Search Documents

By J. R. Dawson, J. A. Glunt

VESTA No. 4 and 5 mines supply most of the high volatile coal required for Jones & Laughlin's byproduct coke plants. Until 1944 all coal produced in these mines was loaded by hand. Pressure to mechanize at Vesta was brought on by the manpower shortage in World War 11, and in 1943 a decision was made to change to mechanical loading. It was the opinion of those concerned that by use of selective mining the coal would be clean enough to be processed by the existing preparation plants. At that time coal cleaning at Jones & Laughlin consisted of hand picking the larger sizes at the mine tipples and wet washing at plants located at the Pittsburgh and Aliquippa Works. A typical section of the Pittsburgh seam as it occurs at Vesta is shown in Fig. 1. The 14 to 16 in. of drawslate immediately over the coal is too soft to be used for roof and must be taken down, leaving the rooster coal just above for roof. In selective mining an attempt is made to mine the coal under the drawslate first and then load out the drawslate separately as refuse. In full seam mining slate and coal are shot down at the same time and loaded out. Mechanical loading at Vesta created new problems. It was found that selective mining, even when carefully applied, increased the refuse in the raw coal to such an extent that the washers at the mills were unable to handle it. Large tonnages of refuse were being transported, a reject disposal problem was created, and good metallurgical coal was being loaded out and lost. In addition, the selective method handicapped operation of the loading machines. Fig. 2 shows how the ash content of the raw coal increased as mechanization proceeded at No. 5 mine. New Preparation Plant: After an exhaustive study of this situation by J & L management, is was decided that a preparation plant should be constructed at the mines, capable of handling full seam mined coal and large enough to process full production of both No. 4 and No. 5 mines. It was decided that from the standpoint of inside operation and haulage the new plant should be located as near as possible to the old No. 5 tipple on the Monongahela River near Vestaburg. Full seam mining at Vesta could be expected to produce a tremendous volume of refuse along with the coal, since 14 to 16 in. of slate would be mined with an average 78 in. of coal. Disposal of this refuse required serious consideration in selecting a plant site. The only area near Vestaburg large enough for disposal of the plant refuse was across the Monongahela River at LaBelle. Ample space was available here, and construction at this location would not interfere with operation at the No. 5 tipple. It had been noted over the years that the sulfur content of the coal produced at Vesta was gradually increasing, and there was every indication that this increase could be expected to continue as the mines developed further from the river. It was decided to construct a three-part separation plant with complete blending facilities to produce both metallurgical and steam coal. In this system an attempt is made to reduce the sulfur in the metallurgical coal in a secondary cleaning process. Construction of the new preparation plant got under way early in 1947 and continued until the spring of 1950. The plant was designed to handle 2400 tph of raw coal containing 30 to 35 pct refuse. Cost of outside buildings and equipment was about $14 million. Total cost of the plant, together with improvements and changes made at this time, was approximately $21 million.

Jan 1, 1957

By Jesse A. Miller

ALTHOUGH the element titanium was discovered by William Gregor in 1790, over a hundred years passed before it was put to commercial use. The first commercial application of titanium was as an alloy additive to iron and steel, and the first ferroalloys were produced domestically in 1906. Titanium pigments were developed somewhat later and have been produced in the United States since 1918. The use of titaniferous material in welding-rod coatings first gained acceptance ill the mid-30's. The metal titanium has only had commercial importance since 1948; domestic production for that year was 10 tons. The relative importance of these major uses of titanium in various forms may he gaged by the consumption of titanium dioxide (Ti02) for these purposes in 1954. Of a total of 440,000 short tons of Ti02 consumed in 1954, 95 percent of the total was consumed for pigments; 2 percent for welding-rod coatings; 1 percent for non-titanium-base alloys and carbide; and 2 percent for miscellaneous uses. The titanium-metal industry is in its infancy, but it has more than doubled its output every year from 1948 to 1954, reaching 5,370 short tons in 1954.

