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By W. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.' It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch's alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By J. R. Schneider

INTRODUCTION Landowners in Texas for many years have freely granted, reserved and leased "oil, gas and other minerals" or interests therein. In recent years we have witnessed much litigation concerning what sub- stances should be included as "other minerals" within the phrase "oil, gas and other minerals," and this question has received the attention of numerous legal scholars. At the South Texas Uranium Seminar held in Corpus Christi, Texas, in September, 1978, Mr. William R. Dodson presented a paper dealing with this very subject and entitled "Uranium - Mineral or Surface? Who Owns It?" In his paper, Mr. Dodson reported on two recent Texas Supreme Court decisions, Acker v. a, 464 S.W.2d 348 (Tex. 1971) and Reed v. Wylie, 554 S.W.2d 169 (Tex. 1977). which held that the particular substance in question in each case is not a mineral within the phrase "oil, gas and other minerals" if substantial quantities of the substance lie so near the surface that production will entail the stripping away and substantial destruction of the surface. Since that time another chapter has been written in the Texas saga of "When is a Mineral not a Mineral?" and it is the intent of this paper to present an update of the Texas law. A review of the early Texas cases so ably covered by Mr. Dodson in his paper will not be repeated, except as is necessary to illustrate the evolution of the legal doc- trine which has been so aptly named "The Surface Destruction Test". BACKGROUND In order to appreciate the genesis of the problem, one must consider that oil and gas production commenced in Texas many years ago, Spindletop came in in 1901. As oil and gas became more valuable, land- owners with considerable frequency sold interest in the oil, gas and mineral estates in their lands, and reserved interest in the oil, gas and mineral estates in their lands when they disposed of their property. Due to the oil and gas background, and perhaps be- cause oil and gas was paramount in the minds of the parties, the traditional language employed in these grants and reservations was "oil, gas and other minerals" or variations thereof. There are literally hundreds of instruments employing this language constituting a link in the chains of title to thous- ands of acres of Texas land. In addition, there are thousands of acres of Texas land held by oil, gas and mineral leases, the primary terms of which have been perpetuated by production, containing similar language in their granting clauses. The severance of the mineral estate from the surface estate results in two separate and distinct estates, each having all of the incidents and attributes of an estate in land. with the surface estate being the serviant estate, and the mineral estate being the dominant estate and having certain easements in the surface estate to explore. produce and remove the minerals. Harris v. Currie. 176 S.W.2d 302, 305 (Tex. 1943). As observed by the court in the Harris case, this is because a grant or reservation of minerals would be wholly worthless if the grantee or reservor co~lld rwt enter upon the land in order to explore for and extract the minerals granted or reserved. Although the Texas law has recognized that an oil and gas lessee has the right to use so much of the surface as is reasonably necessary to produce the minerals. Warren Petroleum Corporation v. Monzingo, 304 S.W.2d 362, 363 (Tex. 1957), recent decisions of the Court have qualified this doctrine. In Getty Oil Company v. Jones. 470 S.W.2d 618 (Tex. 1971). Getty's pumpine, units were interfering with ones self-propelled sprinkler system utilized for irrigating the premises, and Jones sought to require Getty to install the-pumping units in cellars so that the sprinkler system could pass over them. In an effort to accommodate both the surface estate and the mineral estate, the court held (page 622) "...where there is an existing use by the surface owner which would otherwise be precluded or impaired, and where under the established practices in the industry there are alternatives available to the lessee whereby the minerals can be recovered, the rules of reasonable usage of the surface may require the adoption of an alternative by the lessee". Bearing in mind that the "reasonable use doctrine" grew up in the oil and gas industry involving sub- stances which can be produced by methods that do not destroy or deplete the surface estate, the question presented is whether the Texas courts will extend this doctrine to situations where claimants of "other minerals" seek to produce shallow deposits of iron ore, coal, lignite and uranium by surface mining methods which do destroy or deplete the surface estate? The surface destruction test has answered this question in the negative, at least as to iron. coal and lignite. However, the multitude of mineral estates in Texas which have been created by a grant. reservation or lease of "oil, gas and other minerals" will, doubtlessly, continue to fuel the fires of litigation. EARLY TEXAS DECISIONS In view of the evolution of the Surface Destruc- tion Test, an exhaustive review of the early Texas

Jan 1, 1980

By Carroll F. Hardy

The day by day loss of industrial plants to gas and oil is chiefly by default. The coal industry is not selling its superior economy, safety, and other advantages to its customers. THE position of the coal industry has been affected by a wide variety of developments in the production and use of energy. The tempo of development and change has been increasing and the end is not in sight. Legislation is currently being proposed for commercial use of atomic power, and the employment of atomic energy in significant quantity will probably occur about the same time as the decline in production of petroleum and natural gas. But these developments are in the future and have little immediate effect on utilization and marketing of coal. While no one should try to suppress or retard the development of a new and economical source of energy, both the coal and private utility industry should be allowed to question how the nuclear power is to be used, who is to use it, and who is going to pay for it. The taxpayers have a monopoly on fissionable material and the knowledge to employ it. Any commercial use must stem from this source. It is not hard to visualize either taxpayer-subsidized private utility atomic power plants on one hand and super TVA's on the other. In view of the gains of gas and oil in the home heating field, it is interesting to compare the 1940 and 1950 census reports on the kind of fuel used for heating in occupied dwelling units. Table I shows that whereas coal provided 77 pct of the fuel for central heating (furnaces and boilers) in 1940, it was down to 45.4 pct in 1950. However, only about 1 1½ million units were lost in this 10-year period. In the non-central heating category, which principally includes stoves, the percentage declined from 39.2 to 25.6, but the units declined about 2½ million in number. The big increase was in heating units designed to burn gas and oil. Use of wood for central heating declined about one-third. Data on amount of fuels used for residential heating are not available, but information is on hand for residential and comnlercial space heating, see Table 11. Commercial space heating includes office buildings, churches, schools. and similar structures. The annual use of bituminous coal in these two categories declined about 1 million tons in the 10-year period. Other forms of solid fuel showed greater losses, except wood, which remained the same. Domestic stokers reached their high point in 1948 with about 1,200,000 in use. At the end of 1951 there were approximately 1,116,790 stokers in use. Conversions to gas and oil have been from hand-fired heating plants in the ratio of about 7 to 1 compared to stokers. In other words, for every one stoker which has been converted to gas or oil, seven hand-fired units have been converted to gas or oil. A bare recital of these data would indicate that the coal industry is holding its own reasonably well. However, 93.4 pct of the new homes built in 1951 were heated by gas or oil. Oil-burning equipment was installed in 37.8 pct and gas equipment in 55.6 pct of the new homes. This indicates that the public prefers gas when it is available, and that oil is second choice, with all forms of solid fuel apparently used when it is unavoidable. It must be pointed out, however, that during the period of rapid expansion of gas pipelines gas has been sold for house heating at prices that are in some cases actually lower than coal prices, or very nearly on a par. Gas has been sold at wells at far below the comparable price for oil produced from the same wells, and far below its actual worth. This situation is being remedied at the present time by increases in gas prices at the wells. For example, the wellhead price of gas in Texas averaged 7.494 per Mcf in 1952. In 1949 it was 4.59c per Mcf. This increase in price is being reflected in pipeline gas prices, and in most of the markets served by the pipelines the tendency is to get it out of the bargain basement type of sales. The American Gas Association estimates that at the end of 1952 there were in the United States about 11 million customers for gas house-heating, and the Association expects additional gains each year until around 18 million homes will be heated by gas in 1975. By 1975 there should be 60 million dwelling units to be heated in the United States, if dwelling units increase at the same rate as the population. If the gas industry heats 18 million dwelling units by that time, this still leaves 42 million units to be heated by some other fuel. If oil is used to heat 18 million dwelling units in that same year, 24 million would of necessity be heated by coal, coke, wood, electricity, or another fuel. The total number of dwelling units using coal listed in the 1950 Census was 18,776,000, so it would appear that coal has a chance at least to stand still in the tonnage sold for domestic use. In the first quarter of 1953, 2044 domestic stokers

Jan 1, 1955

By W. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.' It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch's alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By G. A. Chadwick, D. Jaffrey

