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By C. R. Sandberg, L. S. Gournay, R. F. Sippel

The effect of fluid-flow rate and fluid viscosity on oil-water relative permeability determinations was studied using the "dynamic flow technique." In this work relative per-nleability curves were obtained for homogeneous small core .samples from several sandstorle outcrop form-utions. Radio-tracers were used for the determination of fluid saturation and for the detection of saturation gradients. Cobalt-60 in the form of cobaltous chloride was used as a water-phase tracer in some of the experiments. Iodine-131 in the form of iodobenzene and Mercury-20-3 in the form of mercury diphenyl were used as oil-phase tracers in other experiments. Flow rates for each phase were varied within a range of 2.5 to 140.6 ml/hr. Oil-phase vis-cosities under flowing condition,> were varied from 0.398 to 1.683 cp. The relative permbilities ob-tained were found to he solely a function of saturation and independent of flow rare, provided there was no .Saturation gradient induced in the core sample by "boundary effect." Even though equilibrium with re-sped to flowing conditions was obtained at the lower flow rates, where a saturation gradient exists, this equilibrium is of a "contingent"-type rather than the "steady-state" equi-librium implicit in the relative per-meability concept. The only effect of increasing the oil or non-wetting phase viscosity was to decrease the flow rate required for the elimina-tion of the boundary effect. Fairly good agreement between experimentally determined and calculated values of the boundary effect was obtained when the non-wet-ring oil phase was the only Flowing phase. INTRODUCTION In the characterization of reservoir rock, as well as in the solution of reservoir production problems, it is most desirable to have reliablc rela-tive permeability measurements for the rock and fluids of interest. Many techniques have been developed for the laboratory determination of the relative permeability of both large and small core samples. In varying degree, difficulties attend the use of all of the methods. Each of the methods requires the metered flow of fluids of known viscosity through the core sample under conditions wherein the pressure drop in the individual flowing phases can be measured or closely approximated. Since the relative permeability is a function of the saturation and distribution of the flowing fluids, some means of obtaining such information is also required. The laboratory determination of the relative permeability of a sample should give the same relative permeability saturation relationship that would exist if the sample were in place in the oil reservoir. The attainment of this objective is complicated by the fact that the use of small core samples for laboratory measurements is usually necessary. As a result, errors in measuring the relative permeability arise from boundary effects at either the fluid input or output ends of the sample; no significant boundary effect is anticipated at the sides of the sample normal to direction of fluid flow. At the input end of the sample a boundary effect exists if the flow fluids are not com- mingled as they would be in the reservoir. At the output end of the sample a boundary effect exists as a result of discontinuity of the capillary properties of the system. Here the flowing fluids leave the small flow channels and enter a collecting system having much enlarged flow channels. Thus, there is a tendency for the wetting phase to be retained by the core sample because of the attraction of the core sample for the wetting fluid. No reference is made to these boundary effects in either Darcy's equation or in the relative permeability concept. As a consequence the saturation effect peculiar to the input end of the core sample may cause an error in the effective permeability measurement, since some portion of the core sample must be utilized for commingling of the flow fluids. At the output portion of the core sample a saturation gradient or a saturation change along the axis of flow results. Since relative permeability is a function of fluid saturation, this saturation gradient may cause a variable permeability measurement, especially since extent and character of the saturation gradient can vary with fluid-flow rate. The most convenient method of minimizing the boundary effect, especially at the output end of the sample, is to flow the fluids of interest through the core sample at such high rates that the capillary forces arc insignificant as compared to the viscous forces involved in the fluid flow. Since recent work of a preliminary nature has indicated that fluid dispersion in the porous medium increases with the flow rate, the high flow minimizes the boundary effect at the input end of the core sample by enhancing the mixing of the fluids.