Jan 1, 1957

With the sinking of the No. 3 Shaft at North Broken Hill Limited, it was necessary to construct adjacent to the shaft a new changehouse for mining and surface personnel.It was also probable that as the older sections of the North and British leases were worked out, all employees at present working in these sections would be transferred to the No. 3 Shaft area. This could ultimately result in all personnel employed by North Broken Hill Limited being concentrated in this area, requiring the construction of new administration offices, workshops, mine store, etc., also in this area.

Jan 1, 1957

Jan 1, 1957

By A. F. Bertuzzi, M. R. Tek, F. H. Poettmann

A method is presented for predicting pressure drop for two-phase fluid flow in horizontal pipes. A set of 267 experimental measurements randomly sampled from approximately 1,000 measurements from various literature sources was used. Pressure gradients calculated by the procedure developed and compared with the experimental values showed a bias of +0.82 per cent and a standard deviation of 20.8 per cent. The advantatges of this method over other available methods of predicting two-phase flow pressure drop are (a) its comparative simplicity of application, (b) its relative independence of flow patterns, (c) its accuracy, which on the basis of a statistical evaluation predicts pressure drop closer than other available methods, and, (d) its ability to satisfactorily correlate laboratory data from various sources while the correlations from these sources do not appear to agree with one another. The method has been reduced to a simplified graphical procedure, suitable for field use. A two-phase f factor is defined and correlated with parameters involving the flowing gas-liquid mass ratio, a Reynolds number for the gas phase, and a Reynolds number for the liquid phase. The choice of parameters allows the correlation to reduce to the usual f factor plot for the limiting conditions of (111 gas or all liquid. INTRODUCTION The mechanics and characteristics of two-phase flow systems have been of interest throughout the industry for some time. In numerous engineering installations such as pipe lines, chemical reactors, and heat exchangers, two-phase flow conditions are of every day occurrence. In oil production operations it has been desirable, in some cases, to consider transporting gas and oil together in a common pipe from oil field to process plant. The trend toward centrally located stock tank batteries in oil fields has resulted in longer gathering pipelines in which more than one fluid phase is flowing. The increase in the producing capacity of oil wells due to new production tech- niques has created the need for review and re-design of many surface gathering lines for properly handling the increased production. Optimum pipe size for the situations described above has become an important factor. The problem which is of interest here involves the ability to predict the relationship between pressure drop, fluid properties, fluid rates, pipe diameter, and pipe length. Although the literature1,5,10,13,18,19 contains various articles dealing with specific cases of the problem, Lock-hart and Martinelli17 proposed the most general solution. Their method has been later modified by Baker:1 Alves2 demonstrated that different flow patterns are possible for a flow mechanism defined by Martinelli such as gas turbulent, liquid turbulent. Baker explained deviations experienced with Martinelli's correlations on the basis that different flow patterns could exist for the same flow mechanism. Using Martinelli's method of correlatioil, Baker correlated data for each flow pattern for the turbulent-turbulent flow mechanism. Bergelin and Gazley6,7 presented a correlation for predicting gas phase

Jan 1, 1957

Six years ago it was my responsibility to give the presidential address, and now that privilege has come my way again. On that occasion we were gathered atWhyalla and I took the opportunity of putting before members some observations on the problems we then faced in Australia, and some gains we had been able to chalk up during those early postwar years. You may recall that we were then just beginning to emerge from the difficulties of postwar reconstructions - of fuel and power shortages, and a grossly inadequate manpower for the tasks facing us. The expansion of manufacturing industry in Australia greatly stimulated by wartime activities, and by the postwar developments of many institutions - ran ahead of the supporting services and of the supply of labour to do thejobs. For many industries this unfortunate state of affairs had meant operating at rates well below their installed capacities and therefore levels of output insufficient for Australia's rapidly growing needs. When I last spoke to you these problems were still with us, though their intensity was beginning to lessen as a result of vigorous efforts by industry and governments to reduce them. But I must confess that my thoughts on that occasion were full of those problems and of the effect they were having on the iron and steel industry of this country-of the coal shortage, the labour shortage, and the many other difficulties we were then faced with - and all at a time when the stepping up of our postwar expansion programme was of vital concern to all of us.What a different picture it is six years later! How greatly has the scene changed for the better. In 1951 Australia's postwar immigration programme was only in...

