoir remain unknown until an appreciable amount of ultimate recovery is obtained. To be of value to the operator, a reliable interpretation of reservoir performance should be available in the early life of the pool to permit an optimum plan of operation. Progress has been made in an understanding of reservoir behavior and the importance of the different factors involved. The material-balance method of estimating oil in place has been proposed as a tool in analyzing reservoir-performance problems.l The solution of such problems by this method ordinarily involves two or more unknown values relating to the nature of the reservoir, and the results

Jan 1, 1945

By Howard I. Epstein, John R. Buzek

Thickeners are simply large tanks, usually circular in shape, which are designed to allow settling of solids and to operate with continuous overflow of clear water and underflow of thick pulp. The dimensions of the thickener are usually such that dewatering of very fine pulps may be accomplished while still overflowing clear water. Some thickeners such as the Center, Hardinge and Hydrotator types combine thickening with filtering2 while others such as the Dorr type are pure thickeners. l .2 , 3 A schematic diagram of the traction type Dorr thickener is shown in [Fig 1]. This type is appropriate for tanks over 15 m (50 ft) in diameter. This tank employs a rotating raking mechanism which moves the settled material toward the central discharge. For this and other thickeners, it is common to have a shallow conical tank bottom in order to conform to the geometry of the raking mechanism, and it is often desirable to elevate the tank for ease of access to the product. When the tank does not rest on the ground, the forces resisted by the cone are large, and thick plates must be employed. The fabrication of these tanks requires temporary supports in order to erect the cone. A flat-bottomed tank could also be used because the settled material would soon form a hardened conical surface. However, because of the presence of large bending forces, even larger plate thicknesses are required than for the conical bottom. Significant cost savings often can be realized by the use of a scalloped-bottomed tank such as the one partially shown in [Fig. 2]. The particular scalloped bottom discussed in this paper employs radial beams forming the outline of the cone-shaped bottom. These beams are supported directly by columns. Cone segments are hung between adjacent beams. The exact geometry of these segments depends upon the cone angle and radius, the number of radial beams, and their inclination. The geometry is chosen to satisfy certain clearance restraints and to utilize the material as efficiently as possible. The resulting thickness of these segments is significantly less than that of the equivalent plate for the tank with a conical bottom. This result, along with the simpler fabrication procedures required, accounts for the cost savings associated with this design. The raking mechanism employed may be the same as for the conventional conical bottom since the settled material soon forms a conical surface. Determination of the internal force mechanism for the scalloped bottom leads to designs that utilized material efficiently and thus maximize the cost savings. The complicated geometry of these bottoms along with the difficulty in analyzing the structure are factors which may have limited the use of scalloped-bottomed tanks to date. When such tanks have been built, the uncertainties associated with the internal forces have led to designs that are somewhat inefficient. In this paper, equations relating the geometric parameters are presented along with simplified closed-form solutions for the internal forces in the cone segments, from which the loads applied to the beams and the loads carried to the cylindrical tank shell can be deduced. An example is presented to show the magnitude of the savings which may be realized with this configuration.

Jan 1, 1979

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally.' Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan,3 show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision; using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by, the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.5 However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: [3fB = 9.20•'./V•Vn- (n-1) • (n+2) /8[1]] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts' as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of, a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsymmetric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat I than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system, of one degree of freedom can be applied: [1E/m[2] fP = 27] Here f, is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: [t~ = 2/f = 7r\/m/E[3]] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson' 1831) [aP = 4 D2.pL•g•h +7rD•y sin a[4]] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, pL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of-the liquid in cm, y the surface tension in dynes per cm and a the supporting angle' or the one required to insure equilibrium, a being smaller than the contact angle ?. Although demonstrated by Poisson, it has not

Jan 1, 1952

By Samuel M. Brock

In recent years society has become increasingly concerned with maintaining and improving the quality of environment. Thus, public interest and concern with pollution problems is now high. This is reflected in recent federal and state efforts to formulate new legislation to prevent pollution and strengthen existing pollution laws. In reviewing literature pertaining to pollution problems, it is possible to distinguish many common elements. The most outstanding of these is the failure of the market to guarantee that private firms responding to price signals generated in the marketplace will make decisions leading to optimal resource use. Cases of market failure in allocating natural resources according to the wants of society frequently are due to the presence of technical externalities, or side-use effects.59 These roughly and generally can be defined as interdependencies among production and consumption units, the impacts of which are exerted other than through the market. They are, in other words, extra-market relationships. The economic unit generating external effects does not take them into account in decision-making. Thus, the tendency is for the unit to produce either more than society desires or not enough. In such cases society often has intervened in the decision-making process. This intervention frequently has taken the form of legislation to regulate production and consumption activities. Thus, a body of institutions, which acts as a constraint in decision-making processes, has materialized. These institutions are often far more influential in their effect upon resource use than are the forces of supply and demand acting in the marketplace. The problem of environmental pollution is essentially the problem of handling residuals which are the byproduct of all production and consumption activities which take place in the economy.2 These residuals are emitted into the air and water and disposed of on the land. They are interrelated, in that efforts to control emissions into the air or water can result in the production of solid wastes, which then present disposal problems. It is convenient to separate residuals by the type of pollution they cause-air, water, and land while remembering that these problems are related and that solutions may require coordinated effort.1 Residuals may be produced in both production processes and consumption. Residuals produced in production by the mineral industry, or firms utilizing its products, range from emission of sulfur dioxide by steam generating plants to radioactive mill tailings produced in the course of mining uranium.. Residuals associated with consumption are generated mainly through transportation of members of the household, space heating, and in the disposal of solid wastes, including refuse and junk autos. Residuals associated with both production and consumption receive attention in ensuing sections of this chapter.

