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By D. C. Lindley, D. H. Gaucher

The displacement of oil by water in a waterflood project is accomplished by the action of transient viscous, gravitational and capillary forces which drive fluid through interconnecting pore spaces toward production wells. The relative importance of each of these forces to the effectiveness of the displacement and the production history depends on properties of the reservoir itself and the manner in which it is operated. There has been considerable discussion'-3 concerning the importance of these factors and the extent to which they control the performance of individual waterflood projects. No data have been presented, however, to demonstrate the effect on waterflood behavior of variations in rock permeability, water-injection rates and mobility ratios in three-dimensional reservoir systems in which viscous, gravitational and capillary forces are allowed to assume the proper relative influence on fluid flow. Much information relevant to water flooding has been gained from the study of field case histories. But, the complexity of the systems involved, the difficulty of defining geometry and obtaining sufficient data, and the fact that the same reservoir is never flooded twice with the same initial conditions, all obscure the role of process variables such as rate. Further, mathematical calculations of waterflood behavior are restricted at this time by available mathematical techniques to highly simplified situations. Scaled models, however, do offer an approach at the present time to evaluation of the effects of the pertinent variables. Several investigators have predicted prototype reservoir behavior from observations of model waterflood performance under a variety of conditions. Two-dimensional aspects of waterflood pattern efficiency have been investigated by Muskat, Aronofsky, Dyes, et al, raig, et al,' and Rapoport, et al. he effects of gravity segregation, viscous fingering and permeability stratification have also been studied in two-dimensional models. Craig, et al," studied the importance of gravitational forces on frontal displacement in three-dimensional models with wells on a five-spot pattern. This work in- vestigates the tendency for water to segregate in homogeneous reservoirs because of gravity and to under-run the oil for a range of water-inject ion rates. The effects of permeability stratifications were investigated by these authors using miscible fluids to simulate water-channeling through permeable strata in systems of negligible capillary force. In this investigation, a three-dimensional model of a five-spot pattern flood was designed to represent typical prototype conditions, and the sand and liquid properties were selected so that capillary, gravitational and viscous pressure gradients were scaled. It was not, however, possible to achieve exact similitude regarding viscous fingering when the more viscous oil was used. The effects of rock stratification on waterflood behavior were studied by changing both the permeability ratio and the position of the more permeable sand stratum in a two-layered, horizontal model. For each type of stratification, constant-rate floods were performed and the rates were varied, in separate experiments, over a tenfold range. To observe the effect of mobility ratio on flood performance, two series of constant-injection-rate floods were performed on the most highly stratified reservoir at a water-oil viscosity ratio of one.

By C. E. Shoenfelt

Jan 1, 1942

By C. E. Shoenfelt

Jan 1, 1942

By F. E. Lathe, L. Hodnett

This paper summarizes extensive data supplied by 40 copper converter plants in 18 countries, and includes a partial analysis and comments on the effect of converter slag composition and temperature on the fomzation and elimination of magnetite and the life of basic and neutral refractories. APRELIMINARY draft of this paper, including data from 26 companies which had submitted replies to a questionnaire, was presented at the Annual Meeting of the AIME held in New York in February, 1956. Publication was delayed in the expectation that additional replies would be received, and justification for the subsequent delay may be found in the fact that the present revised paper contains data from 40 converter plants situated in 18 different countries. The suggestion that a questionnaire be sent to the major copper and copper-nickel plants outside the U.S.S.R. and associated countries arose at the Los Angeles Annual Meeting in February, 1953, where several papers dealing with converter construction and operation were presented. In private discussions which followed, a group of metallurgists and refractories engineers raised the question why practices varied so much at different plants. Why did magnesite brick give superior service to chrome-magnesite in some plants but chrome-magnesite prove superior in others? Would metallurgical studies point the way to the development of still better refractories? Could magnetite formation be prevented in converter slags and reverber-atory furnace mattes? If this was feasible, why was a heavy circulating load of magnetite tolerated, when, in all probability, it increased copper losses in the reverberatory slags and, in some cases, made it necessary to shut down the furnaces periodically to clean out the accumulated magnetite? Was the sole purpose of coating brick with magnetite that of

