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By E. W. Dewing

The solubility of A14C3 in cryolite melts has been determined by holding the melt with aluminum in a graphite crucible for 4 hr at temperature, quenching the crucible in water, and analyzing the frozen salt by CH4 evolution. The solubility is given by log(wt % Al4C3) = 1.298 -1.l74 (wt ratio NaF/AlF3) independent of temperature in the range 985" to 1080°C. Additions ofA1203, .NaCl, CaF2, or LiF up to 10 wt pct do not affect the solubility, provided that LiF and CaF2 are replaced by equivalent NaFin calculating the ratio. The variation with ratio can be accounted for quantitatively on the hypothesis that the Mechanism of solution is Al4C3 + 2AIF3 = 3Al2CF2 since the solubility varies as (aAIF3) 2/3; Mechanisms involving C", C2- , AlC- , A12C2+, and Al2CF+are re-jected. At ratios above 1.5 truces of c;- are also present. It was noticed some years ago in this laboratory that carbon specimens made cathodic in a cryolite bath decrease in diameter over a period of time.' It was also found that cryolite which had been melted with aluminum in a graphite crucible was sometimes yellow, and that A14C3 could be seen intimately embedded in the cryolite crystals. CH, could be recovered by acid attack. There was thus reason to believe that A14C3 had a genuine solubility in molten cryolite, and the object of this work was to measure it. EXPERIMENTAL AND RESULTS A graphite crucible, 2 in. ID and 2.5 in. deep with a close-fitting lid, contained about 150 g of cryolite (plus additives) and about 20 g of 99.99 pct pure Al. It was placed in a vertical Inconel furnace tube, covered with refractory brick to provide thermal insulation, and the top of the tube was roughly sealed with disks of asbestos paper. An alumina tube led argon down to the level of the top of the crucible to expel air, and an alumina sheath with a Pt-10 pct Rh ther-mocouple inside was positioned between the crucible and the wall of the Inconel tube. The tube was heated in an electrical resistance furnace for the desired length of time; the refractory bricks were then removed, and the crucible was lifted out with tongs and quenched in water. After such a crucible was broken open it could be seen that its inner surface was yellow owing to the presence of A1,C3, and sometimes needle-like crystals could be observed (at X75 magnification) growing out into the nielt. It was concluded that Al,C, had been present as a separate phase when the crucible was at tenlperature and that the melt had been saturated: in

Jan 1, 1970

By S. F. Ravitz

In his excellent book on the Principles of Flotation, Warkl makes the following significant statement concerning the theory of flotation: Two questions of first-rate importance must be considered . . . First, it must be decided whether the sulfide minerals require a collector in order that they may float, or whether as has been claimed, they possess an inherent float-ability and need no collector. Second, it must be decided whether the xanthate type of collector can react with or be adsorbed by the unchanged sulfide minerals themselves, or whether, as many claim, reaction with the collector is dependent upon initial oxidation of the mineral surface. In the theory of flotation there are no two questions of greater importance than these. Ravitz and Porter2 presented evidence that galena can be floated without a collector, and even without any reagent, provided oxidation products are thoroughly removed from its surface. They found also that thoroughly cleaned galena floated faster when xanthate was used than when a frother alone or no reagent was used, and that, without a collector, the recovery decreased gradually upon exposure of the mineral to air. Their work, however, has met with considerable criticism.l(127).3-6 This paper is presented to answer the objections that have been raised, and to present additional data that confirin their results. The apparatus used to provide oxygen-free conditions for flotation has been described in detail by Ravitz and Porter. An atmosphere of purified nitrogen was maintained within the apparatus; all water and solutions used were freed of dissolved air, and could be transferred where desired by the use of nitrogen Pressure; nitrogen was used as the gaseous medium for flotation. The flotation cell was essentially a glass cylinder 15 cm. long and 4.6 cm. in diameter. Near the bottom was sealed a fritted glass filter, which broke up the gas into small bubbles, and 6 cm. above this filter was a side arm through which the froth overflowed. The pulp was agitated by a glass impeller, which entered the cell through a mercury seal. For each test 17 grams of galena and 75 ml. of water were placed in the cell, after which the speed of the impeller and the rate of gas flow were adjusted. Water was added gradually during the test to keep the froth level at the proper height. The mineral was prepared and cleaned in the following manner. Exceptionally Pure galena was crushed by hand on a clean bucking board, screened to —I50+ 200 mesh, and deslimed on a 200-mesh sieve with a fine spray of water. It was then boiled on a hot plate for a number of hours with several changes of the desired cleaning solution, after which both the solution and the mineral were placed in the "mineral flask" of the apparatus. The cleaning solution was drained off, and the mineral was boiled with oxygen-free water