The morpho1ogies and orientation relationships of the phases in the Sn-Zn and A1-A13Ni eutectic systems were examined by electron microscopy and X-ray diffraction techniques. In each alloy the "transition" from the lamellar to the fibrous morphology was found to be one of scale, not of type. The minor phase in both systems exhibited certain well developed facets which were not affected by changes in the ingot solidification rate. The crystallographic relationships displayed by the pairs of phases in both systems were also insensitive to the growth rate. In the Sn-Zn alloy, the unique relationship of: growth direction - II [1201 Sn - II [01101 Zn and ribbon interface plane 11 (101) Sn 11 (7012) Zn was determined. The Al-Al3Ni alloy phases did not possess any particular orientation relationship, though the Al3Ni phase invariably grew in the [010] direction and exhibited the same set of facet planes. These results are discussed in relation to current eutectic growth theories and explanations of the "lamellar to fibrous transition". THE lamellar to fibrous transition that occurs in many eutectic alloys has been the subject of considerable speculation and experimental study. In some alloys it can be induced solely by an increase in the solidification rate,'-3 whereas in others the transition supposedly occurs only if the lamellae are forced to grow out of the overall ingot growth direction.4-6 he cause of this latter type of transition has been attributed to deviations of the lamellae from their low energy habit planes;4'5'7 fibers are produced because the sustaining force for lamellar growth (a low energy boundary) is destroyed. Implicit in these explanations is the assumption that fibers are circular in cross-section and completely lacking in low energy inter-phase interfaces. The "natural" growth rate dependent transition has been studied less thoroughly although Tiller8 has attempted a theoretical explanation of it. Tiller's arguments are not completely satisfactory9 but his suggestion that the relative undercoolings of the solid/liquid interface for lamellar and fibrous morphologies are growth rate dependent cannot be totally discounted; it is possible, for instance, that the relative interfacial undercoolings could alter and produce the observed morphology change if the orientation relationships between the phases and the associated interphase bound- ary energies were sensitive to growth rate. Salkind et al." have reported finding a change in the orientation relationships in the A1-A13Ni system accompanying the lamellar to fibrous transition, but contradictory evidence has also been reported for this3'" and another system,12 so the position remains unclear. In an attempt to clarify matters a study was made of the "lamellar to fibrous" transition in the Sn-Zn and A1-A13Ni eutectic systems; the morphologies of these two selected systems are quite similar when viewed by optical microscopy. In the present research the morphologies and morphology changes were investigated by electron microscopy. The orientation relationships existing between the eutectic phases were also determined for both morphologies in both eutectic systems. EXPERIMENTAL PROCEDURE The materials and method of alloy preparation and ingot solidification for the Sn-Zn system have been reported previously.2 In this investigation nine horizontally grown ingots of the highest purity (99.9997 pct) were used. The temperature gradient in the melt was not intentionally varied and was approximately 10°C per cm. Seven growth rates between 1.3 cm per hr and 20 cm per hr were imposed. The A1-A13Ni alloys were prepared from "Spec. Pure" nickel and 99.995 pct aluminum by melting the components in an open alumina crucible and casting the melt into the cold graphite mold. Six ingots of the Al-Al3Ni alloy were unidirectionally solidified at growth rates from 1 cm per hr to 12 cm per hr under high purity argon. A typical ingot was 20 cm long, 1 cm wide, and 0.75 cm to 1.5 cm thick. Samples taken from the bars at positions 12 cm from the nucleation end were examined by conventional orthogonal-section metallo-graphic techniques. When required, samples were mounted for X-ray diffraction analysis using the Laue back-reflection technique with a finely focussed X-ray source. The surfaces of the A1-A13Ni specimens were prepared by mechanically polishing them down to the 1 µ diamond pad stage followed by an electropolish in 80/20 methanol/perchloric acid solution at 0°C and 20 to 30 v. The Sn-Zn specimens were repeatedly polished on an alumina pad and etched in hot dilute (2 pct) nitric acid until the diffraction spots were found to be sharp. Thin films of the alloys were prepared for observation in an electron microscope by spark machining thin discs (0.03 to 0.04 in. thick) from longitudinal and lateral sections of the bars and elec-trolytically thinning them via a jet polishing technique. For the A1-A13Ni eutectic alloy, an 80/20 mixture of ethanol/perchloric acid at 40 v and 20°C was found to be satisfactory. A solution of 70/20/10 methanol/perchloric acid/butylcellosolve at 25 v and 20°C was used on the Sn-Zn alloy. For the former alloy the jet nozzles (cathodes) and the disc clamps were of aluminum;

Jan 1, 1970

By P. L. De Bruyn

The adsorption density of dodecylammonium ions at the quartz-solution interface has been Theadsorptiondensitydetermined as a function of collector concentration and pH. A ten thoushasbeenandfold range of amine salt concentration was covered at neutral pH. Experimental results show that over a thousandfold concentration range at neutral pH, the adsorption density (I) is proportional to the square root of collector concentration. Except at high concentrations, I increases with increases with increasing pH, but in general this effect is surprisingly small. . , . . A critical pH curve has been established for the flotation of quartz with dodecylammonium acetate. The conditions along the flotation curve are correlated with the adsorption measurements. THE behavior of collectors at the mineral-solution interfaces is usually explained in terms of an ionic adsorption process. Through the distribution of collector ions between the solid surface and the- co-existing solution phase the mineral is believed to acquire a water-repellent surface coating. Quantitative adsorption studies have been made on simple flotation systems1-4 only within the last few years. Such investigations were made possible by the adoption of the radiotracer method of analysis. As a consequence of these studies a new parameter has been added to aid the understanding of the flotation process. The research investigation to be discussed in this paper was undertaken to obtain a better understanding of the behavior of a cationic-type collector. This objective was approached through the determination of the distribution of dodecylammonium acetate between the quartz-solution interface and the solution as a function of the collector salt concentration and pH. To bring this investigation to focus on the more practical aspect of flotation research, an attempt was also made to correlate the adsorption results with actual flotation tests. Quartz: A —100 mesh ground crystalline quartz was infrasized; the products of the third and fourth cones were mixed together and reserved for experimental purposes. This stock material was cleaned by leaching in boiling concentrated HC1. After leaching the quartz was rinsed with distilled water until the filtrate showed no trace of chloride ian. It was then washed several times and dried. The qwrtz had a specific surface of 1400 cma per g as deterhined by the krypton gas adsorption method. Collector: The distribution of dodecylammonium acetate between the quartz surface and the solution phase was determined by the radiotracer method of analysis with carbon 14 as the tracer element. The radioactive amine salt with C" synthesized into the hydrocarbon chain5 was supplied by Armour and Co. The tracer element was located adjacent to the polar group. The radioactive salt as received had a specific activity of about 0.14 mc per g. When desired, dilution of this activity was effected by addition of non-radioactive dodecylammonium acetate also supplied by Armour and Co. ........ All other inorganic reagents used in this research were of reagent grade. Conductivity water was used for making up all solutions. Adsorption Tests: Two different experimental methods were used. In the first, to be designated as the agitation method, a weighed amount of quartz and a measured volume of amine salt solution were agitated in a 100-ml or 50-ml glass-stoppered pyrex graduated cylinder. The cylinder was filled with solution up to the stopper, since erratic results were obtained when an air space was left over the suspension. Time of agitation varied from 1 to 2 hr. Preliminary tests at different agitation times showed that the amount adsorbed remained constant for all agitation times exceeding 1/2 hr. After this conditioning period, the solids were separated from the solution by filtration through a Buechner fritted-disk funnel. The solution was re-circulated 10 times or more to allow the fused silica disk to come to equilibrium with it. Determinations of the amount of amine adsorbed on the frit itself indicated that this amount was less than 10 pct by weight of the amine acetate abstracted by 10 g of quartz. The funnel with quartz covered by a thin layer of solution was then centrifuged for approximately 5 min, at which time the moisture content of the solids was reduced to about 5 pct by weight. The wet quartz was blown into a tared beaker, re-weighed and allowed to dry at room temperature. A final weighing was then made to determine the moisture content. The second experimental method, similar to the procedure adopted by Gaudinand Bloecher,' will be referred to as the column method. Two liters of solution were passed through a bed of quartz contained in a Buechner funnel attached to a pyrex separatory funnel by means of a ball and socket joint. Preliminary tests showed that increasing the volume of solution above 2 liters does not give a measurable increase in adsorption. From 4 to 4 1/2 hr were required for 2 liters of solution to pass through the column. The moisture content of the quartz was again reduced to a minimum by centrifuging. A slightly modified column apparatus was used for experimenting with alkaline amine solutions. The same basic unit was used, but the underflow from the Buechner funnel was again fed into a Separafory