Jan 1, 1957

By Frederick C. Langenberg

IT has been shown1 that copper can be removed from iron-base alloys by solvent extraction with molten lead and sodium sulfide slags. In these processes copper removal is favored by a positive deviation of copper in iron from ideal behavior. Chou' determined the distribution of copper between liquid silver and iron and obtained a value for the activity coefficient of copper in iron at 1600°C, y°, of 9.12. Chipman" calculated the activity coefficient from the Fe-Cu phase diagram to be 12 at 1600°C. More recent work by Koros and Chipman" yields a value at 1600°C for y V equal to 8.0. In this latter work, the distribution of copper between silver and iron was measured at 1600°C, while the activity of copper in the silver phase was determined from calculations based on the Ag-Cu phase diagram. The present work presents another value of based on calculations from the Cu-Pb phase diagram, on the heat of mixing data for the Cu-Pb system, and on an experimental study of the distribution of copper between iron and lead at 1600°C. These experiments were part of a larger research on the removal of copper from iron-base alloys conducted at The Pennsylvania State University. Experimental Procedure—The distribution of copper between pure iron and lead at 1600°C was made in the furnace assembly shown in Fig. 1. The melts were made in high purity alumina crucibles under an atmosphere of prepurified argon. Temperatures were read with an optical pyrometer sighted into a %-in. hole drilled in the inductor. Extensive calibration of the optical readings with immersion readings had been carried out previously. The initial charges consisted of 100 g of electrolytic iron and varying weights of copper. The melts were brought rapidly to 1600°C and 75 g of lead added. The temperature was quickly readjusted to 1600°C, and the melts were held for 10 min at this temperature. A sample was then drawn from the iron layer in a fused silica tube. This sample was analyzed to determine the copper content of the iron layer at equilibrium, while the copper content of the lead layer was determined from a material balance. The validity of the material balance was confirmed by a chemical analysis of the entire lead layer for one heat in which the crucible was removed and quenched after the iron sample was taken. The calculated copper content of the lead-rich phase was 1.18 pct; while the entire lead layer analyzed 1.20 pct Cu. The distribution results are shown in Fig. 2. The distribution constant, N,.'r'"/N, is equal to 3.95. Discussion—From the Cu-Pb phase diagram' it can be seen that lead-rich liquid Pb-Cu solutions

Jan 1, 1957

By A. T. Corey, J. H. Henderson, M. R. J. Wyllie, C. H. Rathjens

The results of three-phase relative permeability tests on nine water-wet consolidated Berea sandstone samples are presented as composite ternary diagranls showing isoperms of oil, water and gas. Capillary pressure control was exercised over the flow of gas and oil in the presence of water. The water saturations ranged from 17 to 71 per cent pore volume. A method of calculating both the oil and water permeabilities of a three-phase system from the easily measured gas relative permeability is presented. EXPERIMENTAL PROCEDURE AND RESULTS A renewed interest has been shown in three-phase relative permeability as a result of recent developments involving underground combustion processes, steam injection, and other multiphase displacement processes. The experiments and results described here involved simultaneous flow of oil and gas in consolidated Berea sand with brine present as the wetting phase. Gas and oil relative permeabilities were measured on nine cores with CaC12 brine present as the wetting phase in saturations ranging from 17 to 71 per cent. The average residual liquid saturation of the cores was approximately 20 per cent. In order to make certain that brine was the wetting phase, the test cores were saturated with brine before contact with hydrocarbons. As an added precaution to avoid having oil displace brine from the wetting position as a result of changing wettability, each core was only used twice, i.e., first with a fixed percentage of brine and then for a gas-oil permeability determination with no brine present. The results, therefore, are presented as composite ternary diagrams representing the flow tests on nine individual cores having very similar properties. All tests were made using a modification of the capillary pressure techniquc described elsewhere. The effective oil permeability was measured before gas was introduced using a very small pressure gradient (a few centimeters of oil). This determination was made without selectively wet barriers in contact with the core. The cores were then placed between capillary barriers and gas-oil relative permeability curves obtained. The capillary barriers had been made water repellent with a silicone treatment. In determining gas-oil-water relative permeability in this fashion, control was exercised over the capillary pressure existing between the gas and oil. No control was exercised over the pressure difference existing between the oil and water. Athough an equal pressure gradient was applied to the gas and the oil phases, this pressure gradient does not exist in the water phase. Since the pressure gradient across the core was always much less than the displacement pressure of the fully saturated core, the pressure gradient can have caused only a very slight distortion of the oil-water interfaces. This slight distortion of the oil-water interfaces had a negligible effect on the validity of the oil permeabilities measured. The oil permeability, measured in the presence of water but with no gas present, was in every case equal. within experimental error, to the gas permeability of the gas-oil system when the oil saturation was the same as that of the water. Gas and oil relative permeabilities were plotted as a function of total liquid saturation. It was found that the gas relative permeability curves obtained on cores with brine present were identical with those obtained on the same cores with no brine present. The denominator for calculating oil relative permeabilities was the permeability found by extrapolation to infinite mean pressure (A la Klinken-berg). Fig. 1 illustrates gas-oil relative permeability results obtained on a typical core. The solid permeability curves represent the experimental data. The dashed oil relative permeability curve was calculated using the relationship;