Jan 1, 1976

By D. I. Bardos, Paul A. Beck

The 1100°c isothermal, sections of the V-Fe-Si, V-Co-Si, and V-Ni-Si systems were studied at silicon contents between 0 and 40 at. pct. The single-phase fields in the 30 and 50 at. pct Mn sections of the 1100°C tetrahedron of the V-'Wn-Fe-Si system were also determined. The direction of extension of the elongated O, R, D, and a-Mn Phase fields suggests that the stability of these phases is determined largely by the electron concentration. The peculiar shape of the above ternary a phase fields, as well as of the a phase fields in the V-;Mn-Si and Cr-MTZ-Si systems is accounted for on the assumption that in manganese-(iron-, coball-, nickel-) rich alloys silicon atoms do not exclude d electrons , while in alloys low in the above components they do. This assumption also leads to the expected electronconcentrations for q and ß-Mn phases formed by transition metals with aluminurn. In earlier work it was shown that in ternary alloy systems of transition elements the a a and certain other phases with complex structure, such as the p and R phases,3 form elongated phase fields extending in a direction corresponding to a constant electron concentration. Recently similar behavior was observed in manganese-rich ternary ß-Mn solid solutions with another transition element and with silicon, germanium, or tin,4 confirming earlier indications3 that ß-Mn is also an electron phase. The alloying behavior of silicon in these manganese-rich alloys sug- gested that the four outside electrons of silicon participate in the bonding and that the predominantly d-like bonding electrons are not excluded from the silicon sites. Presumably, some of the normally unoccupied 3d states associated with the silicon atoms are in these alloys lowered to the Fermi level;4 thus silicon behaves as if it, too, were a transition element. The manganese-rich boundary of the a phase in the V-Mn-Si system,4 as well as in the Cr-Mn-Si sys-tem,4,5 extends approximately parallel to the ß-Mn phase boundary, corresponding to the transition ele-mentlike behavior of silicon described above. However, at lower manganese contents (i.e., in the high-vanadium or -chromium region) the a phase field in both ternary systems mentioned extends in a direction roughly perpendicular to that of its manganese-rich boundary, a phenomenon that is apparently inconsistent with the behavior of silicon in the manganese-rich alloys. A similar, although somewhat less pronounced, extension of the a phase occurs also in the high-vanadium (low-iron) region of the V-Fe-Si system at 1175C, but reportedly not in the V-Co-Si or V-Ni-Si systems at the same temperature.5 The present work was undertaken to investigate in more detail the extension of the a phase (as well as of other electron phases that may be present) in the last three systems and to elucidate this phenomenon, which has not been satisfactorily explained previously. EXPERIMENTAL PROCEDURES Most of the alloys were melted in an arc furnace, using a water-cooled copper crucible under helium atmosphere. The transition metals were of better than 99.9 pct purity and the silicon used was 99.98 pct pure. Alloys containing less than 20 pct V were induction-melted in recrystallized alumina crucibles under argon atmosphere.

Jan 1, 1967

By Douglas A. Karvonen

INTRODUCTION Although the economy in the Province of Saskatchewan has historically been agriculturally oriented, a major source of wealth has been realized through natural resources such as petroleum and natural gas, coal and uranium and since the 1960's - potash. Potash or potassium chloride, in the form in which it is presently produced in Saskatchewan, is used primarily as fertilizer, a source of potassium, one of three essential elements required for healthy plant growth, with about 5% of production sold to the chemical industry for use in such products as soap and liquid detergent, glass and ceramics, textiles and some pharmaceuticals. Saskatchewan is estimated to have approximately 40% of known world potash reserves and its ten active mines account for some 25% of annual world production. POTASH CORPORATION OF SASKATCHEWAN In an effort to guarantee a fair and lasting economic benefit to the Province of Saskatchewan, the Potash Corporation of Saskatchewan (PCS) was created on February 4, 1975 through an Order-in-Council under the Crown Corporation's Act and later on April 1, 1976, the Potash Corporation Act provided for its continuation. PCS was given the mandate to acquire ownership of a significant portion of the potash mining capacity in Saskatchewan and to establish an organization capable of operating the facilities, marketing the product, and conducting all of the other activities necessary for a successful corporation competing in the world potash industry. The corporation is the largest potash producing and selling organization in the Western World - or third largest in the world. (See also Figure 1). PCS through its wholly-owned subsidiary, PCS Mining, has acquired a whole or partial interest in five geographically distinct producing properties or divisions, representing today more than 40% of Saskatchewan's potash producing capacity. The acquisition of each division was followed by a program designed to exploit and maximize the particular opportunities at each minesite for increased production. To that end, PCS Mining has taken an active lead in expanding to meet future demand and has implemented expansion programs at all properties except for its Esterhazy Division where it has a long-term processing agreement with International Minerals & Chemical Corporation (Canada) Limited. Through its wholly-owned subsidiaries, PCS Mining, PCS Sales and PCS Transport, this provincial crown corporation has the ability to operate as a producer and marketer of Saskatchewan's potash. In certain instances PCS, the parent company, assists in the financing of various projects undertaken by the subsidiaries and in other cases the subsidiary involved arranges its own financing. POTASH RESERVES As a background to the specific issue of financing, it is helpful to describe briefly the nature of the deposit which supports the industry - our collateral, if you like. The potash beds underlying Saskatchewan are sedimentary rock deposits formed by the gradual evaporation of an inland sea during the Middle Devonian period roughly 400 million years ago. Now known as the Prairie Evaporite, this formation stretches from North Dakota and Northeast Montana through Southern Saskatchewan into North-Central Alberta. These beds lie at mining depths ranging from 950 - 1000m (3,000 ft) below the surface, where conventional mining methods can be used, and to 1,650m (5,000 ft), where solution mining must be