Jan 1, 1943

By S. F. Ravitz

In his excellent book on the Principles of Flotation, Warkl makes the following significant statement concerning the theory of flotation: Two questions of first-rate importance must be considered . . . First, it must be decided whether the sulfide minerals require a collector in order that they may float, or whether as has been claimed, they possess an inherent float-ability and need no collector. Second, it must be decided whether the xanthate type of collector can react with or be adsorbed by the unchanged sulfide minerals themselves, or whether, as many claim, reaction with the collector is dependent upon initial oxidation of the mineral surface. In the theory of flotation there are no two questions of greater importance than these. Ravitz and Porter2 presented evidence that galena can be floated without a collector, and even without any reagent, provided oxidation products are thoroughly removed from its surface. They found also that thoroughly cleaned galena floated faster when xanthate was used than when a frother alone or no reagent was used, and that, without a collector, the recovery decreased gradually upon exposure of the mineral to air. Their work, however, has met with considerable criticism.l(127).3-6 This paper is presented to answer the objections that have been raised, and to present additional data that confirin their results. The apparatus used to provide oxygen-free conditions for flotation has been described in detail by Ravitz and Porter. An atmosphere of purified nitrogen was maintained within the apparatus; all water and solutions used were freed of dissolved air, and could be transferred where desired by the use of nitrogen Pressure; nitrogen was used as the gaseous medium for flotation. The flotation cell was essentially a glass cylinder 15 cm. long and 4.6 cm. in diameter. Near the bottom was sealed a fritted glass filter, which broke up the gas into small bubbles, and 6 cm. above this filter was a side arm through which the froth overflowed. The pulp was agitated by a glass impeller, which entered the cell through a mercury seal. For each test 17 grams of galena and 75 ml. of water were placed in the cell, after which the speed of the impeller and the rate of gas flow were adjusted. Water was added gradually during the test to keep the froth level at the proper height. The mineral was prepared and cleaned in the following manner. Exceptionally Pure galena was crushed by hand on a clean bucking board, screened to —I50+ 200 mesh, and deslimed on a 200-mesh sieve with a fine spray of water. It was then boiled on a hot plate for a number of hours with several changes of the desired cleaning solution, after which both the solution and the mineral were placed in the "mineral flask" of the apparatus. The cleaning solution was drained off, and the mineral was boiled with oxygen-free water

Jan 1, 1943

By AIME AIME

WHEN the present Chairman of the Coal Division, A.I.M.E. applied for membership in the Institute 28 years ago one of his endorsers was Howard N. Eavenson, with whom he has now been associated as a partner in a Pittsburgh consulting coal - mining engineering firm for 22 years. Back of that association was some ten years of operating work in Kentucky. Mr. Alford was born in Philadelphia on Dec. 11, 1887, and was educated in Quaker schools, graduating from Swarthmore with an A.B. in 1909, later receiving a B.S. and an E.M. from the University of Pittsburgh. In the summers of 1907 and 1908 he had his first taste of coal mining as a chainman for the U. S. Coal and Coke Co. in Gary, W. Va. Upon graduating in 1909 he got a job on the by-product coke ovens of the Illinois Steel Co. at Joliet, Ill., but a year later went to Kentucky as superintendent of the Shamrock mine of the St. Bernard Mining Co., by which company he was employed for the next ten years. Successively he was assistant chief engineer, chief engineer, and assistant to the president. His duties were varied, including all the engineering duties commonly associated with coal mining, both underground and on the surface, construction of washing plants, prospecting, reports on new properties, power plants, safety work, and labor relations.