By William E. Harris

Time and experience have demonstrated that by means of the Waelz process zinc, lead, cadmium, arsenic, antimony, bismuth and tin can be volatilized satisfactorily. In this way difficult gold ores are being treated to allow for the recovery of the precious metal. Iron ore containing zinc is being treated to remove the zinc and recover the iron. In Germany, thallium is being recovered in commercial quantities from the zinc oxide fume; indium, germanium and gallium are also concentrated to a degree warranting recovery, even though these rare metals are only recognizable in the ore by means of the spectroscope. The physical, chemical or mineralogical condition of the raw material affects very little the applicability of the process. The name Waelz is derived from the German word Waelzen, meaning a "trundling motion," which very aptly describes the movement of the charge through the slowly rotating kiln. The recovery of zinc and lead by volatilization in a rotary kiln has its origin in a process patented in 1910 by Edward Dedolph, of British Columbia. The Dedolph patent was taken over by the Metallgesell-schaft of Frankfurt-on-Main, Germany, which in cooperation with the Griesheim-Elektron, now a part of a large industrial combine, introduced certain improvements (Ohlmer, Specketer patents), but without bringing the process to a state suitable for large-scale operations. The war temporarily stopped all work on the process, and it was not until after the war that the Krupp Grusonwerk, of Magdeburg-Buckau, Germany, quite independently of the Metallgesellschaft, instituted research work in this field of metallurgy, which in 1923 led to the Waelz process proper. The Krupp Grusonwerk and the Metallgesellschaft A.G. later on collaborated, and by their joint efforts further developed and perfected the Waelz process, which they are marketing together as "Waelz-Gemeinschaft." The process is capable of treating a varied type of material; for instance, oxidized and sulphide zinc ores, calamine (zinc carbonate ore) waste dumps, jig tailings, jig slimes, table concentrate slimes, brass ashes, zinc-bearing iron ores (where the iron sinter is the real objective and the zinc oxide a by-product), electrolytic-zinc leach residues, zinc muffle residues and works sweepings, lead-furnace slags, tin ores and slags, anti-

Jan 1, 1937

By I. J. Polmear

Earlier work revealed that small amounts of silver (< 0,l at. pct) may exert a marked effect on the structure and aging characteristics of certain a1loys based on the Al-Zn-Mg system. Silver additions have now been made to other age-hardening aluminum alloys, and significant effects have been observed in the Al-Mg system and in several Al-Cu-Mg and Al-Mg-Si alloys. Similarities exist between the behavior of alloys from all four systems, notably that in each case silver stimulates nucleation of an intermediate precipitate which forms when the alloys are aged in the medium temperature range (-120" to 220°C). The mechanism for this effect is uncer- IT has been shown that small additions of silver (<0.1 at. pct) may have a marked effect on the structure and age-hardening characteristics of tain although it is suggested it originates in a preferred affinity between magnesium and silver atoms. There is evidence to indicate that the effects of silver are unique to that element. It is suggested that silver atoms interact with vacancies during low-temperature aging of Al-4 pct Cu and certain Al-Cu-Mg alloys. Silver had little effect on Al-8 pct Zn aged at any temperature. Preliminary observations indicate that silver may have interesting effects on the strength properties of Al-Mg alloys, md a the commercial Al-Cu-Mg alloys designated as 2024 and 2618. many alloys based on the Al-Zn-Mg* system.1"&apos;*

Jan 1, 1964

By Max Roesler

Page I. Introduction........................... 78 Location.......................... 78 Scope of Work and Acknowledgments.............. 79 History and Mining...................... 80 I1. Topography and its Interpretation................. 80 III. Petrology............................ 82 Sedimentary Rocks...................... 82 Description....................... 82 Age.......................... 84 Igneous Rocks........................ 85 Diabasic Rocks..................... 86 Dioritic Rocks...................... 87 Granitic Rocks...................... 88 Later Dike Rocks.................... 88 IV. Areal Geology.......................... 88 Rock Types Found in the District............... 88 Distribution of the Various Rock Types............. 89 Surface Distribution................... 89 Vertical Distribution................... 90 Causes of Present Areal and Vertical Distribution of the Various Rock Types..................... 91 Faulting...................... 91 Magmatic Differenti~tion............... 91 Tilting........................ 95 Erosion....................... 96 V. General Description of Ore Deposits................ 96 Nature of Ore ........................ 96 Shap~ and Size of Orebodies.................. 96 Geologic Position....................... 97 Mineralogy......................... 98 Distribution....................... 98 Interpretation...................... 99 Superficial Alteration................... 102 VI. Genesis of the Ore Deposits.................... 104 Previous Theories...................... 104 J. P. Kimball...................... 104