Jan 1, 1956

By Terkel Rosenqvist

THE desulphurization of molten iron and steel is a very complicated process. One way to arrive at a better understanding of this process is to break it down into several simpler chemical processes that can be studied individually in the laboratory. For a study of the different factors that influence the equilibrium distribution of sulphur between liquid metals and slags, several simpler equilibria may be investigated. One very important subject is the determination of the escaping tendency of sulphur in the liquid metal and its dependency on temperature and composition of the melt. Several papers in this field have recently been published.', ' Another subject is the study of the sulphur capacity of the slag. A molten slag is indeed complex, and even if sulphur distribution data for a large variety of molten slags may give empirical data about their desulphurizing power, the importance of the individual components is still not quite clear. It is accepted generally that lime is the most important desulphurizing component in the slag. The present investigation has as its purpose to study the desulphurizing power of lime in its standard state, and to provide a basis for thermodynamic calculations of the desulphurizing power of various lime-containing slags. The standard state of lime at steelmaking temperatures is solid calcium oxide, CaO. It can react with sulphur to form solid calcium sulphide, CaS. The relative stability of calcium oxide and calcium sulphide is expressed by the free energy of the reaction: 2Ca0 (s) + S1 (g) = 2CaS (s) + O2 (g) The existing free energy data for this reaction, listed by Kelley5 nd Osborn,' are uncertain to about 10 kcal and are of limited value for a calculation of equilibrium constants. Under the conditions prevailing in a melting furnace, the sulphur pressure may be expressed conveniently by the ratio H,S/H2 and the oxygen pressure by the ratio H,O/H, (or CO,/CO). The desulphurizing power of calcium oxide may, therefore, be studied by the reaction CaO + HIS = CaS + H2O. A study of this reaction may be complicated by certain side reactions: Water vapor and hydrogen sulphide may react. to form sulphur dioxide, and calcium sulphide may be oxidized to calcium sulphate. A thermodynamic calculation shows that these side reactions will be suppressed to insignificance if the equilibrium is studied in the presence of an excess of hydrogen. The apparatus used is shown in Fig. 1. About 10 g calcium oxide and 20 g calcium sulphide (laboratory qualities) were intimately mixed, and some water was added to make a thick paste. The paste was put into a thimble of zirconium silicate, which was placed within the constant temperature zone of a furnace, and capillary refractory tubes were attached in both ends. After the mixture had been heated in dry hydrogen at 1000°C for several hours all Ca(OH), and CaCO, had decomposed and CaSO, was reduced, so only CaO and CaS remained in the thimble forming a porous plug. The mixture was examined by X-ray diffraction after the initial reduction in dry hydrogen as well as after the subsequent experimental runs up to 1425 °C. It was shown that crystalline calcium oxide and calcium sulphide were always present together in about equal amounts. The unit cell edges were found to be 4.80A for CaO and 5.68A for CaS in good agreement with existing literature values." This shows that the mutual solid solubility is very small, and that the compounds are present in their standard states. Purified hydrogen was passed through water sat-urators kept at constant temperature in a thermostat bath. The amount of water vapor saturation was checked by means of a dew point method, not shown on Fig. 1. The gas mixture was passed through the capillary inlet into the furnace, where it was sifted through the porous plug of calcium oxide and calcium sulphide. The hydrogen sulphide present in the outgoing gas was absorbed in a zinc acetate solution and the hydrogen was collected over water. When one liter of hydrogen had been collected, the amount of hydrogen sulphide was determined by iodometric titration. As one molecule of H,O is used for the formation of each molecule of H,S, the equilibrium ratio H,S/H,O would be , where (H,O) is the molar concentration in the ingoing gas, and (H,S) the molar concentration in the outgoing gas. In the present work (H,S) was always very small compared to (H20). In order for the observed H,S/H20 ratio to represent the true equilibrium ratio the gas flow has to be: 1—Sufficiently slow to give a complete establishment of equilibrium, and 2—sufficiently fast to counteract thermal diffusion. Incomplete reaction would give a value decreasing with increasing flow rate, and thermal diffusion would give a value increasing with decreasing flow rate. When inlet and outlet tubes of about 2 sq mm cross-section were used, the observed gas ratio was independent of the flow rate between 15 and 125 cc per min, Fig. 2. In this range, therefore, the observed gas ratio represents true equilibrium.* For the rest of the in-

Jan 1, 1952

By W. J. Slatosky

W. 0. Philbrook (Cairiegie Institute of Technologyogv—Mr. Slatosky has presented an interesting and constructive paper that represents another step along the way of converting steelmaking from an art to a science. I am confident that his computer will be practical and successful and that with a very few months of experience it will provide a significantly better degree of control than his record of 65 pct of heats within range obtained with the slide-rule calculator . A paper such as this, with a lot of symbols and condensed mathematics, is difficult to comprehend quickly. Since I have had an opportunity to study it carefully, perhaps my evaluation of its validity and accomplishments will save time for others. Mr. Slatosky has correctly used standard principles of stoichiometry and heat balances, which are available to anybody, but he has also brought to them two original contributions: 1) He has developed from operating data some empirical relations for predicting the final FeO content of the slag (at 0.5 pct C end-point) as a function of slag basicity, lance height, and scrap, ore, and scale in the charge. This improves the accuracy of prediction of temperature or scrap requirement compared with assuming an arbitrary, constant FeO content at the end of each heat. There is no assurance yet that exactly the same relations will hold for other furnaces or practices, but similar correlations can be expected. 2) He has combined calculations that are ordinarily carried out laboriously as a number of individual steps into a single, simple linear equation that can readily be fed into a machine. This involved a tremendous amount of painstaking detail work as well as the imagination to see the possibility and work out the steps. While his particular Eqs. [3] and [6] are valid only for the furnace design, charge weight, and blowing time used at Aliquippa Works, only a few numerical values have to be changed to adapt it for other conditions. In order to arrive at a useable solution, Mr. Slatosky had to make some basic assumptions about the process that are similar to those used by others. He neglected variation in some process variables and assumed an arbitrary average value for waste gas analysis and temperature for want of more exact information at the present time. All of these judgments are clearly stated. In addition, some thermody-namic data presently available are not adequate for the job, notably in relation to heats of formation and sensible heat in slag, and some expedient has to be adopted to get around the difficulty. Other people might prefer slightly different judgments about these details and hence obtain somewhat different numerical solutions. This is not of serious importance, however, because the errors accumulate in the "heat loss" term and are largely self-compensating for a constant heat time. Although the extended Eq. l(a) in Appendix I was set up as a rate equation originally, for convenience in using an analogue computer as stated in the paper, the time dependence was removed by later mathematical manipulations and assumptions about the process. The final result is an integration of element and energy balances from initial to final states; this procedure is as legitimate here as in any other form of heat-balance calculation. The formal handling of stoichiometry and thermochemistry appears to be correct, and it is assumed that any arithmetical errors would have come to light in applying the calculations to furnace practice. Mr. Slatosky's approach is not necessarily unique, in that other people might start with apparently different equations or prefer another form of final equation for another type of computer. However, he has presented an accomplished result that appears to be a theoretically sound and practically useful way of applying scientific principles and rapid computation for better control of steelmaking. His success will undoubtedly encourage himself and others to improve on the mathematical model and its use as better informatioq becomes available. John F. Elliott (Massachusetts Institute of Teck-t2ology)-The last comment by Mr. Richards that a calculator is quite unnecessary for an L-D operation ?-equi??es a rebuttal. The L-D furnace is a very high capacity process which places a premium on close control. When one is making steel at rates between 100 and 200 tons per hr, one cannot afford the luxury of an extra 5 or 10 min at the end of a heat correcting for an error that should never have been made in the first place. Mr. Slatosky's paper is a very sound application of the simple principles of stoichiometry and the energy balance. It is a satisfactory and valuable start, but only the start of the development of methods of control for this process. An analysis of the process shows that it should be very suitable to control by a computer. This is especially the case when various grades of steel are to be made. In fact, it would seem that the organizations who are planning new and bigger installations of L-D vessels should consider carefully the advantages that would stem from computer control of a vessel with the operator present to do little more