Jan 1, 1942

DR. PeRsifor Frazer, Philadelphia, Pa. (communication to the Secretary):* Mr. Campbell's very interesting contribution, after complimentary mention, finally decides against the acceptance of the classification proposed by me in a paper bearing the same title and read at the Wilkes-Barre meeting, May, 1877.2 That paper was written primarily for the Second Geological

Jan 1, 1906

By Tilden Cummings

The extractive mineral industries share a number of common characteristics and basic problems which are completely different from those associated with manufacturing and mercantile operations. These industries now supply about 95% of the inanimate energy consumed in this country, and share with agriculture in providing virtually all of our basic raw materials. Mineral producers, like farmers, are subject to the economic hazards of fluctuating markets and prices. Unlike farmers, however, they cannot renew the productivity of the earth, but must seek continually for new sources of supply. The necessity for exploration and development of new reserves, to replace those used up by production, introduces additional factors of economic risk. These operations require the expenditure of large amounts of capital, often well in advance of any assurance of profitability. Commercial banks that understand these special problems can provide a variety of constructive financial services to the mineral industries. The history of cooperation between banks and mining enterprises has yet to be written, but there is every indication that it would encompass a period of hundreds of years. Records refer to depository and lending services by the early European private bankers involving precious metals and jewels. Many of the exploratory voyages to the Far East and the New World were organized with the financial backing of wealthy syndicates, some of which also provided banking services, in the hope of finding new sources of gold and other precious minerals. In the United States many large banks are closely identified with the development of some of the larger mineral deposits such as the Mesabi Range and the gold fields of California.

Jan 5, 1965

By B. Trafton, H. L. Hartman

An earlier paper1 introduced a rapid solution for mine ventilation network problems, employing the digital computer. In this paper, refinements and additions to the computer program which expand its scope of application and a solution to a ventilation network having a coal-mine configuration are presented. The revised program-written in FORTRAN for the IBM 7074 computer in Penn State's Computation Center-is applicable to any mine ventilation network employing natural splitting and having its fan located externally. It accomplishes the following: 1) Distributes an assumed total quantity of air flow among all airways of the network, performing iterations until an acceptable level of error is attained and the flow in each airway is known. 2) Computes the pressure drop (head loss) in all airways and the overall network and mine head losses. 3) Determines the operating point for the mine and a given fan, adjusting all air flows and head losses to the actual values. The basis of analysis used is the Hardy Cross method of successive approximation for solution of any fluid network, explained in detail in the earlier article. In brief, corrections to assumed air flows are computed for all the loops of a network; following distribution to the airways of each loop, the process is repeated until acceptable accuracy is attained. When a hand or desk-calculator solution is used, there is advantage to close approximation of the actual flows in the original assumption of air-flow distribution in the network. Since publication of the previous paper, in which assumption of initial quantities was also necessary in the computer solution, the program has been modified to make the first distribution itself, assigning the total quantity to one specified path in a split and then proceeding to correct the flows. The number of iterations required for a high-accuracy solution is little affected, at least in networks of few loops, 10 to 15 being sufficient to reduce the error to 1 pct or less. The principal limitation of the original program was that it contained no provision for handling a fan. Further, it did not determine the overall head loss in the network and was not designed for multiple parallel openings, such as occur in coal mines. The revised program was written to overcome these disadvantages and also to print out the adjusted flows for all airways, corrected for the system operating point. At the present time, the program can handle only an external fan. The procedure employed in solving a ventilation network is now as follows: 1) Input data consisting of airway characteristics and loop designation along with assumed direction of flow, for each branch of the network and any trunk airways, are fed into the computer. 2) Employing the resistance relationship, where R is resistance, K is friction factor, P is perimeter, L is length, A is area, and n is number of airways (where multiple intakes and returns are employed); values are computed for all airways. 3) An arbitrary, continuous route of flow through the circuit—from beginning to end—is selected and the path identified by airway numbers and read in. 4) Based on a total assumed quantity of flow Q (usually 100,000 cfm.) the computer employs the procedure described in the previous article in distributing quantities of flow among all the airways until a satisfactory level of accuracy has been attained (in the current program, the machine is turned off when the cumulative corrective error in cfm, is reduced to five times the number of airways). 5) Airway head losses H are calculated by the relation H = R Q2 and cumulated along the original designated flow route to find the overall head loss for the network. Trunk airways are then included to obtain the mine head.