Jan 1, 1985

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By Richard F. Hinds, F. O. Reudelhuber

Application of the conventional depletion drive calculation methods to volatile oil reservoirs results in erroneous estimates of ultimate recovery. In view of the increasing number and importance of volatile oil reservoirs, a special technique has been developed which will result in more realistic predictions using laboratory data obtained from reservoir fluid studies of a specific type. The experimental data are designed to permit continuous material accounting and, therefrom, provide the hy-clrocarbon composition of both the flowing oil and gas phases. The resultant well-stream composition data are then used directly in surface recovery calculations utilizing equilibrium ratios. A step by step procedure, specifically designed for routine use by the practicing reservoir engineer, is presented in an appendix. An actual study performed on a deep Mid-Continent reservoir is used ay an il-lustrathe example. INTRODUCTION It has been a practice for many years to utilize the conventional ma- terial balance methods in conjunction with relative permeability concepts for the prediction of recovery from solution gas drive reservoirs.' Those who have performed such calculations recognize that compromises of several types are necessary in order to reduce the calculations to a reasonable degree of complexity. The most serious assumption involved results from the necessity of treating the produced oil and gas as separate fluids, independent of each other in their behavior. It is further assumed that the gas which is evolved in the reservoir as a result of pressure decline will not yield liquid upon the reduction of pressure and temperature resulting from production through surface equipment. Although these shortcomings have been recognized,' it has been difficult to attempt refinement of calculation procedures since the laboratory data available normally were not of the proper type or extent to permit such calculations. Three general procedures have been available for depletion drive calculations when laboratory fluid data are of the conventional type. Differential Procedure The most simple, and most widely used, method requires use of the formation volume factor and gas sol- ubility data obtained from a differential liberation performed at reservoir temperature. This procedure ignores the differences existing between the fluid behavior in the reservoir and its behavior as it is produced through surface separation equipment. The errors introduced are not serious when dealing with very low volatility fluids and this method may be utilized if the laboratory data indicate only slight differences between the differential data and the flash data obtained from separator tests. Modified Differential Procedure This method was developed when it became apparent that medium volatility fluids evidenced a wide difference between the flash and differential data. The differential data are adjusted by changing from a residual oil basis to a stock tank oil basis. All that is required is multiplication of the differential data by the ratio of residual oil to stock tank oil relative volumes existing for the original reservoir fluid at the determined saturation pressure. This procedure generally results in increased calculated ul-timate recovery; however, such results should be viewed critically. Upon examination it may become apparent that the results are influenced by errors in reservoir liquid

Jan 1, 1958

By Whitman E. Brown, Louis J. Erck

L. A. ROE*—This paper is one of great value to the iron ore industry. The Humphreys spiral is a relatively new tool and gives promise of being quite useful in solving certain problems of iron ore beneficiation. Spirals have been tested on a martite ore at the Benson mine of Jones and Laughlin Steel Corp. in northern New York State. Our New York ore is considerably different, physically and mineralogically, than the one mentioned in this paper, and contains only 25 pct iron. This ore can be processed on spirals to give a concentrate containing 62 pct iron with an 85 pct recovery. On our particular ore we found operating difficulties when the spiral feed was coarser than 14 mesh. These were chiefly due to excessive "build-up" of locked middlings in the spiral circuit. In extreme cases these middling particles would accumulate to such an extent that the plant had to be shut down and the spiral surge tanks cleaned out. It is interesting to note that there exists a close relationship between the results of tabling a given iron ore and concentration of this same ore on Humphreys spirals. The size range of the ore must, of course, be within those limits acceptable to spiral concentration. Comparative tests on several of our mar-tite ores showed tabling results to be the same as spiral results. The authors make no mention of the use of a tailing stream splitter (now available from the spiral manufacturer) which is a useful tool in studying iron losses in the tailings stream. 011 our particular martite ore we found a considerable accumulation of fine-sized iron ore particles in the outside portion of the tailings stream. This fraction may be amenable to further treatment. E. H. ROSE*—The authors have concluded an interesting piece of work and this paper is an excellent factual account of a rapid and somewhat unusual transi-;ion in practice in the plant described. Perhaps it was modesty on their part which caused them so casually to limit to one sentence the fact that "several other methods of concentration on the fine ores representative of the Hill Trumbull group . . . failed to produce consistently an acceptable grade and recovery of finished product." The fact is that they were confronted by a difficult mineral-dressing problem and they are to be congratulated on their courage and persistence in staying with it until a satisfactory solution was evolved. A visitor to the plant might have been mildly astonished, as I was, to see one type of concentrator handling that part of the load early in the 1947 season, its experimental replacement by another a little later, and then in 1948 to see that both types had simply disappeared and their place taken by the spirals which were operating as placidly as though they had been there all the time. In working out economic methods of beneficiating Alabama red ore, most of which development is still ahead of us, it is likely that we also will pass through a period of successive disappointments, for we too have a problem where it is next to impossible either to "guess 'end right in the first place," or, because full-scale operating cost is such an important factor, to lay the ultimate answer on the line in advance by means of laboratory experimentation. Iron ore being what it is instead of what it used to be, it is encouraging to have the example the authors have given us today that a tough nut that will not crack on the first blow or the second is apt to do so on the third or fourth.