Jan 1, 1962

By James P. Connell

HISTORICAL BACKGROUND The American Concrete Institute defines shotcrete as "mortar or concrete conveyed through a hose and pneumatically projected at high velocity onto a surface." This definition thus includes what is traditionally known as gunite, which is a pneumatically applied mortar. In mining practice, the term shotcrete is restricted to pneumatically applied concrete, and this differentiation will be used in this chapter. In 1914, following the invention of the mortar gun in 1907, then chief engineer of the US Bureau of Mines (USBM) George Rice developed the gunite process for underground test work at the USBM facility at Bruceton, PA. After World War I, gunite was used extensively in American mines and was also utilized for underground civil works such as the San Jacinto tunnel in California. The greatest development was in Europe where, as early as 1911, gunite was successfully used as an overlay for deteriorated tunnel linings. In 1951, the Swiss firm Aliva developed a pneumatic gun capable of handling coarse aggregate, thus making possible the first use of shotcrete at the Maggia hydropower development. Initially, shotcrete was used to reduce manpower requirements for forming and placing conventional concrete. However, by 1954 Sonderegger was reporting that the structural advantages of shotcrete were derived from its flexibility and from the fact that it could be applied almost immediately after the opening had been made. The incorporation of wire mesh into the shotcrete led to the new Austrian tunnel method or NATM. The use of shotcrete in American mines has been implemented more recently. This delay seems to be due to previously unsuccessful experiences with gunite as a structural material and to the US reliance on wood or steel supports in main-line haulageways. The long experience with the apparently more substantial rigid supports led mine operators to be reluctant to accept the new and seemingly unrealistic lighter shotcrete support. APPLICATION REQUIREMENTS Shotcrete is a relatively new material for use in underground support systems. Consequently, experienced miners are not always available who are capable of applying the material effectively. Shotcrete, particularly in the small cross sections typical of mine shafts or haulageways, is applied in cramped quarters under less than ideal conditions. Adequate lighting should be made available. The surface should be clean and free of running or dripping water. It may be necessary to collect flowing water in plastic pipes or water collection devices. Any dry cement dust from previous shotcrete applications should be washed from the surface in order to assure a good bond. The US Bureau of Reclamation (USBR) while shooting test panels at the Cunningham tunnel in 1974, found that experienced shotcrete operators were able to obtain up to three times greater compressive strengths than were obtained by unskilled operators using the same equipment and shotcrete mix. ENVIRONMENTAL AND SAFETY REQUIREMENTS Since sodium and potassium hydroxide, as well as other moderately toxic compounds, are often contained in shotcrete (particularly where accelerators are used), safety precautions must be taken to prevent skin and respiratory irritation. Nozzlemen and helpers are required to wear gloves, protective clothing, and ventilation hoods with a filtered air supply. Respirators approved by USBM, equipped with chemical filters that will not pass the caustic mists, may be permitted in lieu of hoods if goggles or safety glasses are worn. Protective ointments are available to reduce skin irritation. All air and shotcrete feed hoses should be equipped with safety-type couplings and secured with safety chains at each coupling to prevent whipping in the event of a hose or coupling failure. Some environmental effects can take place down-stream from the development face being supported. The accelerator compounds, as well as the portland cement used in the shotcrete, will be found in the rebound material which falls to the invert of the heading. Since these compounds may be leached from the rebound material and carried by the drainage system, it may be necessary to install neutralizing or other water treatment facilities. Investigations may find that the final reaction with other compounds being leached from the mining operations may result in a more or less environmentally acceptable end product. USES OF SHOTCRETE General Uses Shotcrete, as a combination of cement, aggregate, and accelerator, is utilized for underground openings such as shafts, adits, haulageways, and service chambers for the following general purposes : (1) primary sup¬port; (2) final lining; (3) protective covering for excavated surfaces that are altered when exposed to air (the protective covering may be of a temporary or final nature); (4) protective covering for steel or wooden supports, rockbolts and rockbolt plates, heads, nuts, and other mats, including wire fabric, used to prevent rock-falls; and (5) as a lagging material in place of timber, steel, or concrete between steel or wooden supports. These applications can be grouped into three general use categories: shotcrete used as a rock sealant, shotcrete used as a safety measure, and shotcrete used as a structural support. Use as a Rock Sealant Thin applications of shotcrete can reduce or prevent slaking of shales or other rocks that are altered when exposed to the wetting and drying cycles created by mine ventilation circuits. While shotcrete may be effective in preventing such rock alteration, at the present time it is not as economical or efficient as other commercial sealants. However, if the sealant property can be incorporated into the structural support capability, the added contribution is usually helpful. Thin applications are not usually sufficient if the alteration of the

Jan 1, 1982

By P. W. Gilles, B. D. Pollock

THE pioneering work of Steinitz1 and Steinitz, Binder, and Moskowitz2 has shown conclusively the existence at high temperature of two additional phases in the molybdenum-boron system and thus brings to a total of six the number of structures appearing in this system. To the structures Mo2B, MOB, and Mo2B5 they have added MO3B2, a new -MOB form, and have shown that MOB,, which has the same range of composition as Mo2B5, is only a high temperature structure of the latter. This solid solution, interestingly enough, includes neither of the compositions corresponding to the stoichiomet-ric compounds, MOB, or Mo2B5, but rather at all temperatures has intermediate values of composition. These workers have also, in the course of their work, measured melting points, transition temperatures, eutectic and peritectic points in the system and have shown that Mo3B2, because of its dispro-portionation at low temperature to Mo2B and MOB, is stable only in a limited high temperature range. During the course of the present work on the vaporization properties of the molybdenum-boron compounds, a few transition temperatures were observed. When the report of the other workers appeared, it was decided to repeat, in part, their study of the system. As a result, considerable evidence has been obtained that substantiates the specific kinds of melting processes they report as well as the general features of their diagram. However, a marked difference was found between the temperatures they report and the ones observed in this study, with the latter being higher. The purposes of this paper are to present the evidence obtained in this laboratory that verifies their diagram of the system, to give some important temperatures in the system, to compare them with those previously published, and to seek an explanation of the difference. Samples The metal starting material was 400 mesh molybdenum powder with a purity stated by the manufacturer to be 99.9 pct. The initial treatment, designed to remove volatile contamination, consisted of heating in a vacuum for 10 min to a temperature of from 800" to 1000°C during which a loss of 0.3 to 0.4 pct occurred. An assay following this treatment showed it to be 99.4 pct pure, with the principal impurity probably being oxygen. The boron starting material was obtained from the Cooper Metallurgical Laboratories and the Fair-mount Chemical Co. as 325 mesh powder with manufacturers' analyses of 99 pct or better. Initial treatment consisted of heating in molybdenum in a vacuum at about 1700°C for 10 min. During this time a loss of 3.5 pct occurred. An assay following this treatment showed the different samples to have purities ranging from 95.5 to 99.0 pct with iron and carbon as the principal impurities. Following the initial treatment, the elements were combined to form stocks of Mo2B and MOB by heating pressed mixtures in a vacuum to 1100" to 1200°C to accomplish reaction and to 1500" to 1900°C for a few minutes to evaporate the more volatile impurities. Analysis of the two compounds for boron by a modification of the method of Blumenthal3 and for molybdenum by the lead-molybdate method indicated them to have purities greater than 99 pct. The individual samples to be studied had compositions in the Mo2B-MOB range and consisted of mixtures of the stock compounds. Procedure As is usually the case in high temperature work the selection of containers for the samples posed some problems. For vapor pressure studies tantalum crucibles, allowing little contact with the pressed samples, were used and some of the observations made during these experiments are pertinent to the study of the phase diagram. Most of the experiments, however, were performed in graphite containers, as were those of the previous authors. Two kinds of spectroscopic grade graphite crucibles were used. One was a % in. cylinder, 3/4 in. high, containing seven 3/16 in. holes drilled 1/2 in. deep into which were packed samples of the different mixtures weighing 250 to 500 milligrams. The other, consisting of separate crucibles, was prepared by drilling 3/16 in. holes, 1/2 in. deep into 1/4 in. graphite rods % in. long. The 7/8 in. cylinder was heated directly by induction while the small crucibles were packed in a tantalum heating element for induction heating. All heating was done in a high vacuum system in which the pressure was generally less than 1x10-5mm and never rose above 2x10-5mm when the samples were hot. The general pattern of the heating in graphite was to heat rapidly to a temperature somewhat below the desired one, then to raise the temperature slowly. The samples were held for 2 to 5 min at the maximum temperature, which in all cases was far higher than that needed to produce reaction. The short time was employed to reduce possible contamination by the crucible material and to reduce composition changes that would occur because of vaporization. After examination following the heating, the samples were reheated to a higher temperature. Temperatures were measured with a Leeds and Northrup disappearing filament optical pyrometer, certified by the National Bureau of Standards, by sighting through a window at the top of the vacuum