Jan 1, 1964

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett' have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By Frederick Bacorn

THE paper of Reno H.. Sales on Ore Deposits at Butte, Mont.,' is a careful and painstaking work, an important contribution to the literature of the subject. As is almost inevitable in a work of such magnitude, a few misstatements occur; and some of these I shall endeavor to point out. Mr. Sales has also fallen into error, as I think, in the application of his theory of ore deposition; and while the modification which I venture to suggest is a minor one geologically, it is of great economic importance. I refer to Mr. Sales's idea of an outward migration of mineralizing solutions from a supposed central copper zone. In order that I may make myself plain, I must first epitomize the theory as a whole, which I understand to be this: All of the Butte ore deposits (save those along the Continental fault, not herein considered) are derived from solutions of magmatic origin, which, at the beginning of their ascent from a great depth, were, acid in reaction, hot, and were carriers of copper, zinc, manganese and other metals. As they departed from their point of origin they lost heat, and, because of reactions with the wall rock, became more and more alkaline. The metal deposited from these solutions in their hot condition was principally copper; and, as they cooled, they deposited less and less copper and more and more manganese and zinc, until the copper practically disappeared. With this theory in general I have no fault to find, nor have I, it must be stated, the qualifications necessary to enable me to pass upon it critically; but it seems to me to be reasonable and probable, and is one which I am quite willing to accept.

Jan 8, 1914

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By J. C. Todd

The volume of air needed to move the combustion wave through each acre-foot of the reservoir is a very important quantity for engineering economic analyses. A new method, which involves backflowing the injection well, has been developed for determining the air requirement .for the forward combustion thermal pilot in the Delaware-Childers field. The method depends on measurement of the total volume of air injected and measurement of the pore volume in the zone swept out by the combustion front. The basic premise of the method is that the pore volume of the swept zone contains air, while the formation around this zone contains flue gas, oil and water. The pore volume of the swept zone is determined by blowing down the pilot section of the formation through the injection well after the pilot is shut down. Oxygen balance is used to differentiate between air from the swept zone and flue gas from the surrounding formation. Data indicate that air'is produced from the swept zone by relatively efficient miscible displacement by the flue gas. The pore volume occupied by the air in the swept zone is determined by simple PVT relationships. The average temperature of the swept zone is calculated by heat balance from the total amount of heat generated during the pilot and losses to the surrounding formation. The new method was applied successfully at the conclusion of the pilot in the Delaware-Childers field; the air required for the reservoir conditions involved was calculated to be 19.2 MMscf/acre-ft of reservoir swept. INTRODUCTION One of the most important pieces of information to be found from a forward combustion pilot is the air requirement; that is, the volume of air needed to move the combustion wave through each acre-foot of the reservoir. Compression costs per barrel of oil recovered, which are a direct function of the air requirement, are a large portion of the expenses incurred in the thermal recovery process. Thus, the profitability of thermal recovery depends largely on the air requirement, which is a measure of the amount of fuel deposited and burned in the thermal recovery process. Several attempts have been made to correlate crude oil properties with fuel deposition and, hence, air requirement.l*2 Other attempts have been made by our laboratory to find the air requirement by material balance, gravity survey, pressure transient analysis,3 magnetic survey and the poten-tiometric model. Better methods are needed to predict more accurately the economics of fieldwide application of the process. Another method of finding the air requirement consists of operating a pilot thermal project for several years. This is followed by an extensive coring program to define the volume swept by the combustion wave. The air requirement is found from the total injected air divided by the volume of the swept region found from the coring operation. This method is costly; an adequate coring program usually costs several hundred thousand dollars. A thermal pilot was operated in a watered-out portion of the Delaware-Childers field, Bartlesville sand, from Nov., 1960, until May 3, 1965. One of the primary purposes of this pilot operation was to determine the air requirement for economic calculations which determine the advisability of expanding the project to the entire 128,000 acre-ft field. Barnes4 has described the result of this pilot operation,, including calculation of the air requirement from limited coring data. The value obtained, as calculated, was 15.8 MMscf/acre-ft. One purpose of this report is to describe a new method of finding the air requirement from a thermal pilot operation. A second purpose is to describe the application of this method to the Delaware-Childers thermal pilot. THEORY AND DESCRIPTION OF THE METHOD The combustion zone in the forward combustion process is propagated from injection w producing