Jan 1, 1950

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By H. E. Stamm, H. H. Spain, R. C. Rumble

This paper presents a reservoir analyzer study of the performance of the Woodbine formation in the East Texas basin. The study was made possible by the compilation of available information on the configuration. thickness and the pressure drawdown of the formation. The investigation was made of the pressure variations in the basin incident to production from the several Woodbine reservoirs. In addition, the apparent compressibility of Woodbine water was evaluated so that the potential water yield of the formation could be determined. The distribution of permeability of the Woodbine sand and the interference between producing areas were also investigated. In conjunction with this basic study of the Woodbine sand, an acceptable match of the production-pressure relationship in the East Texas Field was established on the analyzer. INTRODUCTION When production is taken from a reservoir contiguous to an aquifer, the resultant pressure gradient causes a water influx into the reservoir. For some years it has been the practice to predict the performance of water drive reservoirs with mathematical equations that relate the water influx into reservoirs to their pressure behavior. A rigorous solution of these equations is quite complex: hence, the conventional method requires the simplifying assumptions that the formation have constant thickness, permeability and poiosity, and that it have a known and regular shape. It is necessary to use performance records of the reservoir in question to determine the equation constants that make the results of the mathematical calculations duplicate the reservoir history. The values of the constants determined in this manner sometimes differ so greatly from theoretical or measured values that the constants appear unreasonable. The equation constants comprise such factors as the thickness, porosity and permeability of the formation, and the viscosity and compressibility of water. Usually the thickness, porosity and viscosity are known within a reasonable degree of certainty. whereas the formation permeability and the water compressibility are known with considerably less certainty. Hence. permeability and compressibility values are arbitrarily selected that will make the mathematical equations duplicate the reservoir behavior. In many reservoir studies the value of the compressibility of water thus selected has exceeded the reported value by a factor of from severalfold to manyfold. Whether this excessive value results from the inadequacy of the mathematical approach to take into account the shape irregularities and the heterogeneities of the aquifer, or is due to some type of formation compaction and decrease of porosity has not been established. Because of the significance of the potential water yield of formations with reference not only to oil reservoirs but to water resources as well, it is very important that a representative value for the effective water compressibility be determined. One of the best known examples of a field for which it has been possible in the past to predict the future reservoir pressure is the East Texas Field. Until about 1943 it was possible by means of mathematical equations to duplicate past pressure behavior and to predict with a high degree of accuracy the reservoir pressure of the field. Since 1943, however, the calculated pressures have deviated progressively from the observed pressures to such a degree that in recent years, it has

Jan 1, 1951

By H. H. Spain, R. C. Rumble, H. E. Stamm

This paper presents a reservoir analyzer study of the performance of the Woodbine formation in the East Texas basin. The study was made possible by the compilation of available information on the configuration. thickness and the pressure drawdown of the formation. The investigation was made of the pressure variations in the basin incident to production from the several Woodbine reservoirs. In addition, the apparent compressibility of Woodbine water was evaluated so that the potential water yield of the formation could be determined. The distribution of permeability of the Woodbine sand and the interference between producing areas were also investigated. In conjunction with this basic study of the Woodbine sand, an acceptable match of the production-pressure relationship in the East Texas Field was established on the analyzer. INTRODUCTION When production is taken from a reservoir contiguous to an aquifer, the resultant pressure gradient causes a water influx into the reservoir. For some years it has been the practice to predict the performance of water drive reservoirs with mathematical equations that relate the water influx into reservoirs to their pressure behavior. A rigorous solution of these equations is quite complex: hence, the conventional method requires the simplifying assumptions that the formation have constant thickness, permeability and poiosity, and that it have a known and regular shape. It is necessary to use performance records of the reservoir in question to determine the equation constants that make the results of the mathematical calculations duplicate the reservoir history. The values of the constants determined in this manner sometimes differ so greatly from theoretical or measured values that the constants appear unreasonable. The equation constants comprise such factors as the thickness, porosity and permeability of the formation, and the viscosity and compressibility of water. Usually the thickness, porosity and viscosity are known within a reasonable degree of certainty. whereas the formation permeability and the water compressibility are known with considerably less certainty. Hence. permeability and compressibility values are arbitrarily selected that will make the mathematical equations duplicate the reservoir behavior. In many reservoir studies the value of the compressibility of water thus selected has exceeded the reported value by a factor of from severalfold to manyfold. Whether this excessive value results from the inadequacy of the mathematical approach to take into account the shape irregularities and the heterogeneities of the aquifer, or is due to some type of formation compaction and decrease of porosity has not been established. Because of the significance of the potential water yield of formations with reference not only to oil reservoirs but to water resources as well, it is very important that a representative value for the effective water compressibility be determined. One of the best known examples of a field for which it has been possible in the past to predict the future reservoir pressure is the East Texas Field. Until about 1943 it was possible by means of mathematical equations to duplicate past pressure behavior and to predict with a high degree of accuracy the reservoir pressure of the field. Since 1943, however, the calculated pressures have deviated progressively from the observed pressures to such a degree that in recent years, it has