Jan 1, 1917

By Arthur F. Wendt

The earliest knowledge of copper-ores in the Southwest was derived from the Mexicans, who, in the latter part of the last century, discovered and worked the Santa Rita copper mines, now situated

Jan 1, 1887

By J. S. Woodward, F. B. Plummer

The measurement of the rate of flow of liquids through sands dates back to 1856, when H. d Arcyb, a French physicist, carried out his classic experiments on the flow of water through sand layers. The earliest recorded data on relationships of pressure to flow of fluids through porous rocks in this country are those of Newell 23 in 1885. The first comprehensive studies of flow were made in 1898 by King15, who measured the rate of flow of water and air through consolidated and uncon-solidated sands and published the results. From 1900 to 1920 there appears to have been little interest in permeability. In 1920 the increase in demand for oil led the U. S. Bureau of Mines to begin a series of experiments to determine subsurface relationships of oil and water and the characteristics of their flow. Mills18 studied the relationship of flow of liquids to text- and structure of the sands, and Melcher17 in 1925 made a quantitative study of effect of changes in pressure on rate of flow of crude oil through Oklahoma oil sands. Since 1930 the importance of flow measurements to production of oil and gas has been emphasized by a large number of excellent investigations. Among these the works of Fettke9.10, BarbI.2, Cloud6, Nutting24-", Bot-set4, Nevin22, Tickell32.33, Fancher, Lewis and Barnes8, Moore, Schilthuis and Hurst19, and Wyckoff, Botset and Muskat"-39 have contributed much to our knowledge of the technique of permeability measurements and to the laws of liquid and gas flow through porous sands. The application of their work has led to the establishment of laboratories for measuring the permeability and porosity of oil sands by most of the large companies. All the investigations, except those of Wyckoff, Botset and Muskat, and Moore, Schilthuis and Hurst deal with linear flow; that is, flow in a more or less straight line through a given cross-sectional area of sand. Three years ago, at the University of Texas, experiments were started to measure radial flow of liquids through sands; that is, flow from all directions toward a central opening—the conditions that operate in a

Jan 1, 1937

By A. D. Hodges

The great mining region of Peru is a mountainous belt of country, running nearly the whole length of the republic, and comprising the two grand ranges of the Andes with the elevated table-lands between them. On the east of this belt are the extensive plains and fertile valleys of the Amazon and its tributaries. On the west is a narrow strip of coast 20 to 50 miles wide, for the most part a sandy desert, but producing abundant crops where irrigated ; and here are found petroleum (Department of Piura), salt (at Huacho and elsewhere), nitrate of soda in enormous amounts at the south, silver in a few localities (Province of Tarapaca), copper and other mineral products. The Western Cordillera, running nearly parallel with the shoreline, rises like a wall on the eastern side of the coast-belt, with passes from 15,000 to 18,000 feet high and peaks attaining 18,000 to 20,000 feet. Further east, at a varying distance, is the Eastern Cordillera, composed of broken mountain ranges which, considered as one group, have a general parallelism with the western chain, but individually vary greatly in direction, sometimes running nearly east and west, in places projecting out into the Amazonian lands, or here and there curving around to unite with the western ridge, and with this enclosing immense inter-alpine plains. These general features are indicated in Fig. 1. The surface of these plains is uneven and traversed by lower ranges of hills which surround large lakes, or rolling pampas, or fertile valleys; and through many of these last run rivers of considerable size. The whole country has a high altitude (averaging up to 15,000 or 16,000 feet), and slopes gradually north and east towards the Amazon, into which drain all its waters. Its bounding mountain chains are scored on all sides by narrow, picturesque and pre-