Jan 1, 1970

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-

By P. F. Gnirk, J. B. Cheatham

The results of combined analytical and experimental studies involving simulated multiple bit-tooth penetration into mck are incorporated into a drilling rate equation for roller-cone bits assuming rather idealized downhole conditions. In particular, it is assumed that the rock behaves statically in a ductile fashion during bit-tooth penetration and that the rock chips are instantaneously removed from the bottom of the drill hole. The general analysis demonstrates an application of plasticity theory for the rock/bit-tooth interaction to the formulation of an upper limit on rotary drilling rate. INTRODUCTION Extensive experimentation involving single and indexed bit-tooth penetration into rock in a confining pressure environment has demonstrated that the chip formation process is of a ductile, or pseudoplastic, nature at sufficiently low differential pressures so as to be of interest in rotary drilling. Coincident with the experimentation, analytical consideration has been given to the theoretical problems of single and indexed bit-tooth penetration into rock. In general, the analyses have assumed that the rock behaves statically in a rigid-plastic fashion and obeys the Mohr-Coulomb yield criterion. The quantitative comparison between experimental and calculated values of bit-tooth load required for chip formation has been remarkably good for a variety of rocks commonly encountered in drilling and at simulated differential pressures as low as 500 to 1,000 psi. Results obtained recently for indexed bit-tooth penetration indicate that the work (or energy) required to produce a unit volume of rock chip can be minimized by a proper combination of bit-tooth spacing and bit-tooth load for a given rock type and differential pressure. By utilizing this information, it is possible to formulate a drilling rate equation, at least in a preliminary fashion, for a roller-cone bit performing under rather idealized downhole conditions. In particular, through the use of characteristic dimensionless quantities pertinent to a roller-cone bit and to indexed bit-tooth penetration, interrelationships among bit weight, rotary speed, rotary power, bit diameter, rock strength and bit-tooth shape and spacing can be explicitly expressed. In the formulation of the equations, however, it is assumed that the rock chips are instantaneously removed from the bottom of the drill hole and- that the rock behaves in a ductile manner during bit-tooth penetration. In addition, the effects of bit-tooth load application and penetration by a yawed tooth at an oblique angle are neglected. Although the analysis is presented in the light of some rather restrictive conditions, it does demonstrate a method of applying fundamental rock/bit-tooth interaction data, obtained by combining the results of analysis and experiment to the formulation of a drilling rate equation for rotary drilling. JNDEXED BIT-TOOTH/ROCK INTERACTION PREVIOUS RESULTS The mechanics of bit-tooth/rock interaction under simulated conditions of borehole environment have been extensively described in a number of papers.l-ll In particular, the effects of differential pressure, mechanical properties of rock, pore fluid, bit-tooth shape and spacing, rate of bit-tooth load application and dynamic filtration below the bit-tooth have been investigated experimentally. From a sequence of experiments.1-4 it was demonstrated that, for dry rock at atmospheric pore pressure, the mode of chip formation exhibits a transition, with increasing confining pressure, from predominantly brittle to predominantly ductile. This transition

Jan 1, 1970

By R. F. Rolsten

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

Jan 1, 1960

By M. Garfinkle, W. D. Klopp, W. R. Witzke

The tensile properties of binary W-Re alloys containing up to 33 at. pct Re were determined at temperatures from 78" to 3630°F. Elongations as high as 260 pct were observed in electron-beam-melted tungsten containing 23 at. pct Re when tensile-tested at 3630°F after a 1-hr anneal at 3090°F. All alloys tested under these conditions with rhenium contents between 20 and 28 at. pct exhibited elongations of at least 200 pct. These alloys also showed enhanced grain growth rates. The values of strain-rate sensitivity ranged between 0.2 and 0.3 for the alloys exhibiting high elongations. Houlezler, for swaged alloys tested just above the re-crystallization temperature, strain-rate sensitivities as high as 0.8 were observed. The high-temperature strengths of the high-rhenium-content alloys were also less than those of alloys with intermediate rhenium contents. ALLOYING with rhenium has two distinct effects on the mechanical properties of tungsten. One effect occurs in dilute solid solutions and is most clearly seen in the lowering of the hardness and of the ductile-brittle transition temperature at about 5 at. pct Re.1-3 The second effect occurs in the concentrated solid solution at about 25 at. pct Re, and is characterized by twinning and a larger decrease in the ductile-brittle transition temperature. An aspect of the high-rhenium-content alloy which has received little attention is the higher-than-usual tensile ductility at 3500°F.3 Anomalous high ductility has been observed in several other alloy systems. usually associated with a phase transformation or a solid-solubility limit.4'5 The phenomenon is now commonly termed superplasticity. High-strain-rate sensitivities6 and grain boundary sliding7 have been reported for materials that undergo superplastic deformation. Also, it has been found that superplastic materials usually have a very fine grain structure (less than 10 pm).8 and it has been proposedg that such a structure alone is sufficient for superplasticity. The purpose of the present study was to further characterize the high-temperature tensile properties of W-Re alloys to determine the conditions under which they might be superplastic. Tensile and selected strain-rate sensitivity tests were conducted on alloys containing 0 to 33.3 at. pct Re at temperatures from 78" to 3630°F. Grain-growth rates were also determined on most alloys at 3630°F. Fig. 1 indicates the compositions evaluated and their locations relative to the solvus line in the tungsten-rich end of the W-Re phase diagram. Twelve binary W-Re alloys containing up to 33.3 at pct Re were double electron-beam-melted and subsequently fabricated to 0.3-in. rod by extrusion and swaging. The starting materials were commercial powders of tungsten and rhenium with impurity levels as listed in Table I. The various blended W-Re compositions were hydrostatically pressed at 70 ksi. The pressed bars were drip-melted into 1.5-in.-diam ingots and then remelted into 2-in.-diam ingots at a chamber pressure of 10~5 torr. The ingots were canned in molybdenum and extruded to round bar at a reduction ratio of 6:l. The alloy extrusions were swaged to about an 80 pct reduction at 2100" to 2900°F. Buttonhead tensile specimens with a reduced section diameter of 0.16 in. and a gage length of 1.0 in. were centerless-ground from the swaged bars