Jan 1, 1951

By H. I. Aaronson

ONLY limited studies have been made of pro-eutectoid a morphology in hypoeutectoid Ti-Cr alloys during previous investigations, 1-3 The nature of the eutectoid reaction, ß?a + TiCr2, has been considered in somewhat more detail.1,2,4,4 Inasmuch as the proeutectoid ferrite reaction in plain carbon steels has recently been extensively investigated in this laboratory, advantage has been taken of the opportunity to compare the morphologies developed in two rather different eutectoid systems in order to permit a preliminary estimate to be made of the degree of generality which may be ascribed to the various results obtained. Experimental Procedure The chemical analyses of the alloys used are given in Table I. The 7.22 pct Cr alloy was prepared by the Battelle Memorial Institute from iodide titanium and high purity chromium. The initial ingot was made by arc melting a master alloy and iodide titanium. The resultant ingot was twice remelted. by the consumable electrode technique. Upset forging at 950°C reduced the final ingot to 3/4 in. sq bars. The 10.94 pct Cr alloy was prepared by the Titanium Metals Corp. of America from sponge titanium and chromium of ordinary purity. This alloy was melted twice by the consumable electrode technique, forged at 1200° to a 3/4 in. sq bar, and rolled at 815°C to a 1/2 in. round. Specimens 1/4 in. x 1/4 in. x 1/16 in. were cut from the 7.22 pct Cr alloy; halves of disks 1/2 in. in dlam and 1/16 in. thick served as specimens of the 10.94 pct Cr alloy. These specimens were individually encapsulated in Vycor, Each capsule was evacuated three times to a pressure of 2 to 6 x lo-' mm Hg and flushed twice with a reduced pressure of argon prior to sealing. The inclusion of two small packets of zirconium chips permitted the capsules to be outgassed and internally gettered, without heating the specimen, prior to heat treatment. The specimens were solution annealed for 40 min at 1000°C, isothermally reacted in deoxidized lead pots, and quenched in iced water. Most of the isothermal reaction treatments were carried out at 25" intervals between 725° and 550°C on specimens of the 7.22 pct Cr alloy and at 650°C on specimens of the 10.94 pct Cr alloy. Results and Discussion Morphologies of Proeutectoid a*—Kinetics of the ß?a Reaction: Fig. 1 shows the TTT-curves for the beginning of the proeutectoid a and the eutectoid reactions in the temperature range investigated in the 7.22 pct Cr alloy. The M, temperature in this alloy is below 0°C. The curve for the beginning of the proeutectoid a reaction is in good agreement with that of Frost, Parris, Hirsch, Doig, and Schwartz' for a 7.54 pct Cr alloy, appears at considerably earlier reaction times than the corresponding curve presented by Rostoker4 for a 7 pct Cr alloy, and lies athwart the curve of Spachner and co-workers11 for an 8 pct Cr alloy. Differences in criteria for the beginning of the a reaction and the relatively high rate of this reaction at lower temperatures presumably account for some of these divergences and may also explain, in part, the apparent failure of an iodide-base 7.22 pct Cr alloy to react more slowly than sponge-base 7 to 8 pct Cr alloys. Grain Boundary Allotriomorphs: Crystals of this morphology nucleate at and grow preferentially and more or less smoothly along the matrix grain boundaries.5-7 Allotriomorphs are the first morphology to precipitate at most grain boundaries at reaction temperatures from 725°C, the highest temperature studied, at least through 575°C. Fig. 2 Shows typical allotriomorphs, formed during an early stage of transformation at 725°C. Grain boundary allotriomorphs are not the predc=iaant morphology at late reaction times at any temperature studied. However; from 725" through