Jan 1, 1954

By James R. Stuart

AS the available remaining properties of iron ore reserves on the Mesabi Range are opened up for mining, the various properties located under lake beds are brought nearer an active status. The actual physical problems involved in stripping these properties do not act as a deterrent so much as the legal and political problems that are encountered. When it is proposed to destroy a natural lake that has been used by the public for many years, much local as well as state opposition may be encountered regarding its destruction. Public hearings must be held and some adverse publicity is likely to result. The ownership of the ore under the lake and the rights of the abutting property owners must be settled, and protection from damage caused by a disturbance in surface and subsurface drainage is likely to be demanded by property owners some distance from the proposed mine area. The Embarrass Mine, located near Biwabik, Minn., falls into this classification. A portion of the orebody lies under what was formerly Syracuse Lake, this body of water having been removed in the process of stripping the mine. An additional problem in the case of a meandered body of water is the establishment of a meander line that can be projected downward as mining progresses to form the basis for a satisfactory division between lake bed and upland ore shipments for royalty purposes. Fig. 1 illustrates the complications encountered in maintaining these divisions. A balance point was agreed upon in the center of the lake to make an equable division of lake bed ore to the abutting properties. The entire lake bed has since been adjudged the property of Minnesota. Lake Characteristics Lake bed stripping problems with which this paper is concerned necessarily are limited to a specific type of lake, namely the glacial lakes of the Lake Superior region. One characteristic common to these bodies of water is a deposit of fine black mud or silt on the bottom, frequently underlain by a layer of impervious blue clay. This is also true of the muskeg areas of the region, which present almost identical problems as lakes in stripping. The actual removal of the water and the lake bed material is a routine matter more or less standardized as to equipment, and the period of time required can be estimated easily on the basis of volume and capacity. More important than the foregoing is the execution of preliminary work, and above all, the timing involved. An account could be prepared based entirely on statistical and cost data which would give a very fair picture of the time required and cash outlay needed to effect the removal of a body of water preliminary to stripping the orebody. However, the real interest from the standpoint of the operator and the engineer who carry responsibility for completion of the job lies in the unexpected emergencies and the action of various materials involved in the stripping when the balance has been upset through diversion of water courses and the reduction of the lake level. Runoff and Drainage Lakes are located in natural basins that catch all the rain water and runoff water for a considerable area. Where a lake is involved having an inlet and outlet or a sizeable water course running through it, the drainage area may include a watershed covering many square miles. All available data then must be collected to supply a history extending over as many years for which information can be gathered on the flow of streams, annual rain and snowfall, and most important, the peak flows to be expected. Where the diversion of a stream around the stripping area is a part of the problem, this last factor is of great importance since it controls the cross-section to be selected for the diversion channel and the volume to be removed in its excavation, as well as affecting the hydraulic considerations to be met in the design of the completed channel. Characteristic material in the overburden found at the Embarrass Mine is illustrated in Fig. 2. Well Pumping Pumping from the well holes was started well in advance of the draining of the lake. Fig. 3 shows a gradual lowering of the water table with no noticeable fluctuations during the period in which the lake was being dewatered. Unfortunately, because of tight ground, a maximum flow to the wells was not maintained. This retarded the rate at which the water table was reduced so that in the course of stripping the excavation soon extended below the water table, and the great bulk of the pumping was handled from a system of sumps in the pit itself. Any dewatering program projected by prepumping from wells, a glorified well point system, would have to be started well in advance of the stripping to be of any great advantage. Preliminary drainage of the surface over the mine area is entirely apart from the actual elimination of the lake bed itself. Since the lake is what is called a perched water table because of the impervious character of the lake bottom, the adjoining surface may be dewatered below the surface of the existing lake and the flow will not be affected by the proximity of that body of water. This condition actually has been demonstrated through the establishment of a number of observation holes where a small churn drill was used to put down the holes and a 3-in. pipe was installed for taking water level

Jan 1, 1952

By Robert H. Merrill

INTRODUCTION In most cases, the design of an underground mine is based upon the premise that the ground either will cave or will be stable. This chapter concerns the design of a mine in ground that will cave readily or with some as¬sistance, such as by long-hole drilling and blasting. Some of the more widely used caving systems of mining are panel caving, block caving, sublevel caving, and large pillar recovery. Some of the less widely used systems are glory-hole, top slicing, and induction caving. Al¬though the common practice of pillar robbing is not usually considered to be a caving system, this subject will be treated as a part of this chapter. BASICS OF CAVING Caving systems are most successful in ground that will cave in sizes that will flow through openings and grizzlies, and will easily load in cars or on belts for haul¬age. The ground most likely to cave well is highly frac¬tured and contains breaks, flaws, or other discontinui¬ties that form planes of weakness. Also, caving action can be greatly enhanced if the host rock itself is low in compressive, shear, and tensile strength. Ideally, a cav¬ing system of mining is best employed when the criteria for caving is a feature of the ore body and the develop¬ment drifts, haulageways, and drawpoints can be mined in a highly competent rock beneath the mineralized zone. However, the development is often in the same, or similar, fractured rock and the openings require sub¬stantial artificial support to assure stability. Several clues can be assembled to identify potential caving ground; however, for borderline cases, no sure method has been devised to date. The diamond-drill cores taken for exploration can provide an excellent clue provided drilling is performed carefully by experienced drillers. For example, if the ground is cored in such a manner that the breaks in the core are caused more by failure of the rock than by whipping core barrels, plugged drill bits, or other drilling causes, and the intact core lengths are consistently long [say, 0.6 to 3 m (2 to 10 ft) of unbroken core], there is little reason to believe the ground will cave without considerable as¬sistance. This is especially true for rocks with compres¬sive strengths above 34.5 MPa (5000 psi) and tensile strengths above 2.1 MPa (300 psi). On the other hand, if core recovery is low (below 80%) and the recovered ore is broken in small pieces and the breaks are along obvious weaknesses in the rock, the chances are excel¬lent that the ground will cave. This is true even when the rock between the defects has high compressive and tensile strength. Another clue has already been mentioned, that is, the measurement of the physical properties of the rock and the natural planes of weakness or defects in the rock. The planes of weakness in the rock can often be detected from outcrops, cores, or other exposures of the rock under consideration. Some rock types are known to be strong and will sustain large, unsupported open¬ings and would be difficult to cave intentionally. Yet the same rock type can also contain unbonded or weak planes of weakness or fractures, and in these locations the rock would undoubtedly cave with little assistance. Therefore, although the inherent strength of the rock is a factor in caving, the natural defects in the rock are more often the deciding factor. DESIGN CONCEPTS For the most part, the design of openings for caving ground is a problem of the interaction of openings over a relatively large area of the mine. To illustrate, Fig. 1 is a simplified section of a series of openings along the grizzly level or draw level of a block caving or panel caving development, and above this opening is a simpli¬fied section of a room-and-pillar arrangement on the undercut level. At this stage of the development, the stresses around the openings on the grizzly level are only moderately influenced by the openings on the undercut level and vice versa. Therefore, the stresses around the openings are approximated by the stresses around single or multiple openings in rock, the values of which are de¬scribed in the literature (Obert, Duvall, and Merrill, 1960; Obert and Duvall, 1967). Once the pillars on the undercut level are blasted (Fig. 2), the situation changes abruptly. The undercut opening (prior to caving) now can be approximated as an ovaloidal opening above the grizzly drifts and this opening tends to shield the vertical stress field. As the caved stage is drawn the stope approximates a much larger rectangular or square opening filled with rock, and if the rock is not sustaining a major portion of the stress field, this opening can be considered (for en¬gineering purposes) to be empty and the stresses that interact between the larger and the smaller openings take on a totally new perspective (see Fig. 3). Next, let the material cave to the surface, and let the caving ma¬terial sustain some stress, but much less than if the ma¬terial were intact. This condition is similar to a soft inclusion in a rigid body and has been treated in the literature (for example, Donnell, 1941). At this point in time, the grizzly drifts are subjected to the stress con-