Jan 1, 1957

By Paul A. Beck, A. H. Lutts

IN a previous paper' isothermal softening and X-ray line sharpening data were reported for the annealing at 350°C of single crystals of pure aluminum rolled on the (110) plane in the [112] direction. It was shown that, after rolling to 80 pct reduction in area and careful etching in such a manner as to eliminate extraneous orientations by removing surface material and disturbed areas adjacent to saw cuts, the specimens may be extensively annealed at 350°C without any observable recrys-tallization. At the same temperature, the line broadening caused by cold rolling was found to disappear practically completely after less than 200 sec of annealing. The present work was undertaken in order to study the temperature dependence of line sharpening and of the initial softening with high purity

Jan 1, 1957

By S. M. Runke

The pegmatite investigations at the Rapid City, S. Dak., Experiment Station during; the pact 3 years have been primarily a study of recovering beryl from nonlithium-bearing pegmatite rock by continuous-testing methods. Beryl concentrates containing 25 to 88 percent beryl were produced from rock that ranged in beryl content from 0.1 to 2.5 percent. The beryl recovery ranged upward from 70 percent but averaged better than 80 percent. Although promising results have been obtained with flotation methods for upgrading these concentrates to standard specifications, additional work is needed to improve and simplify the procedure. In addition, it was demonstrated that several potentially useful coproducts could also be recovered from pegmatite rock. The principal coproducts were mica, feldspar, and quartz. A heavy-mineral product also was made from pegmatites containing tin, tantalum, and columbium. The recovery if these minerals in products meeting the specifications of the commercial users has been reserved for future study. The investigations also included studies on extraction of beryllium from both high-grade beryl and flotation concentrates of medium beryllium content. The procedure investigated consisted of sintering beryl or beryl flotation concentrates with limestone, acid curing the resulting sinter with sulfuric acid to dissolve the beryllium, and water leaching to extract the beryllium. Over 90 percent of the beryllium was extracted by this procedure. Most of the optimum conditions and quantities of reagents were determined for dissolving the beryllium. As aluminum and iron also were taken into solution by the acid, further research is needed on methods of recovering high-grade beryllium salts from the solutions containing these elements.