Jan 1, 1958

By J. S. Aronofsky

The first step in a quantitative analysis ot the mechanism of oil displacement by water in a fractured reservoir is usually conceded to be the solution of the differential equation describing the saturation distribution of two immiscible fluids flowing in a porous medium, where the capillary pressure is taken into account. In such a system the production mechanism may consist of displacement of oil both by the flow of water due to natural or artificially imposed pressure gradients and by imbibition, which implies a flow of water not due to external pressure gradients. Owing to the presence of the two oil displacement mechanisms, the mathematical model given by the differential equation intended to describe the system may not properly represent the behavior of the physical system. In fact, in the reservoir the rate of water advance may be very slow, and in the case of a fractured reservoir with a great number of large fractures, the pressure difference determining the flow of water through the matrix may be much less than 1 lb/'psi over lengths of a few feet. In such a case, imbi-bition (the exchange between oil in the matrix and water in the fractures resulting from capillary forces) may become, with time. a significant element of the production mechanism. It occurred Lo the authors, however, that without going into a physical analysis of the process of production, it might be possible by means of simple abstract reasoning to throw some light on the variation of recovery with time under conditions occurring in a highly fractured oil reservoir with rising water table. The object of this paper is to present both the reasoning and its application to a reservoir of the highly fractured type. Specifically, the analysis given here was undertaken to try to explain the increase of recovery (as defined later) with time as observed in this reservoir, without having to assume unlikely variations in the reservoir parameters with depth. This attempt has been successful as will become clear upon comparison of the computed recoveries with the actual field data. ABSTRACT MODEL Let us consider a small volume. of porous matrix saturated with oil at time, t = 0. Let the process of oil displacement by water start at time, t = t,,. At some time, t, the process will have terminated. Then a volume of oil equal to or smaller than the original oil contained in the matrix will have been produced. The first basic assumption that describes the model and guides the forthcoming reasoning is that the oil production from the small volume. dv, is a continuous monotonic function of time and that it converges to a finite limit. Such an assumption is not inconsistent with the results of laboratory waterflood tests as well as with results of imbibition tests where this is, in fact, observed. The second basic assumption is that none of the properties which determine the rate of convergence change sufficiently during the process to affect this rate or the limit. Let it be assumed that the form of the function of time relative to production from the matrix volume. dv, is given by where V,(t) is the volume of oil produced up to that time t. R is the limit toward which the recovery converges, A is a constant giving the rate of convergence, and V,(t) is the volume of oil originally in place in the volume, dv. It should be noted that recovery at time I will be understood here to he It follows that r. tends to R as t tends to infinity. CONSTRUCTION OF RESERVOIR FROM ABSTRACT MODEL Let the reservoir consist of a series of identical blocks of porous matrix stacked vertically and separated by fractures. Let each of these blocks satisfy the conditions of our abstract model. These conditions are: (1) that recovery is a continuous mono-tonic function of time converging to finite limit, and (2) none of the properties that determine the rate of convergence change sufficiently to affect the rate or the limit. Let water be rising in fractures so that oil production from any part of the block starts when the water comes in conLact with it. TOTAL RECOVERY FROM THE RESERVOIR COMPARED TO RECOVERY FROM A SINGLE MODEL ELEMENT As stipulated in Eq. 1, in the case of the abstract model,

By G. Derge, Ling Yang, John Henderson

Self-diffusion coefficients of aluminum have been measured by the capillary reservoir technique in liquids of the CaO-SiO2-Al2O3 system containirg equimolar portions of CaO and SiO2, in the temperature range 1400o to 1520oC. For the melt containing 6.0 mole pct Al2O3 the results can be expressed by the equation D = [(4.3 * 0.3) x 104] exp [(-85,000 * 17,500)/RT]cm~sec-'; for the melt containing 12.5 mole pct Al2O3, by the equation D = (5.4 i 0.2) exp [(-60,000 * 10,00O)/RT] cm2sec-: A concept of the constitution of these melts has been developed which proposes that the ratios O/(Si +Al) and Al2 O3/CaO determine the dominant species present. In recent years considerable work has been done on the system CaO-SiO2-A12O3 with a view to elucidating the structure of liquids of this system. Conductivity,' electromotive force, 3 density,4 and activity5 measurements have all contributed to an understanding of the problem, but as yet there is no entirely satisfactory theory that can account for all the observed experimental results. In principle, measurements of self-diffusion coefficients should give further information which is not obtainable in other ways. Self-diffusion coefficients for calcium, silicon,6 and oxygen7 have been measured. The present investigation extends the series of self-diffusion coefficient measurements to include aluminum and develops a concept of constitution for liquids of this system which is compatible with all the observed experimental results. EXPERIMENTAL The technique used in the measurement of the self-diffusion coefficient of aluminum was the capillary-reservoir method,8 A126 being incorporated in the melt contained in the capillary and inactive aluminum in the reservoir melt. This method was chosen because it minimizes convection currents' in the diffusion zone. It has the further advantage that the boundary conditions are such that a slight modifica- tion of Anderson and saddington's8 solution of Fick's Law yields an equation which requires measurements only of the length and the initial and final average specific activities of the solidified melt within the capillary. where t is the diffusion time, Co is the average specific activity of the melt contained in the capillary at t = O, C is the average specific activity of the melt contained in the capillary at t = t, 1is the length of the capillary, and D is the self-diffusion coefficient. The equation is of somewhat different form than those previously applied to high temperature diffusion studies because the specific activity of the melt in the reservoir was negligible both before and after diffusion. The diffusion apparatus is shown schematically in Fig. 1. It consisted of a silicon carbide resistance furnace containing the inactive melt in a graphite crucible, internal dimensions 7/8 by 4 in., enclosed in a 1 1/4- by 1 1/2- by 30-in. McDanel tube. A 3/8-in. McDanel thermocouple sheath to which graphite radiation shields and a graphite protection tube were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube the capillaries could be lowered into or raised out of the melt. Temperature was measured with a Pt-Pt 13 pct Rh thermocouple which was calibrated periodically against a standard couple. The furnace temperature was controlled to ± 5°C through the thermocouple immersed in the melt. Temperature variation over the depth of the melt was less than ± 3°C. The inactive melts were prepared from pure native quartz, assaying better than 99.9 pct SiO2, A.R. grade A12O3 and A.R. grade CaCO,. The same quartz and CaCO3 were used in preparing the active melts, the