Jan 1, 1982

By D. T. Peters, S. Floreen

The age hardening behavior of an Fe-8Ni-13Mo alloy was studied after the matrix had been varied to produce either ferrite, cold u~orked ferrite, or nzassive nzartensite. The aging behavior of the cold worked ferrite and murtensite structures were very similar. The martensite aging kinetics were much different from those observed in earlier studies of aging of maraging steels, even though the martensite wzatri.r had the same dislocation structure as those found in maraging steels. The results suggest that the previously observed precipitation kinetics of maraging steels ?nay have been controlled by the nucleation be-haviov, which in turn were dictated by the alloy compositions and the resultant identities of the precipitating phases. IT is well known that the rate of precipitation from solid solution depends not only on the degree of super-saturation, but also on the density and distribution of dislocations in the matrix structure. These imperfections often act as nucleation sites, and may also enhance atomic mobility. 'Thus, the presence of dislocations is important since the type and distribution of precipitates may be determined by them. The precipitate density and morphology in turn affects the mechanical properties of the alloy. A number of studies have been devoted to the precipitation characteristics in various types of maraging steels.'-" These are iron-base alloys containing 10 to 25 pct Ni along with other substitutional elements such as Mo, Ti, Al, and so forth, that are used to produce age hardening. The carbon contents of these steels are quite low, and carbide precipitation is not believed to play any significant role in the aging reactions. After solution annealing and cooling these alloys generally transfclrm to a bcc lath or massive martensite structure characterized by elongated martensite platelets that are separated from each other by low angle boundaries, and that contain a very high dislocation den~it~.~~~~~~~~-~~ Age hardening is then conducted at temperatures on the order of 800" to 1000°F to produce substitutional element precipitation within the massive martensite matrix. Most of the aging studies to date have revealed several common traits in these alloys, regardless of the particular identity of the precipitation elements. Generally hardening has been found to be extremely rapid, with incubation times that approach zero. The agng kinetics, at least up to the time when reversion of the martensite matrix to austenite begins to predominate, frequently follow a AX/~~ = ktn type law, where x is hardness or electrical resistivity, t is the time, and k and n are constants. The values of n are frequently on the order of 0.2 to 0.5, which are well below the idealized values of n based on diffusion controlled precipitate growth models. Finally, the observed activation energy values are typically on the order of 30 kcal per mole, and thus are well below the nominal value of about 60 kcal per mole found for substitutional element diffusion in ferrite. The common explanation of these observations is that the precipitation kinetics are controlled by the massive martensite matrix structure. Thus, the absence of any noticeable incubation time has been attributed, after ~ahn," to the fact that the precipitate nucleation on dislocations may occur without a finite activation energy barrier. The low values of the activation energy are generally assumed to be due to enhanced diffusivity in the highly faulted structure. If this explanation that the precipitation kinetics are dominated by the matrix structure is correct then one should observe a distinct difference in lunetics between aging in a martensitic matrix and aging the same alloy when it has a ferritic matrix. Such a comparison cannot be made with conventional maraging compositions, but could be made with the alloy used in the present study. In addition, the ferritic structure of the present alloy could be cold worked to produce a high dislocation density so that one could determine whether ferrite in this condition would age similarly to martensite. EXPERIMENTAL PROCEDURE The composition of the alloy used in this study was 8.1 pct Ni, 13.0 pct Mo, 0.10 pct Al, 0.13 pct Ti, 0.012 pct C, bal Fe. The alloy was prepared as a 40 lb vacuum induction melt. The heat was homogenized and hot forged at 2100°F to 2 by 2 in. bar, and then hot rolled at 1900°F to $ in. bar stock. The aging lunetics were followed by Rockwell C hardness and electrical resistivity measurements. Samples for hardness testing were prepared as small strips approximately 2 by $ by 4 in. thick. Electrical resistivity was studied on cylindrical samples approximately 2 in. long by 0.1 in. diam. The method for making the alloy either martensitic or ferritic was based on the fact that the alloy showed a closed y loop type of phase diagram. At high temperatures, above approximately 24003F, the alloy was entirely ferritic. Small samples on the order of the dimensions described above remained entirely ferritic after iced-brine quenching from this temperature. In practice, a heat treatment of 1 hr in an inert atmosphere at 2500°F followed by water quenching was used to produce the ferritic microstructure. These samples were quite coarse grained and usually en-

Jan 1, 1970

By L. D. Jaffe, R. K. Pitler

IT would clearly be advantageous to produce molten titanium, suitable for alloying and casting, directly from the relatively inexpensive tetra-chloride, without using a metallic reducing agent. Accordingly, a preliminary investigation has been made of the production of titanium by hydrogen reduction of the tetrachloride in an electric arc furnace. For the reaction: TiCl4(g) + 2H2(g) ? Ti(s) + 4HCl(g), Lockhart and his colleagues' have calculated equilibrium constants at 800" to 1500°K, based on tables of Brewer.' Extrapolating these data on the assumption that the heat of reaction varies linearly with temperature, and using Brewer's value for the heat of fusion, there is obtained for the reaction: TiCl4(g) + 2H2(g) ? Ti(l) + 4HCl(g) an equilibrium constant at 2100°K (100" above the melting point) Kp = (PHCl)4/pTlcl4 (Ph2)2 = 0.167 atm. If this is correct, starting with hydrogen saturated with TiC14 at 25°C, where the vapor pressure of the latter3 is 12.6 mm, and maintaining the overall pressure at 1 atm, 99 1/4 pct of the TiC14 would be reduced to Ti at equilibrium. An arc furnace designed for the melting of titanium and lined with water-cooled copper was used for the preliminary experimental check. Its inside diameter was 2 7/16 in. and height 6 in. The water-cooled electrode was tipped with 3/4 in. diam tung-sten. In the one run carried out, the furnace was charged with a starting batch of 293.35 g of scrap titanium,' analyzing 99.24 pct Ti. After the system was twice pumped out and flushed with argon to remove air, the arc was struck in argon and kept at 400 amp dc, electrode negative, for 1 min to melt the starting batch. Commercial tank hydrogen, dried by passing over silica gel and bubbled through technical grade TiC14 at room temperature, was then admitted to the furnace. The inlet tube directed this gas downward toward the arc and melt; the gas outlet was at the top of the furnace. The quantity of gas passed through was not measured accurately but is estimated to be about 50 liters per min at a few mm of mercury above atmospheric pressure. The arc was held in the H2-TiC14 mixture at 400 amp with little difficulty. After 10 min the arc burned through the copper lining above the melt, admitting water and ending the run. (This had happened frequently in straight melting runs under argon, and is not thought due to the atmosphere used.) In the furnace were found an ingot, several small pieces, and a little metallic powder, evidently formed when water entered the hot furnace. Some titanium also clung to the electrode. The portions were weighed and separately analyzed for titanium. Their total weight was 321.76 g of 94.82 pct overall purity. Much of the impurity consisted of tungsten broken off when the titanium was removed from the electrode. No detailed impurity analysis was made because the starting materials were impure and flooding the furnace introduced further contamination. Thus, the metal recovered contained 305.08 g Ti, as compared to 291.12 g in the starting batch. Titanium could not have been carried over from previous melting runs in the furnace, as the interior was sandblasted and the electrode ground clean before the run. Evidently at least 13.96 g of Ti were produced from TiCl4. Since this would require complete reduction of 430 liters of TiCl, gas at 12.6 mm of Hg, the efficiency of the process must have been rather high. Experimental work is continuing. No reason is seen why the process could not be scaled up to the size of a 30-ton steel-melting arc furnace. In a large unit there would be a large molten pool from which liquid metal could be withdrawn for alloying and casting. The problems of electrodes and power supply are similar to those arising in arc furnaces for melting titanium. Unreacted TiC14 and the HC1 in the exhaust gases could be recovered; unreacted H2 could be dried and re-used. The melt would be saturated with hydrogen, whose solubility in liquid titanium is unknown. Small amounts of hydrogen seem to have little effect on the properties of titanium.5 If the amount introduced was so large as to impair properties or cause casting difficulties, it could be reduced by holding the melt under an inert gas or by pumping on it, prior to casting. Acknowledgment The authors would like to thank I. Preble and M. Goldman for their valuable aid in the experimental work and the thermodynamic calculations, respectively. References 1R. J. Lockhart, J. J. Ward, M. J. Hussey, and J. W. Clegg: In unpublished report, "U. S. Air Force Project Rand. Titanium and Titanium Base Alloys." Battelle Memorial Institute (1949) 37-44. 2 L. Brewer et al: Chemistry and Metallurgy of Miscellaneous Materials—Thermodynamics. Ed. by L. L. Quill. pp 13-39, 60-192. (1950). McGraw-Hill Book Co. 3 K. Arii: Scientific Reports. Tohoku Imp. Univ. (1933) 22, 182. 4 R. S. Dean, J. R. Long, F. S. Wartman, and E. L. Anderson: Transactions AIME (1946) 166, 369-381; Metals Technology (Feb. 1946) TP 1961E. * R. I. Jaffee and I. E. Campbell: Transactions AIME (1949) 185, 646-654; Journal of Metals (Sept. 1949) TP 26813.