Jan 1, 1888

Trans. Pamphlet Volume Number Title Author Meeting and Page* 1033 Relation of Air Presaure to Drilling H. W. Seamon New York 66, 743. 766 Speeds of Hammer Drills . Feb. 1921 1034 Time Factor in Depletion of Mines J. W. Roberts New York 66, 711 Feb., 1921 1035 Calculation of Ore Tonnage and Grade J. E. Harding New York 66, 117, 122 from Drill-hole Samples Feb., 1921 1038 Diacuasion of Papers Presented in 1920 1041 Run-off and Mine Drainage H. N. Eavenson New York 66. 624. 630 Feb.. 1921 1043 The Health of the Underground Worker A. J. Lanza New York Feb, 1921 1045 Dust-ventilation Studies in Metal D. Harrington New York 66, 272, 288 Mines Feb., 1921 1046 Discussion of Papers Presented at New York Meeting, 1921 1072 Breakage and Heat Treatment of Rock- B. F. Tillson New York 66. 758 drill Steel Feb., 1921 1073 Discussion of Papers Presented at New York Meeting, 1921 1076-M Analysis of Some Drill-ateel Teats F. B. Foley New York 66,789 Feb.. 1921 1077-M Application of Magnetic Analysis to C. W. Burrows New York 66, -796 Rock Drills Feb., 1921 1078-M Heat Treatment of Rock-drill Steel G. H. Gilman New York 66.779 Feb., 1921 1080 What is the Ideal Drill Steel? F. H. kingdon New York 66, 807 Feb.. 1921 1081 Rock Drill-Steels, etc. W. T. Ober New York 66,814 Feb.. 1921 1082-C Underground Mine Development, Its J. B. Dilworth Wilkes-Barre 66,715, 761 Definition and Valuation Sent.. 1921 1081 Drill Steel from Hollow Ingots P. A. E. Armstrong New York 66,809 Feb., 1921 1068 Authors&apos; Replies to Recent Discussion 1092 Heat Treatment of Rock Drill Steel A.E.Perkins New York 66,811 Feb., 1921 1096-M Octagonal Ventilation Shaft of Davis- J. L. Bruce Wilkes-Barre 66. 252, 608 Daly Copper Co. Sept., 1921 1100-C Determination of Electrical Equip- G. Bright Wilkes-Barre 66,580,606 ment for a Mine Hoist Sept., 1921

Jan 1, 1927

ROBERT H. LEACH, Chairman ROBERT F. MEHL, Past-Chairman D. K. CRAMPTON, Vice-Chairman E. M. WISE. Vice-Chairman W. M. CORSE, Treasurer LOUIS JORDAN, Secretary 29 West&apos; 39th St., New York, N. Y. Executive Committee 1940 1941 ARTHUR PHILLIPS W. P. SYKES L. E. SCHUMACHER E. A. ANDERSON CARL E. SWARTZ D. L. COLWELL 1942

Jan 1, 1939

By R. E. Hoffman, R. A. Ward

The self-diffusion coefficient in high purity nickel has been measured over the temperature range 870&apos; to 1248°C. The results are described by the relation D = 1.27 exp[—-66,800/RT 1cm2ec-1. The measured activation energy correlates satisfactorily with absolute melting point, heat of fusion, and heat of sublimation. KNOWING the rates of self-diffusion is important in the understanding of many metallurgical reactions. However, in spite of the rather widespread interest in nickel, both commercially and in fundamental investigations, no measurement of the self-diffusion in solid nickel has previously been re- ported." In connection with a program of measuring rates of diffusion in some nickel alloys, self-diffusion in pure nickel has been investigated over a rather wide temperature range by combining a sectioning technique and a surface counting technique.