Jan 1, 1970

By R. D. Nelson, F. E. Bowman

Evidence has been found for a (010)a?(111)B[102]a /,11[341]/B crystallographic relationship between the monoclinic a and B phases of plutonium during the a?B transformation. The results of an X-ray diffraction study, where [010] fiber textured a samples were used in the absence of suitable single crystals indicate that the (OIO)a planes become (111)B planes upon transformation under near-equilibrium conditions. The transformation strain along the fiber axis, which was the [010] direction, was measured dila-tomekically; the measured 8.5 pct expansion compares favorably with the 8.44 pct expansion in the in-terplanar spacing represented by the (010)a?(111)B relationship. From plots of the atom positions in each of the related planes, a correspondence was deduced between the [102]a, direction and the [341]B direction. Further analysis of the two lattice structures in the light of this relationship revealed a rotation about the [102] direction of 1 deg 43 min and a slight shearing in this same direction of about 30 min. THIS paper discusses the (B crystal structure of plutonium and the orientation relationship existing between the monoclinic a and B phases during the a?ß transformation. The kinetics of the a?ß and (3 — a transformations have received extensive consideration, and because of the crystallographic complexity of these phases, the question of the mechanisms by which these transformations occur is especially intriguing. Nelson and Shyne1 evaluated the existing experimental evidence and concluded, from the indirect evidence available, that both the ß ? a and a ? ß transformations occur by a martensitic process. Their data reveal the anisotropic nature of these transformations which suggests the existence of specific crystallographic relationships between the parent and product phases. In this paper, we are concerned with the confirmation of the existence of such a relationship resulting from the a ? ß transformation and the derivation of the crystallographic details necessary to specify it. EXPERIMENTAL RESULTS X-ray diffraction and dilatometric data were obtained from samples of a plutonium having a [010] fiber texture. These cylindrical specimens, approximately 1 cm in diam, were prepared by transforming the ß phase to a under the influence of a uniaxially applied compressive load.' The [0l0] direction is parallel to the direction of applied stress; it is also perpendicular to the (010) planes. This correspondence between the plane normal and the direction having the same indices is, in the monoclinic a plutonium structure, restricted solely to this (010)[010] combination. Such a specimen was mounted in an evacuated, elevated temperature specimen holder on an X-ray dif-fractometer so that the diffracting surface was perpendicular to the fiber axis. The a diffraction pattern, Fig. 1, taken at about 115ºC, revealed the predominance of the (020) reflection. This monoclinic, P 21/rn space group yields no (0k0) reflections when k is odd. The temperature was raised slowly to 160°C to effect the complete transformation to the phase; then it was lowered to 120°C so that a diffraction pattern of the ß could be obtained near the a = ß equilibrium temperature for direct comparison with the a at the same temperature. The (3 diffraction pattern, Fig. 2, obtained under these conditions showed a (222) reflection relatively much more intense than in the random pattern. The other reflections appearing with sig-