Jan 1, 1951

By M. I. Brittan

Discussion Dr R. E. Robinson (Fellow): The author must be congratulated on a very meticulous and self-contained piece of work. It is indeed a pleasure to read a paper that is so clearly and systematically laid out, and where the conclusions and the testwork conducted have been so clearly described. The paper is complete in itself, which makes it very difficult for someone who is not intimately involved in the whole Torco project to make any comments on its content. However, two points that, strictly speaking, fall outside the scope of the paper are of considerable interest. The first relates to the particle size of the material treated. In the paper, the testwork is confined to one standard particle size (minus 60 plus 100 mesh). The essential feature of the paper is to indicate that the rate-controlling reaction in the whole segregation process is the rate of reaction of the ore particles with the reducing agent and the hydrogen chloride. One wonders, therefore, to what extent this relatively slow rate of reaction is affected by the particle size of the ore itself. One imagines that the reaction must take place by contact of the hydrogen chloride with the surface of the mineral particles, and it is reasonable to suspect that the rate of diffusion of the copper ions to the surface is a relatively slow process and is thus the limiting factor in this particular rate of reaction. It is possible, for example, that the improvement obtained, when the ore is subjected to reducing conditions before the chlorination, is due to a breakdown in the crystal structure of the original particle. This breakdown is brought about by the reduction and by the consequent increase in surface area available for reaction with hydrogen chloride. Can the author indicate whether any work has been done along these lines, and whether it has been established that the reaction depends on the surface area available? The second point relates to the application of this kinetic study to the actual operation of a Torco reactor. It was once planned to feed the sodium chloride, together with the reducing agent, into the top of the segregation chamber. In the paper, the author mentions that it has now been established that the segregation chamber behaves, to all intents and purposes, as a fluidized bed, and that there is, therefore, a rapid evolution of gas in the lower regions of the chamber, which, it is imagined, displaces the gas phase rapidly. Since the reaction between sodium chloride, water vapour, and the aluminium silicates in the ore is extremely rapid, one wonders how much of the hydrogen chloride produced is removed from the reaction zone before it has had time to react with the copper minerals. The extremely low consumption of sodium chloride (which is a vital feature of the Torco process) must depend on an extremely rapid circulation of the hydrogen chloride gas to all the ore particles in the segregation chamber. One wonders, therefore, if a system for the introduction of the sodium chloride into the bottom regions of the chamber might not result in even greater efficiency in the utilization of sodium chloride. ProC D. D. Howat (Fellow): All of us who have been concerned with the study of chemical reactions at high temperatures are keenly interested in kinetics and are well aware that this is not an easy study experimentally. Dr. Brittan is to be congratulated on the development of neat experimental methods and for his full discussion of the results obtained. Although the segregation process for the extraction of copper from oxide and silicate ores has been known for almost fifty years, the fundamental chemical and physical changes involved have been little understood and the fundamental data are very scanty. The work now in progress at A.A.R.L., together with that sponsored by the Anglo American Corporation in other research institutions throughout the world, is bound to produce new fundamental data and a much more complete understanding of this rather fascinating process. It is already apparent that some of the old and well-worn chemical reactions that were postulated to occur, just cannot take place in the way which was formerly accepted. Dr Brittan's work, carefully conducted and thoroughly analyzed as it has been, still leaves us with one great outstanding problem. The thermodynamic data and the possible reactions set out in Table I (page 281) of his paper leave us asking, in complete despair, how can copper be converted into a volatile chloride in the presence of HCl, CO and carbon at temperatures about 800°C? The thermodynamics all combine to show that copper should be reduced to metal as the first step in the process. This brings us right up against the second problem. If copper were reduced to the metal how would HCI convert it to the volatile chloride? On top of these problems is the unknown reason for the very high speed of reaction between CO, HCI and the ground copper ore. Still further into the region of the unknown is the reaction by which gaseous hydrochloric acid is produced in the actual process. Perhaps Dr Brittan is feeling grateful that he doesn't have to try to explain this reaction-at this stage of the research programme at least. The results very clearly show that both CO and HCl gas are essential for rapid production of the volatile copper chloride. Dr Brittan states that 18 minutes were required to attain 83 per cent extraction with HCl gas alone and this was reduced to 4 minutes when CO was

Jan 2, 1970

By R. W. Bartlett

The rates of oxidation of tungsten have been determined at temperatures between 1320" and 3170°C and oxygen pressures to 1 amn using a surface -recession measurement technique. Above approximately 2000°C and 10-6 atm the rate is independent of temperature and can be calculated from gas collision theory assuming a constant reaction probability, e, of 0.06. Oxygen molecules react at surface sites where oxygen atoms have previously chemisorbed. This provides a direct pressure dependence at low pressures but at high pressures tungsten oxide molecule s form an adjacent gas boundary layer which lowers the PO2 at the tungsten surface. A correction for this effect using free-convection theory fits the rate data over the entire oxygen-pressure range from 10-8 to 1 atrn as well as data using O2-A mixtures. Below 10-6 atrn and above 2000°C, e decreases with increasing temperature because of desorption of oxygen atoms. Below 2000°C the rate decreases with decreasing temperature at all oxygen pressures following an apparent activation energy of 42 kcal per mole and depending on (Po2)n with n varying between 0.55 and 0.80. MOST of the previous tungsten oxidation studies have employed gravimetric methods and have been limited to temperatures below 1000°C where the weight loss associated with evaporation of tungsten oxides is negligible compared with the weight gain from oxidation.' At higher temperatures, oxygen-consumption rates have been determined from pressure measurements, usually at constant flow rates, by Langmuir,2 Eisinger,3 Becker, Becker, and Brandes,4 and Anderson.5 The sensitivity of this method decreases with increasing pressure and, with the exception of Langmuir's work, these investigations were confined to pressures below 10-6 atm. Above approximately 1300°C, depending on the oxygen pressure, the rate of oxide evaporation is greater than the oxide-formation rate and the recession of the tungsten surface can be measured optically without interference from an oxide layer. This was first done by Perkins and crooks6 who heated tungsten rods in air pressures from 1 to 40 torr at temperatures between 1300" and 3000°C. The present investigation of the oxidation kinetics of tungsten at high temperatures emphasizes oxygen pressures from 10-6 to 1 atm. This is the range of interest for earth atmosphere re-entry applications of tungsten for which little data were previously available. APPARATUS The apparatus is a modification of the type used by Perkins and crooks.' Ground tungsten seal rods, 6 in. long by 0.125 in. diam, were mounted vertically between two water-cooled electrodes, one fixed and the other having free vertical travel. The movable counter-weighted electrode is prevented from undergoing horizontal displacement by three sets of runners mounted at 120-deg intervals. Electrical contact is made by means of a water-cooled mercury pool. A 24-in. vacuum bell jar having a volume of approximately 267 liters was used as the reaction chamber with the sample holder mounted in the middle of the chamber. Power was supplied from an 800-amp dc variable power supply. Temperature readings were made by means of a Latronics automatic two-color recording pyrometer. With this instrument, corrections for emissivity are not necessary provided the spectral emissivi-ties at two closely spaced wavelengths are equal. Supporting measurements were made with a micro-optical pyrometer corrected for emissivity of bare tungsten and window absorptivity. The micro-optical pyrometer was calibrated against a National Bureau of Standards calibrated tungsten lamp and both pyrometers were periodically checked against the melting points of tungsten and molybdenum using the oxidation apparatus. Above 10-6 atm, pressures were measured with an Alphatron gage calibrated against a McCleod gage. At 10-6 atm, a hot-filament ionization gage was employed. A magnified image of the self-illuminated tungsten rod was formed using a 360-mm objective lens mounted outside the bell jar. When the experiment exceeded 1 hr, the image was focused on a ground-glass plate about 10 ft from the tungsten rod at about X8 and the recession of the thickness of this image was monitored with a Gaertner cathe-tometer. When faster rates were encountered, a 35-mm time-lapse cinecamera with a telephoto lens and bellows extension was substituted for the ground-glass plate and cathetometer. Diameter recession rates were determined from the photograph image projected on the screen of an analytical film reader. EXPERIMENTAL PROCEDURE After installing the rod in the apparatus and cleaning it with acetone, the system was evacuated to 5 1 x 10-5 torr. Before oxygen was introduced,

Jan 1, 1964

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

By A. Lubinski

In drilling operations, attention generally is given to hole angles rather than to changes of angle, in spite of the fact that the latter are responsible for drilling and production troubles. The paper presents means for specifying maximum permissible changes of hole angle to insure a trouble-free hole, using a minimum amount of surveys. It is expected that the paper will result in a decrease of drilling costs, not only by avoiding troubles, but also by removing the fear of such troubles. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS Excessive dog-legs result in such troubles as fatigue failures of drill pipe, fatigue failures of drill-collar connections, worn tool joints and drill pipe, key seats, grooved casing, etc. Most of these detrimental effects greatly increase with the amount of tension to which drill pipe is subjected in the dog-leg. Therefore, the closer a dog-leg is to the total anticipated depth, the greater becomes its acceptable severity. Very large collar-to-hole clearances will cause fatigue of drill-collar connections and shorten their life, even in very mild dog-legs. Another finding regarding fatiguing of collar connections in dog-legs is that rotating with the bit off bottom sometimes may be worse than drilling with the full weight of drill collars on the bit, mainly in highly inclined holes when the inclination decreases with depth in the dog-leg. Means are given for specifying maximum dog-legs compatible with trouble-free holes. An inexpensive technique proposed is to take inclinometer or directional surveys far apart; then, if an excessive dog-leg is detected in some interval, intermediate close-spaced surveys are run in this interval. The application of the findings should result in a decrease of drilling costs, not only by avoiding troubles, but mainly by removing the fear of such troubles. The result would be much more frequent drilling with heavy weights on bit, regardless of hole deviation. Because of errors inherent to their use, presently available surveys are not very suitable for detecting dog-legs. There is a need for instruments especially adapted to dog-leg surveys. Crooked hole drilling rules should fall into two distinct categories—(1) those whose purpose is to bottom the hole as desired, and (2) those whose purpose is to insure a trouble-free hole. Three kinds of first-category rules in usage today are as follows. 1. A means to bottom the hole as desired is to prevent the bottom of the hole from being horizontally too far from the surface location; this may be achieved by keeping the hole inclination below some maximum permissible value such as, for instance, 5. 2. Another means to achieve the same goal is to limit the rate at which the inclination is allowed to increase with depth. A frequently used rate is 1/1,000 ft. In other words, a maximum deviation of l° is allowed at 1,000 ft, 2 at 2,000 ft, 3 at 3,000 ft, etc. 3. Whenever application of the first two means precludes carrying the full weight on bit required for most economical drilling, then the best course is to take advantage of the natural tendency of the hole to drift updip, displace the surface location accordingly and impose a target area within which the hole should be bottomed. This method has already been successfully applied,'.' and its usage probably will become more frequent in the future. Means for calculating the amount of necessary surface location displacement are avail-able.3'5'6 If in high-dip formations the full weight on bit should result in unreasonably great deviations, the situation could be remedied by increasing the size of collars and (if needed) the size of both hole and collars,351 or in some cases by using several stabilizers. Rules which would fall into the second category (i.e., rules whose purpose is to insure a trouble-free hole) are seldom specified today. It is vaguely believed that following Rules 1 and 2 of the first category will automatically prevent troubles. Actually, this is not true. If at some depth the only specified rule is that the hole inclination must be less than 4", the hole may be lost if the deviation suddenly drops from 4 to 2, or if the direction of the drift changes, etc. Rule 3 of the first category is generally used in conjunction with a rule belonging to the second category, namely, that the hole curvature' (dog-leg severity) must not exceed the arbitrarily chosen value of 1½ /100 ft. Moreover, when using this rule, the industry is not clear over what depth intervals the hole curvature should be measured. All this results in a frequent fear