Jan 1, 1957

By C. Norman Cochran, James L. Brandt

ALTHOUGH gas in aluminum and its effect on aluminum products have been the subject of a number of papers, not many quantitative determinations of the hydrogen content of solid aluminum and its alloys have been recorded in the literature. For solid aluminum samples, four investigators have reported hydrogen contents which appear reasonable compared with the hydrogen solubility of 0.7 ml per 100 g, STP, in molten aluminum at 660°C established by Ransley and Neufeld' and verified by Opie and Grant' and Ransley and Talbot. Sloman," who used a vacuum fusion procedure, reported the hydrogen content of some high purity aluminum as 0.66 ml per 100 g, STP. Griffith and Mallett, employing the tin fusion method, reported the internal hydrogen content of six different aluminum alloys as ranging from less than 0.1 ml per 100 g, STP, for 1100 alloy to 0.7 ml per 100 g, STP, for 4043 alloy (previously 43S, a 5 pct Si alloy). Eborall and Ransley," using a solid extraction of the gases at 600°C, reported hydrogen contents ranging from 0.1 ml per 100 g, STP, to 1 ml per 100 g, STP. Ransley and Talbot reported that several thousand analyses on 99.2 pct and higher purity aluminum as well as Duralumin type alloys indicated hydrogen contents ranging from 0.1 ml per 100 g, STP, to 0.5 ml per 100 g, STP.

Jan 1, 1957

By A Guinier

RECIPITATION in alloys is undoubtedly one of the most essential phase transformations in metallurgy and, besides, it is a phenomenon of great interest to physicists. It seems then that it can be chosen as a topic for an Annual IMD Lecture. Of course, the subject is a very wide one and I shall discuss here only a very restricted part of it. I should like to show why it is now considered that there is, at the beginning of the process, a stage distinct from the real precipitation, which is the pre-precipitation. We shall be chiefly interested in the atomic structure of the metal in this preprecipi-tation stage. Numerous reviews on this subject have been published recently.', ' The latest was given by H. K. Hardyh t the last meeting of the Institute of Metals in London. One of the most complete articles has been written by the late Dr. Geisler." I should like, at the beginning of this lecture, to pay a tribute to the memory of our friend Arthur Geisler. Some of the ideas which will be developed here are different from those advocated by him. But everybody knows the considerable progress in experiment and in theory which we owe to him and, personally, I deeply feel how fruitful have been the long discussions which we have had during many years. Experimental Basis of the Precipitation Problems Let us recall the essential facts pertaining to the problem of the precipitation. The starting point and the final one are well known. The initial stage is the supersaturated solid solution before quenching. The dissolved atoms replace some of the atoms of the solvent at the points of a definite lattice. It is generally considered that the distribution of the atoms is completely random, and that the lattice distortions are relatively weak. These assumptions are only an approximation. It has now beenproven", that, in some cases, the dissolved atoms have a tendency to segregate to form very small nuclei. These fluctuations of composition are greater than the normal statistical fluctuations in a purely random alloy. We shall see the role played by these nuclei later. The final state is obtained by a very long annealing at such a temperature that an equilibrium is reached in a reasonable time. The alloy is then composed of a matrix which is a saturated solid solution, much poorer than the initial one. Imbedded

Jan 1, 1957

By H. I-Lieh Huang, O. D. Sherby, J. E. Dorn

RECENT investigations1-4 have suggested that the total plastic strain, C, for high temperature creep under a given stress can be correlated by means of a temperature-compensated time, te- where t is the duration of test, e is the base of natural logarithms, aH is the activation energy for creep, R is the gas constant, and T is the absolute temperature. A typical set of data on which this deduction was based is given in Fig. la. Inasmuch as the e-in t curves for the various temperatures are identical except for their displacement along the In t axis where f and are appropriate functions. If the increase in creep rate with an increase in temperature is exclusively ascribable to a single process involv- ing thermal activation, (T) should equal RT and therefore it = constant [2] where ?= te Assuming the validity of this relationship, ? = ?2 at the same strain, or where the subscripts refer to two alternate test conditions.