Jan 1, 1957

By A. I. Blank, S. E. Maddigan

Many experimental and theoretical investigations have been made on the processes involved in annealing and recrystallization of metals. Most of these, however, have treated the time element as constant and heat-treatments used have been for relatively short times. Aside from the early work by Carpenter and Elam,&apos; the few that have investigated the effect of time on the processes have usually done so for fairly short time periods. During recent years the growing interest in long-time creep properties of metals and alloys under stress has made increasingly important a better knowledge of the recrystallization during prolonged heating. The recrystallization temperature of 70-30 brass given by Clark and White" in 1932 was somewhat above 400°F. (204°C.) but under 500" (260°C.), whereas in our laboratory recrystallization has been observed in creep specimens at 204°C., the lowest temperature of Clark and White&apos;s range. Since the creep properties are quite different above and below the recrystallization temperature, erroneous conclusions can readily be drawn by the application of short-time recrystallization data to creep problems. It was thus considered of both practical and theoretical value to make long-time annealing studies near the minimum recrystallization temperature. In this way useful additions could be made to data on recrystallization temperatures and, since the reactions in this range are relatively slow, additional insight could be obtained into the factors involved in annealing. Several comprehensive reviews of recrystallization processes have been written,3-6 therefore only a brief review of the generally accepted facts will be given here. Though the effects of heat-treatment usually are expressed as related to observations with varying temperatures, it is logical to assume that the same order of occurrence will exist with time as a variable. Thus, we may postulate that with increasing time we mill observe the following

Jan 1, 1940

By S. E. Maddigan, A. I. Blank

Many experimental and theoretical investigations have been made on the processes involved in annealing and recrystallization of metals. Most of these, however, have treated the time element as constant and heat-treatments used have been for relatively short times. Aside from the early work by Carpenter and Elam,&apos; the few that have investigated the effect of time on the processes have usually done so for fairly short time periods. During recent years the growing interest in long-time creep properties of metals and alloys under stress has made increasingly important a better knowledge of the recrystallization during prolonged heating. The recrystallization temperature of 70-30 brass given by Clark and White" in 1932 was somewhat above 400°F. (204°C.) but under 500" (260°C.), whereas in our laboratory recrystallization has been observed in creep specimens at 204°C., the lowest temperature of Clark and White&apos;s range. Since the creep properties are quite different above and below the recrystallization temperature, erroneous conclusions can readily be drawn by the application of short-time recrystallization data to creep problems. It was thus considered of both practical and theoretical value to make long-time annealing studies near the minimum recrystallization temperature. In this way useful additions could be made to data on recrystallization temperatures and, since the reactions in this range are relatively slow, additional insight could be obtained into the factors involved in annealing. Several comprehensive reviews of recrystallization processes have been written,3-6 therefore only a brief review of the generally accepted facts will be given here. Though the effects of heat-treatment usually are expressed as related to observations with varying temperatures, it is logical to assume that the same order of occurrence will exist with time as a variable. Thus, we may postulate that with increasing time we mill observe the following

Jan 1, 1940

By H. Kenyon Burch

INTRODUCTION THE Inspiration Consolidated Copper Co.&apos;s plant at Miami, Ariz., was designed and built to make possible the profitable working of a low-grade, finely disseminated copper deposit containing 100,000,000 tons of ore averaging 1.64 per cent. in copper. From the-beginning it was evident that the-plant could not, be kept integral but that a break would have to be made somewhere in the flow-sheet, removing at least the concentrator to a site more suitable than any available near the mine. It was finally decided, after considering numerous arrangements, to do the coarse crushing at the mine, to store the crushed ore in a bin from which it could be loaded into railroad cars and to haul it to the concentrator, an excellent site for which was available about 1 ¾ miles from the mine. The original intention was to equip a plant to treat 7,500 tons of ore per clay, but through the acquisition and proving up of additional ore reserves, the introduction of the Ohio caving system, and the excellent results obtained in the test mill (which made it possible to treat a lower-grade ore than had been thought possible) it was evident that a plant of much greater capacity should be supplied. It was, therefore, decided to treat approximately 15,000 tons of ore per day, the duties of the four main divisions to be as follows:

Jan 9, 1916

By T. Prof. Ph. D. Egleston

(Read at the Amenia Meeting, October, 1877.) THE copper-bearing rocks of Lake Superior are composed of a series of metamorphic rocks, comprised under the names of amygdaloid and conglomerate, in which the copper and silver found with them are pseudomorphs. These rocks, generally, have well-defined walls which cause them to separate easily. Generally, the country rock is sterile, but it occasionally rises into the copper-bearing rock, and then carries copper. Usually, the amygdaloids carry copper, and the greenstones or melaphyres which encase them do not. There is a very generally received opinion that the copper in these beds occurs in shoots. This does not appear to be proved, though the opinion seems to have some foundation from the experience of the Calumet & Hecla Mine, where a body of poor rock has been left, which, on the mine map, shows a general direction. The theory may be true of that individual mine, but too little work has been done in the other mines to draw any decided conclusion. The copper is very unequally disseminated in the rock, if any given piece be taken as an example, but, if the whole copper-bearing series be considered, its distribution is uniform. It may prove that there are certain directions in which the copper has been deposited more abundantly than in others, and these may be found to correspond with certain geological causes, but up to the present time the knowledge gained is not sufficient to warrant any general conclusion. These rocks are supplemented by a series of true fissure veins, of which there are several systems, making the amount of native copper very large. Unfortunately, except in the fissure veins, known as "mass-mines," the copper is so scattered through the rock, and is in such a fine state of division, that, although it is not always difficult to mine, it is always difficult to dress it sufficiently too make it pay. The metal is so uniformly distributed through these copper-bearing rocks that detached pieces, called " float," are found in digging on almost any land in the country. These pieces vary from very small fragments, weighing not more than a few ounces,, up to many pounds. III one instance, in making an excavation for a cellar of a

Jan 1, 1878

By Granville S. Borden

The fruits of industry are divided between capital, labor, and governments. Capital takes its redemption and remuneration through profits or dividends; labor takes its share through wages; governments take their share through taxes. Each must have a just share, and the question of what is a just share and the question of who-shall make the allocation are vital current political and economic issues. Certain political philosophies con- tend that government should take all the fruits and that some dictator or politician should have irrevocable discretion and power to distribute the fruits. Believers in democracy and free enterprise adhere to the view that capital is entitled to redemption and fair remuneration; that labor shall have a fair wage; and that governments shall make equitable levies. But since all human beings, both individually and in groups, are inherently selfish, there are many variable views in regard to the question of what ratios shall be applied in a division of the fruits and who shall have the power to fix these ratios. Perhaps all parties should devote more energy to means of increasing the crop, and not so much time to quarreling over a division of the existing crop. Moreover, all three parties must guard against killing the goose that lays the mineral eggs. For example, if the tax burden becomes oppressive and the taxpayer refuses to carry it, then business stagnates, with consequent unemployment, reduction of profits, and curtailment of government revenue. If a producer assumes the increased tax burden, marginal operations must be closed down, and again the consequences are increased unemployment and diminished government revenue. Quite often an increase in a rate of tax results in a reduction of government revenue. Perhaps the worst detrimental feature of selfishness and greed on the part of any one of the three distributees of the fruits of industry is the retardation of expansion of the enterprise. Growth means new jobs, more government revenue, better trade, and better standards of living. Explorations and discoveries have resulted in tremendous contributions

Jan 1, 1959

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies.

Jan 1, 1957

By Robert P. Uhley, LeRoy Scharon

TEST gravity surveys were made in the Washington County barite district of Missouri on property owned by the Baroid Sales Division of the National Lead Co. This property is located just northeast of Richwoods in the northeastern corner of Washington County, Fig. 1. The area to which the surveys were confined comprised approximately 5000 acres, of which some 525 acres were surveyed gravitationally. Gravity observations were made at 2600 points within the area, observations being confined to relatively clear and gently sloping ground. Part of the area was heavily wooded, and the terrain too rugged for either the occurrence of a commercial barite deposit or a feasible gravity survey. The relief along the central drainage, Ditch Creek, was about 140 ft, the maxi- mum difference in elevation being 400 ft in a distance of 3 ½ miles.