By L. A. Wilson, P. J. Root

The relative costs of heating a reservoir by steam injection and by combustion have been examined. The comparison was based on a model similar to that proposed by Chu.' The cost of boiler feed water, the price of fuel, pressure and plant capacity were parameters in determin-ing the costs of air compression and steam generation. The analyses compare the cost of heating to the same radius by the two methods. Results suggest that the two primary factors for comparison are the price of fuel and the amount of crude burned during underground combustion. The cost of fuel has a greater effect on the cost of heat from steam than it does on its cost by combustion. As a result, analyses indicate that when the price of fuel is low, steam may be unequivocally cheaper than air. The influence of heat loss is such, however, that as the heated radius increases combustion becomes relatively more competitive depending upon the amount of crude burned. This implies that steam may be cheaper for small stimulation jobs (huff and puff) but combustion may be more economically attractive for heating large areas (flooding). INTRODUCTION Use of thermal methods of recovery is an accepted fact today. After an induction period of several years, processes are being widely used that involve reservoir heating to augment recovery. Of the several techniques, steam injection and forward combustion appear to be destined to dominate the field. Although the objectives of both are the same, the basic differences between generating heat in situ and injecting heat after surface generation influence the cost in different ways. This study compares the cost of heating a reservoir either by steam injection or by forward combustion. There has been no consideration of recovery. Presumably, recovery from the swept region would be high in either case. The sole consideration was the cost of heating to the same radial distance by either process. PROCEDURE THE MODEL The basis for comparison was a mathematical model similar to that used by Chu' for combustion. The model simulates a radial heat wave in two-dimensional cylindricaI coordinates. It includes heat generation, conduction and convection within the reservoir and conduction in the bounding formations. Thus, heat losses from the formation are considered. Three significant modifications were made. 1. Equal logarithmic increments rather than equal increments were used for the mesh spacing in the r direction. By this technique large distances were simulated with relatively few mesh spaces. 2. A backward difference approximation to the convection term was used to avoid troublesome oscillations which result from a central difference approximation when the convection term is large. 3. The radial increments of the combustion zone motion were not necessarily uniquely related to the mesh configuration. The cumbersome step function introduced by the heat of vaporization of steam was circumvented by assuming the enthalpy of the steam to be a linear function of temperature between reservoir temperature and steam temperature. This is equivalent to assuming an average heat capacity numerically equal to the difference between the enthalpy of saturated steam and the enthalpy of water at reservoir temperature divided by the difference between the two temperatures. Heat losses obtained by this model are in essential agreement with those obtained by the analytical solution of Rubenshtein.' A detailed description of the model is presented in the Appendix. Using the model, the times required to heat to particular radial distances were obtained as a function of injection rate and other physical parameters. For the steam case, injected fluid was assumed to be saturated steam at pressures of either 500, 1,000 or 1,500 psia. The corresponding temperatures are 467, 544 and 596F, respectively. Thickness ranged from 10 to 50 ft and injection rate ranged from 100,000 to 1 million Ib/D. Reservoir and overburden temperatures at the injection well were assumed to be that of saturated steam at the injection pressure. The effect of maintaining the overburden temperature at the well at a different temperature (initial reservoir temperature) was examined with no significant change in behavior. The influence of wellbore heat losses for the steam case was determined in the following manner. The rates of heat loss as a function of time were estimated using an approach similar to that suggested by Ramey." he data were based on injection through 2%-in. tubing in 7-in. casing. Integration of these data over the entire iniection period yielded the total heat loss. Total heat losses were then corrected to their equivalents in steam (this number resulted from dividing the total heat loss by the latent heat). This was considered additional steam required to accomplish the reservoir heating and the total cost was increased accordingly.

Jan 1, 1967

By J. W. Graham

For many years the author has been cognizant of the difficulty encountered by some in treating with the water influx formulas for unsteady-state fluid flow as pertain to the material balance equation. This has particularly applied in establishing reservoir performance and identifying reservoir pressure, which to the practicing engineer has entailed a trial-and-error procedure, and for others has necessitated resorting to computing devices and reiteration processes. In retrospect this difficulty stems from the fact that reservoir pressure in the material balance formulas, as well as associated with the water influx equations, is an inexplicit term, and the work reported in the past is irrefutable. However, what will be presented in this paper is another approach to the problem, whereby the entire material balance equation will be treated by the Laplace transformation, and reservoir pressure which hereto has been inexplicit, can now be isolated by mathematical procedure to relate that parameter with all the factors contributing to its change. This is the simplification entailed, that treats first with an undersaturated oil reservoir as an integrated effect from the inception of production. The second phase pertains to saturated oil reservoirs that encompass a survey traverse. Although both methods of approach are necessarily different in aspect, the most interesting fact is that the mathematics so deduced are identical. Both the linear and radial water-drive systems are incorporated. for which an illustrated factual example is offered for the latter, treating with a saturated oil reservoir. INTRODUCTIO N What is performed in this work is the simplification of an involved computation by advanced analysis. Although such may be construed as a contradiction when one treats with higher mathematics; nevertheless, when direction is given to such an undertaking the results car. be most revealing. Likewise, it is to be mentioned that the bases for these mathematics have been developed on the expediency of the occasion. This is not to be inferred as a qualification of this work, but rather the demands frequently placed upon the author in his private prac- tice in meeting a time limit. A situation, instead of being fraught with hazards, often has given emphasis to creative thought. What will be entailed in this work is the simplification of the material balance formulas by the Laplace Transformation., Although this reveals entirely new horizons that will be given expression in a forthcoming tract, it suffices in the present instance to limit our attention to this phase of the development that treats both with an undersaturated and saturated oil reservoir. To orient the reader's thoughts as to what is involved in this simplification is the recognition that reservoir pressure, as such, is an inexplicit term in the material balance equation. This is the independent parameter that defines the total history of performance in the author's' unsteady-state water influx formulas, as well as the basis for the physical dependency of fluid behavior within the formation as prescribed in the Schil-thuis' material balance equation. Therefore, to isolate reservoir pressure, which is the most essential factor in any reservoir study, is rather a cumbersome procedure entailing either a trial-and-error calculation for the engineer; or as some prefer, a reiteration process performed on a computing device. However, once such an equation can be transcribed as a Laplace transformation, this inexplicitness so expressed can be alleviated to identify reservoir pressure as an explicit function of all the factors contributing to its change. This is the simplification encompassed, that will treat first with an undersaturated oil reservoir as an integrated effect from the inception of production, and secondly, with a saturated oil reservoir as a survey traverse. Although the two approaches are necessarily different because of the uhvsics involved. it is an interesting commentary that the mathematics are identical, showing the interdependency of the two methods. In order to acquaint the reader with this development, the simplest case will be treated first; namely, an under-saturated oil reservoir subject to a linear water drive. However, what may be construed for this example as an idealistic case is actually a most practical application in certain parts of the world, where the size of the fields are so large that radial water-drive approaches the configuration of a linear drive. Further, to avoid the repetition of much symbolism, frequent references will be made to the work of the author and an associate on Laplace Transformations3,