Jan 1, 1962

By Jim D. Mote, Eugenia M. Howard, Willis L. Barmore, John E. Dorn

The effect of stress and temperature on the creep rate of Ag-33 at. pct A1 and Ag-33 at. pct Al-1 at. pct Zn for prismatic slip was determined over a range of temperatures from 440º to 700°K. The alloys exhibited a brief initial inverted transient creep over which the creep rate increased slightly to a steady-state value which depended only on the stress and temperature, regardless of the previous strain history. The steady-state creep rates were found to be given by: where the activation energy is independent of the stress and strain and agrees fairly well with that estimated for diffusion. The observed creep behavior was shown to be in qualitative agreement with a model based on the stress-induced local disordering in the vicinity of a dislocation. OVER the past fifteen years, considerable progress has been made in correlating the experimen-entally observed plastic behavior of pure metals over each temperature range with one or more of a series of theoretical strain-rate controlling dislocation mechanisms. Despite the current interest in the plastic behavior of intermediate phases and inter metallic compounds, however, very little has been done in identifying the operative dislocation mechanisms in these materials. It is anticipated that the plastic behavior of intermediate phases can be rationalized in terms of the same dislocation mechanisms that are appropriate to pure metals and a solid solutions, provided the additional complexities arising from crystal structure, bonding, long-range order, short-range order, and defect lattices are taken into account. As part of a more extensive investigation on the plastic behavior of intermediate phases, Mote, Tanaka, and Dorn1 recently reported on the effect of temperature on the yield strength for prismatic slip in the hexagonal Ag-33 at. pct A1 intermediate phase as recorded in Fig. 1: Over Region I the deformation was observed to take place as a result of the thermally-activated Peierls mechanism, and over Region II the athermal disordering mechanism applied. The experimental data at that time, however, were not sufficiently extensive to identify the thermally activated mechanisms operative over Region III. It is the purpose of this investigation to attempt to identify the mechanisms that are operative over this high-temperature region. It will be shown that the same mechanism operates all over Region Ill, although the activation energy for this mechanism is in good agreement with that for diffusion, the process cannot be attributed either to the motion of jogged screw dislocations or the climb of edge dislocations. The results, however, are in good qualitative agreement with stress-induced disordering localized at dislocations. EXPERIMENTAL PROCEDURE The alloys studied in this investigation were prepared from silver, aluminum, and zinc (each of purity greater than 99.995 pet) by induction melting under an argon atmosphere and chill casting in a copper mold. Rectangular bar single crystal specimens (1/4 by 1/8 in. in cross-sect ion) of Ag-33 at. pct Al were grown in vacuum by a modified Bridgman technique. Similar Ag-33 at. pct Zn specimens were produced by an identical technique employing an argon atmosphere. The specimens were so oriented that the angle 90-Xo between the tensile axis and the normal to the prismatic plane and the angle A, between the tensile axis and the slip direction were 45 ± 1 deg. The effect of a change in temperature on the creep rate and a change in stress on the creep rate were determined over the temperature range

Jan 1, 1963

By Carl Benedicks

IT is well known by every one who has had to deal with boiler tubes that these are often seriously affected by a sort of corrosion, occurring as a local pitting, that frequently causes a perforation of the tube in a rather short time. The characteristic appearance of this corrosion is shown in Fig. 1. A very similar corrosion occurs in condenser tubes (Fig. 2).1 A study of the microstructure or local chemical composition of the metal (iron; 70 :30 brass) fails to reveal any cause for this pitting. Of course one might possibly assume the starting point-to be some oxide particle, causing an electrolytic local action, but this in no way explains the continued corrosion, progressing even when the assumed oxide particle must have disappeared. By the excellent work done by the Corrosion Research Committee of the Institute of Metals, and communicated, in October, 1923, to the Institution of Engineers and Shipbuilders in Newcastle-on-tyne, stress was laid on the fact that a content of entangled air has a very obnoxious effect. In the following correspondence, Sir George Goodwin stated that "engineers have, for a long time past, regarded air as the big enemy to be fought against in all questions of corrosion"2 and Kenneth Fraser pointed out that the most vital point is "the avoidance or removal of possibly the chief cause of present day corrosion, i. e. entrapped air and gases brought out of solution."' In their reply, however, the authors state that they had "never for a moment believed that entangled air was responsible for the beginnings of corrosion, and express the opinion that the gradual liberation of air could not account for localized corrosion."4 On consulting the many textbooks on corrosion, as that