Jan 1, 1954

In the seven years that have elapsed since the AIME World Symposium on Mining and Metallurgy of Lead and Zinc, there have been a number of significant milling innovations and trends implemented in lead-zinc flowsheets to either improve grade and recovery or to control escalating mill costs. First, mill controls and instrumentation, which only had a foot in the door in 1970, have become increasingly common. In Australia, research into automatic crushing control has been implemented by Mount Isa Mines, and in virtually any large lead-zinc mill worldwide, an assortment of on-stream x-ray analyzers, grinding circuit controls, level detection devices, and reagent metering methods can be found. The increased circuit control offered to mill operators by this new technology points to more efficient flowsheets, as well as to a greater dependence upon computer-controlled operation.

Jan 11, 1977

By Arne Paus-Jenssen

Some aspects of the policies developed by Saskatchewan with respect to the provincial potash industry are discussed. The provincial potash policy was developed initially to deal with problems associated with an excess supply and consisted of output restrictions and floor prices. Changing market conditions led to a situation of rapidly increasing prices and revenues for the potash producers, and the nature of the policy problem switched from one of stabilizing the industry to one of levying increased taxes to enable the government to capture a portion of the revenues. The first part of the paper explains why a provincial potash policy was developed, the problems it attempted to deal with and how. The second part is an attempt to examine, from a public policy point of view, the impact of these policies on the potash industry.

Jan 1, 1977

By P. E. Baker

Approximate solutions are presented for the heat-flow equations in a loss-free linear system with a moving source and with heat transfer by convection and conduction, representing in situ combustion in an oil reservoir. The rate of heat generation and the velocity vf of the source (flame front) are assumed constant. A cold front or convection front caused by the cooling effect of in-jected air develops behind the flame front and moves with velocity vc, which is determined by the thermal properties of the air and rock. Because of thermal conduction the fronts are not sharp; i.e., they do not represent temperature discontinuities. The following solutions apply after a sufficiently long time. where Q is heat generated per unit volume of formation, k is thermal conductivity, CF is volumetric heat capacity, a is thermal diffusivity, and subscripts 1 and 2 refer to values behind and ahead of the flame front, respectively. The parameter CF2 is contained in v . Te is initial reservoir temper- . C2 e ature and air-injection temperature. Other mathematically possible solutions are presented. The different solutions result from the use of different values for various physical parameters. The solution just presented is thought to be most commonly applicable. INTRODUCTION In this paper, approximate analytical expressions are derived for the temperature profile developed in the underground combustion method of oil recovery. A qualitative description of the process may be found in a paper by Tadema.1 The flame front is regarded as a moving source with a constant rate of heat generation. Heat transfer is by conduction and convection. Previous publications, of which a few are cited here, 2-5 have also attacked this problem and have presented solutions pertaining to different methods of approximating or idealizing the process studied. The present paper also treats an idealized case: linear flow is assumed for heat and fluids, and vaporization and condensation effects are neglected. The results obtained are similar to those derived by Bailey and Larkin,3 but are obtained by an entirely different procedure. The method used here should give considerably greater insight into the physics of the in situ combustion process. Four types of cases are considered, distinguished by thermal and fluid-flow properties of the system. A constant rate of heat generation and constant rate of flame-front advance are assumed. Flame-front temperature is determined for each case using a heat balance which involves the entire temperature profile. The applicability of the different solutions to real systems is discussed after they are all presented. Again, this is done for the purpose of understanding better the physics of the process. Consideration of the nonapplicable solutions and of the reasons for their not applying is significant. In a paper by Cooperman,4 the only case solved is one considered here as not applicable. Fluid flow, as such (pressures, saturations, oil recovery, etc.), is not treated. This subject has been covered in a paper by Wilson, et al.6 Also, we are not concerned with requirements for continuance of the process; we only attempt to determine the temperature history for cases where the process has continued for some time. PHYSICAL SYSTEM AND APPROACH TO PROBLEM A linear flow (heat and fluid) system is assumed and the x-axis is taken parallel to the flow direction. The combustion zone (flame front) is vertical,