Jan 1, 1970

P. L. Pratt (University of Birmingham, Birmingham, England)—The author has measured the hardening effect of isolated edge and screw dislocation boundaries in a remarkably elegant manner, and he proposes that the detailed structure of the boundary determines its effectiveness as a barrier to slip although "there are still unknown details of the distribution which may be extremely important." On p. 678 the author states "that for a good crystal (one having a yield of about 30 psi) a change in annealing temperature from 300" to 400 °C resulted in a negligible shift in the level of the stress-strain curve." Is this in agreement with the results of the earlier paper by Li, Washburn, and Parker8 in which such a change of temperature produced notable hardening in crystals with a yield of about 30 psi? Or were these earlier crystals, of the same nominal purity, less perfect than those used in this work? The experiment illustrated in Fig. 15, p. 681, shows that the boundary has sharpened after annealing at 400 °C, the temperature at which the hardening effect first becomes apparent. Did the author verify that no sharpening of the boundary occurred at, say, 300 °C where no hardening was found? This would seem to be an important check on the proposed mechanism, especially since zinc of this purity should polygonize at temperatures well below 400 °C within the annealing times used here. There seem to be at least two alternative explanations which could fit these facts: 1—The boundary may sharpen at 300 °C or even lower temperatures but be unable to contribute greatly to the hardening until jogged by thermal vacancies and other impurity atoms after 400 °C anneal. This mechan- ism, discussed in the earlier paper,' is believed to account for the thermal hardening observed by Blank'" in NaCl, as stated elsewhere: and by results from recent experiments which tend to confirm this view. 2—The dislocations in the diffuse boundary may be locked by impurity atoms at 300 °C and thus only sharpen the boundary at 400 °C with the aid of thermal vacancies. In this case it would be difficult to distinguish between the two sources of hardening (sharpening or jogging), using metal of this purity. Jack Washburn (author's reply)—The author wishes to thank Dr. Pratt for his discussion. In connection with his first comment, it should be pointed out that the temperature of testing in the present series of experiments was —196°C, whereas, in the earlier experiments he referred to,' it was 20°C. Therefore, the yield values should not be directly compared. It is likely that the crystals used in the present work were initially more perfect macroscopically than the large shear specimens used previously. The small size of the test section in the kink specimens made it possible to select regions of the large crystals, from which they were acid-cut, that were free of observable small angle boundaries. The sharpening of a microscopically diffuse boundary such as that in Fig. 15 begins in zinc of this purity well below 300°C. However, it is probably not justified to conclude that because a boundary looks sharp under the microscope it has attained the ideal structure. The author agrees with Dr. Pratt that jogging of dislocation lines is one of the structural features of a small angle boundary that should be important in determining its strengthening effect. More detailed information concerning the changes in boundary structure as a

Jan 1, 1956

By C. K. Eilerts, J. D. Ham

Laboratory research has been conducted to evaluate the characteristic effects of condensate saturation on the mobility of gas in typical reservoir rocks. A pump with two pistons provided phases in equilibrium at controlled flow rates and constant liquid-vapor volume ratios. Core samples were tested in a holder that permitted sealing steady-state phases in the pore spaces under flow test pressures for weighing with sufficient precision to give an accurate measure of the attained saturations. Parameters of the study were pressure, apparent velocity, flowing liquid-vapor volume ratio, fluid composition, core material and length-to-diameter ratio. Tests were conducted at 515 and 1,515 psia to determine the effect of pressure on the mobility-saturation relationship. Influence of the apparent velocities 0.30, 0.15 and 0.07 cm/sec and of five liquid-vapor volume ratios from 0.0001 to 0.01 was determined at 515 psia The principal fluid system was nitrogen and and separator liquid from a Gulf Coast condensate, but the effect of a condensate of different viscosity was also determined. The significance of a possible concentration of liquid near the outlet end of the test cores was investigated. Core materials included a consolidated sandstone and a low-permeability limestone. Relative mobility and liquid-vapor volume ratio relationships are concluded to be dependent on pressure, saturation and, to a lesser extent, on velocity. For each porous medium and fluid there is a minimum saturation essential to two-phase flow, and high velocities of flow have only limited effect on saturations in this range. INTRODUCTION It is now recognized that knowledge of the availability of a reservoir gas — the period that gas may be recovered from a reservoir at a given rate — is as important as the estimate of gas in place. When reservoir conditions are such that pressure decline owing to production will result in retrograde condensation, liquid saturation can increase in the structure around the production well in a way that may restrict flow capacity, and hence future availability. l Based on a numerical solution of transient radial flow of single-phase gas-condensate fluids, 2 a program for computing the accumulation of condensate in a reservoir and the effect of this condensate on deliverability has been developed. During this development a need evolved for data that described the influence of pressure, velocity of flow and condensed liquid on mobility as recovery progressed. This paper presents the results of experimental investigation to obtain insight into the mobility relationship at reservoir pressures of gas-condensate fluids. A core holder for flow tests at reservoir pressure was developed to weigh the core and its fluid contents under pressure to determine saturation. A specially constructed pump was used to drive a two-phase fluid through the core until a steady state prevailed. The core was used as a differential device, and properties measured were intensive rather than extensive. APPARATUS Fig. 1 shows a schematic representation of the major pieces of equipment used in the mobility determination. The weighable core holder is connected to a two-piston, constant-displacement pump. Attainment of steady-state flow is indicated by stability of the flow differential read from the high-pressure manometer. WEIGHABLE CORE HOLDER An important part of the data needed was the mobility-saturation relationship. This required that mobilities and saturations be measured at pressures, flow velocities and liquid-vapor volume ratios characteristic of condensate reservoirs.