Jan 1, 1957

By Jules E. Jenkins

IN the past quarter century the seismograph has played an increasingly important role in evaluating vibratory effects transmitted to adjacent communities by industrial blasting operations. In this period research has advanced through two major phases—from falling pin seismometers to three-component recording seismographs. The initial phase of this research is now regarded as the era of recording, during which the seismograph merely recorded occasional events. It has emerged from this stage into the era of control and analysis and in this later period has been recognized as a full-fledged industrial tool. Although the falling pin machines of earlier years indicated probable amplitudes of industrial blasting vibrations, they gave no reliable measure of such displacements, nor did they provide essential information concerning direction or frequency of motion. The first contribution of the three-component recording seismograph was the weight-for-distance formula developed by the U. S. Bureau of Mines. This empirical formula enabled users of commercial explosives to determine beforehand the probable vibratory effects of a blast when the weight of the explosives charge and the distance from the shot point were known. This formula has withstood the test of time and is still applicable for blasts detonated by instantaneous methods. The second major contribution of the three-component recording seismograph followed the introduction in 1945 of short period or millisecond delay detonation. This might be described as a two-stage contribution, the first of which revealed a 50 pct reduction in the vibration magnitude when millisecond detonation was used rather than instantaneous discharge. This second part of this double contribution led to the discovery of the vibration dip phenomena, see Fig. 1. In Fig. 1 the horizontal coordinates indicate the displacements amplitude in inches, and the vertical coordinates, the explosive weight in pounds. The top curve is that of the U. S. Bureau of Mines for instantaneous detonation. Its curvature conforms to the two-thirds power of the explosive weight as provided in the weight-for-distance formula; hence the vibratory effects increase in proportion to an increase in the explosive charge. If the other curves shown below are temporarily disregarded, it may be considered that the entire area below this top curve represents both useful and waste energy. As mentioned previously, when millisecond delay detonation was first investigated it was found that in general the U. S. Bureau of Mines curve could be decreased by about 50 pct, or to the position of the middle curve. At the outset it was assumed that this curve would likewise increase in some proportion to the explosive charge, as did the top curve, that is, the curve would indicate a continuous upswing. As seismographic data accumulated this assumption was found to be erroneous in part. It was discovered that

Jan 1, 1957

By R. D. Westervelt

IN JULY 1954, the first iron ore from the deposits in the Knob Lake vicinity was mined and shipped to Seven Islands. The beginning of the production may well be the greatest advance in Canadian economy in the past fifty years. In 1955, the Canadian iron ore output was more than twice that of 1954, an in-crease due principally to the iron ore shipments from the Knob Lake area. Previous to this, Canada's iron production was 1.85 per cent of the world's output. Now, this percentage has risen to approximately 5.5 per cent and shows every indication of increasing further as the production rate from the area is increased. In 1955 the Iron Ore Company of Canada shipped over 7 million tons of iron ore and expects to ship over 10 million tons in 1956. Present facilities may be enlarged to handle up to 20 million tons per year. If the expected I 0 million tons per year are exported, Canada's iron exports will be second only to her wheat and newsprint exports. Before production began from the Knob Lake deposits, years of development were necessary in the area. Geologists spent several summers mapping the general area in order to unravel the complicated stratigraphy and petrology. Particular attention was paid to the mapping of the iron formation and all stages of alteration from fresh iron formation to ore were observed.

Jan 1, 1957

By Robert L. Rough

The 1954 field tests consisted of six experimental shots in relatively deep holes in a sandstone similar to many oil-bearing sandstones. Water-injection measurements were made before and after each shot to establish the change in conductivity of the fluid caused by the shot. The pressure pulse produced by the shot was recorded in nearby holes to monitor the shot and to determine if any relation existed between the change in conductivity and the nature of the pressure pulse. The results of water-injection tests showed the range of conductivity of fluid before and after shooting with two different types of explosives. Because of the large spread in data for similar shots, not enough information was available to evaluate the differences in increased conductivity produced by the two explosives or any relation between the increased conductivity and the nature of the pressure pulse. However, these results, with the results of other tests involving explosive shots in rock, provide guidance for future research on the oil-well-shooting problem.

Jan 1, 1957

By Herty, C. H.