Jan 4, 1925

By W. P. Z. German

Some attention should be given to definitions. The term "unit operation " may have at least two meanings. One meaning is the merging of titles and the development and operation of the unitized area, as if it were one tract of land held under a single oil and gas lease, according to a definite program intended to accomplish a maximum recovery from the pool as a whole at a minimum of cost. It is incomplete when the royalty owners do not also merge their titles to their oil and gas rights in the area, and is complete when they do. The other meaning is not accompanied by any merger of titles, but the development and operation of the area is in accordance, as nearly as reasonably practicable, with such a program. This second conception may be nothing more than a cooperative development and operation plan, but in this paper it is regarded as more than that. If there cannot be unit operation without a merger of titles, it would seem that the state cannot require unit operation, for it cannot require a merging of titles; but if it may consist in requiring each and all of the leaseholders to develop and operate or to submit to a development and operation according to some such common plan as is referred to above without at the same time requiring a merger of titles, it would seem that unit operation may be required by the state. Whether the states have this power is the subject to be herein considered. If the state can so bind the several lessees, it also can so bind the several lessors. The writer does not know what would be an ideal plan for the development and operation of a pool; but it takes into account the fact that the accumulation of gas and oil is not uniform throughout the formation; that often free gas, highly compressed, occupies the upper portions of the reservoir, the oil with compressed gas in solution coming next in order; that at places oil is not overlain by free gas, and sometimes there are peaks where free gas is not immediately underlain by any oil; and the fact that these substances are held under a uniformly distributed pressure, generally referred to as "rock pressure." It also recognizes that the most efficient utilization of this naturally existing reservoir pressure in the recovery of the oil requires that there be no operation of wells completed into areas where gas only has accumulated, for this diminishes the

Jan 1, 1931

By N. Standish

Heat transfer coefficients have been measured in beds of various packings irrigated with mercury and molten fusible alloy countercurrent to hot gases. The measured coefficients for both systems were found to increase with gas velocities and liquid rates. Correlations were determined which show this dependence and also indicate that heat transfer in these systems is influenced by the liquid flow characteristics and the thermal conductivity of the gas and the solid packings. A heat transfer model has beer2 proposed which explains the various features of the experimental results. On the basis of this study, which gives an insight into the heat exchange in the melting zone of the blast furnace, it was concluded that by comparison with the furnace stack heat transfer coefficients are about 1.5 times higher in the melting zone. EACH year large tonnages of metal are produced in operations which, in part, involve liquid metal irrigation of "packings" countercurrent to hot gases. The melting zone in blast furnaces and in cupolas is a good example of packings irrigated with a liquid melt countercurrent to gases. In all instances of this kind large amounts of heat are exchanged and it is desirable to have some knowledge of heat transfer phenomena involved in these systems. So far the most common method of analyzing furnace efficiencies, fuel requirements, and the general thermal state of the furnace has been through the use of heat balances. As heat balances are essentially statements of the first law of thermodynamics they give no real indication of the factors which govern heat transfer between phases in the various zones of blast furnaces. Hence, rational improvement in production efficiency and the development of theoretical models is only possible if the heat transfer characteristics are known at every stage of the process and related to the important variables involved. This has been generally recognized for some time but it was only recently that Kitaev et al.' have produced a comprehensive treatment of heat transfer in solid-gas countercurrent systems such as the blast furnace stack and the packed bed regenerator. Using their treatment it is now possible to predict the effect of particle size, thermal conductivity, bed porosity, and the flow rates of both the gas and the solid material on the heat transfer in the blast furnace stack. However, the stack of a blast furnace is only one part of an integral unit for which the heat transfer analysis cannot be complete without also considering the heat exchange in the melting zone. The complexity of heat transfer processes in this region of the furnace has so far escaped quantitative description. Yet, the melting zone accounts for a greater amount of heat exchange than all the other zones of the furnace put together. Moreover, if the reduction of oxides in the melting zone proceeds in part in the liquid state the importance of heat transfer on furnace productivity and on the metal and slag temperatures is obvious. THEORY Heat transfer for two-phase flow in packed beds is a complex problem involving a number of heat exchange paths for which interphase areas are not known with any degree of certainty. Analytical solution is, therefore, difficult. This difficulty is emphasized by noting that Rabinovich~ and Luck have only recently solved the steady-state heat transfer for simplified two-phase heat exchangers of known area. However, useful progress can be made for the system considered by making a not unreasonable assumption that the usual heat transfer considerations apply and restricting treatment to the steady state. For these conditions the rate of heat transfer dq in a height dz of a packed bed of unit area is: dq = UaATdz [I.] Integration of Eq. [I] then gives the total heat transferred: assuming both U, the overall heat transfer coefficient, and a, the interphase area, to be independent of bed height. Since a, in these systems, is unknown it is convenient to combine this term with U. The group U, then represents the overall heat transfer coefficient on a volumetric basis. If AT is linear with q, then for a bed of unit volume Eq. [Z] can be integrated to give: is the log mean of terminal temperature differences. From Eq. [3] U, can be readily calculated as q and {AT)im are experimentally obtained quantities, but a difficulty arises in interpreting its meaning. Two approaches are possible depending on whether the effect of packing in the transfer of heat is neglected or not. If the packing is thermally decoupled then the resistance concept gives the relationship: which states that the overall resistance is the sum of the gas phase and the liquid phase resistances (assuming areas are equal throughout). Because the resistance to heat transfer in liquid metals is negligible by comparison with that of the gas,4 Eq. [4] can be simplified, i.e.:

Jan 1, 1969