By J. M. Smith, D. Kunii

Effective thermal conductivities of sandstones filled with stagnant fluids were measured using a steady-state technique. Data were obtained for seven sandstone samples, taken from four different locations and ranging in permeability from 18 to 590 md. The measurements with gases (helium, nitrogen, air and carbon dioxide) covered a pressure range from 0.039 psia to 400 psig. Data were taken for four liquids — n-heptane, methyl alcohol, 79.8 weight per cent glycerol-water solution and pure water at atmospheric pressure. The experimental results were used to evaluate the theoretical equations for predicting stagnant conductivities developed earlier 4 The low-pressure measurements permitted evaluation of the consolidation parameter bpDp/ks (necessary to utilize the theory) for the various types of sandstones. Using these characteristic values, the tbeoretical equations correlated well with the experimental conductivity data for the several fluids and rock samples. INTRODUCTION An aspect of heat transfer in solid-fluid systems of considerable current interest is the effective thermal conductivity of porous media. The stimulus for study of the subject arises from the need for sound procedures for designing thermal methods of petroleum production. The general system occurs when there exists a flow of fluid through the pores of the solid material. However, a logical starting point in developing a theory for predicting the effective thermal conductivity in the general system is to attack the special case when the porous solid is filled with stagnant fluid. Since the flow rates anticipated in thermal production processes are very low, such stagnant conductivities k,O are also of practical significance. Kunii and Smith4 recently reviewed the existing data for stagnant conductivities and proposed a theory for heat transfer in porous rocks. This leads to equations for predicting the stagnant conductivity as a function of the properties of the fluid and solid phases. The existing experimental information1-3,5,7,8 covered a range of porosities and agreed well with the theory. However, the available data were insufficient to examine critically the effects of two important properties on koe, — the thermal conductivity of the fluid and the pressure. The objectives of the present study are twofold: (1) to measure the effect on koe of (a) the pressure for gases, and (L) the thermal conductivity of the fluid kg for bloth gases and liquids; and (2) to determine for rocks of different porosities and permeabilities the apparent solid conductivity ks and the consolidation parameter bpDp/ks required in applying the theoletical equations. Measurements extrapolated to zero pressure are helpful in evaluating ks and the consolidation parameter. However, the extrapolations must be based upon data obtained at low pressures because in small pores the molecular conductivity of the fluid may be unusually depressed. This occurs when the mean free path of the molecules is of the same order of magnitude as the pore diameter, that is, in small-diameter pores at low pressures. The phenomenon has been studied recently by Schotte6in beds of unconsolidated fine particles. With particles in the size range of 45 to 200 microns, a significant reduction of kg with pressure was found even at absolute pressures greater than 1 atm. In the sandstones employed in the present investigation, pore diameters lower than those experienced by Schotte are likely, so that the effect would presumably be greater. SCOPE OF MEASUREMENTS Stagnant conductivities were measured for four types of sandstones using a total of seven samples. The characteristics of the samples, including porosity and permeability values, are given in Table