Iron oxide (FeO) plays an extremely important part in the manufacture of iron and steel. In the three major processes- blast-furnace, open-hearth, and Bessemer converter-iron oxide is the chemically predominant compound and controls to a large ex- tent the operation of the furnaces and the composition and quality of their respective products. In order to emphasize the importance of iron oxide in each process, they will be considered individually in some detail. THE OPEN-HEARTH FURNACE. Iron oxide is introduced into the open-hearth furnace in four ways : 1. The scrap charged into the open hearth is oxidized by the furnace gases, the amount of oxide formed depending primarily on the amount and type of scrap charged. It has been found' that with large scrap, 1.7 Ib. of FeO is formed per 100 Ib. of scrap charged, whereas with scrap of medium size about 5.3 Ib. of FeO is formed per 100 Ib. of scrap charged, when the period between the charging of the scrap and the addition of hot metal is 3 hours. 2. The decomposition of the limestone sets free CO, by the reaction

Jan 1, 1957

Jan 1, 1957

By W. F. Carew, H. D. Kessler, F. A. Crossley

AS part of a program on phase relationships and transformation processes of titanium alloy systems, the titanium-rich corner of the Ti-Mo-V system has been investigated. This region was surveyed primarily to supply information toward the development of a creep resistant, weldable alloy, with a minimum alloy content, for use in the 425° to 550 °C range. Specifically, the investigation was directed toward the development of a stable ß alloy with less total alloying additions than is found in the Ti-30 pet Mo alloy. A secondary objective was the development of a creep resistant, weldable a-ß alloy for application around 300°C. Molybdenum was selected as primary additive to titanium on the basis of an investigation1 which showed that the Ti-30 pet Mo alloy had promising elevated temperature tensile properties. Furthermore, aging studies1 showed no tendency for this

Jan 1, 1957

By J. P. Heller, H. B. Bradley, A. S. Odeh

It is an accepted procedure to represent oil field displacement problems in which the pressure is relatively constant by a potentiometric model. Variations in reservoir permeability thickness product are represented in the model by proportional variations in electrolyte depth. It is shown that significant errors are present wherever these variations are of such magnitude that the consequent differences in the electrolyte depth in the model or any regions therein are appreciable in comparison with their respective horizontal dimensions. To demonstrate the order of magnitude of this error, a hypothetical linear oil field in which permeability varies linearly with distance was treated both analytic.ally and by potentiometric model. The results obtained from the model are compared with the exact solution for various configurations of linear geometry. Deviations in flow times up to 11 per cent were observed. It is confirmed that these discrepancies can be reduced by increasing the areal scale and/or decreasing the vertical scale of the model. It is the purpose of this work to assist in the design of potentiometric models by indicating the relationship between this error and the chosen scale factors. INTRODUCTION The fundamental geometrical criterion which determines whether the pressure distribution in an oil or gas reservoir may be simulated in a conventional potentiometric model is the requirement that all reservoir parameters be constant along any vertical line between its upper and lower boundaries. This situation never obtains exactly; nevertheless, it is usually assumed that there is no permeability stratification within the section of interest, that all wells completely penetrate the sand, that there are no gravitational effects, and that variations in thickness of the sand are small compared to the horizontal extent of the field. In these ways the reservoir problem is reduced to two dimensions in which there is no variation of pressure in the vertical direction within the limits of the sand. Variations in sand thickness and/or horizontal pesmeability may be taken into account as described by Muskat, by considering the fluid conductivity of the reservoir in its horizontal plane to be proportional to the product of permeability and sand thickness. If the variations in sand thickness are small compared to the horizontal dimensions of the reservoir, then it is a good approximation to consider the reservoir problem to be essentially two dimensional. The same approximation, however, is made in the simulation of the assumed two-dimensional reservoir by the electrolytic model. The model, if it is to take into account variations of permeability-thickness product, must of necessity be made in three dimensions, that is, with variable depth. Most potentiometric model studies and theoretical treatments reported in the literature to date2,3,4,5,6,7,8 are those in which either an average permeability was used or a constant permeability was assumed. This is understandable since detailed permeability data are not usually available for the majority of reservoirs. Many investigators have recognized that the failure to incorporate permeability variations within a reservoir in model studies leads to serious error in predictions made

Jan 1, 1957