Jan 1, 1959

By Stanly A. Easton

SEVEN years ago there was installed in the hospital of the Bunker Hill & Sullivan Mining & Concentrating Co. at Kellogg, Idaho, an ultra-violet ray quartz lamp, the standard equipment which is found everywhere in the offices of physicians and among usual hospital equipment. The use of this lamp was con- fined largely to treatment of pathological cases, still treatment of under-nourished children, run-down anemic people, both men and women, and, as a general tonic, was part of the routine hospital procedure. At the latitude of the Ceur d'Alene district and especially because of the position of the towns in deep canyons, with much overcast and cloudy weather, sunshine is not plentiful at any time of the year; for many of the winter months there is scarcely any. Underground workers, particularly during the winter, have little sun- shine; it is not unusual to have none at all for weeks at a time. Treatment by the ultra-violet ray lamp in the hospital has resulted in many extraordinary benefits but the use of the lamp is expensive and limited. Some weeks ago attention was directed to the automatic solarium equipment of the Burdick Corporation. The doctors strongly recommended the increased use of the ultra-violet lamp for its curative powers and tonic effects, urging that it be made accessible to all employees. Real interest was . . also displayed by employees with the possibility of securing ultra-violet ray treatment for themselves and families under better conditions than it was possible to have by the limited use of the lamp at the hospital. This resulted in the installation of the so-called sun room or automatic solarium as an adjunct to the mine change-house. An annex was built to the change-house, with dressing rooms for women, children and men from other departments, and the outfit put into use on Sept. 5, 1929. The installation consists of an escalator, or

Jan 1, 1929

By A. L. Hay

The Sydney coal field, the largest and most valuable in Nova Scotia, is situated on the northeastern coast of the Island of Cape Breton, extending from Mira Bay on the south to Cape Dauphin on the north, a distance of 30 miles, and has a general dip northeast under the sea. (Fig. 1. The field embraces the mining villages of Morien, Birchgrove and Reserve and the towns of Dominion, Glace Bay, Waterford and Sydney Mines. The city of Sydney is situated about midway between the northern and southern extremities of the field and on the western fringe of the productive coal measures. Sydney harbor crosses the coal field, cutting off direct rail connection between Sydney Mines and the greater part of the field to the southeast. (Fig. 2.) The coal measures are exposed in the cliffs on the coast line, which rise to an average height of 30 ft., and are almost continuous throughout the length of the field. The portion of the coal field under land forms a small segment of a circle, the greatest distance from the coast landwards is 9 miles, and it occupies an area of 200 sq. miles. The greatest distance developed seawards from the shore by mining operations is 2 miles. The strata maintain a regularity of dip at this distance, proving a submarine area of about 70 sq, miles. How much further the coal field extends seawards is unknown, but the indications are that it extends far beyond the present economical working limit and in all probability there is a vast submarine coal field. The productive coal measures are of Carboniferous age, these being underlain by beds of sandstone, locally classed as millstone grit, which define the southern limit of the field, while a spur of syenitic hills cuts off the coal-bearing strata on the north. Two main anticlinal folds having a general course easterly divide the field into three basins named from north to south: Sydney Mines-Lingan, Glace Bay and Morien. So far as the portion of the coal field already developed is concerned the general effect of these folds is to vary the direction and dip of the strata at different points of the several basins. The strata dip seawards at the average rate of 6 per cent. along the axes of the basins. On both sides of the several basins, the strata have a dip varying from 7 to 40

Jan 1, 1930

By Robert Mehl

IN examining the progress of metallurgical science, the critic must remember that most of our present knowledge of metals and alloys has been accumulated through the needs of industry and commerce rather than through the desire and efforts of a large body of scientists interested primarily in developing a science of metals. The progress of metallurgy, scientifically speaking, has been irregular, and little given to the exhaus-tive exploitation of important scientific fields. The experienced engineer now recognizes the need for the development of the basic science upon which his engineering rests. In addition to the increase in knowledge which results from the normal requirements of industry, a development of the basic science of the behavior of metals and alloys is as desirable in metallurgy as in any other branch of science and engineering. The continued growth of the science of metals-as of every other science-requires studious attention to the principles that underlie the behavior of matter, with the result that knowledge in the several fields of interest should continue to increase. Among the various subjects recognized as important in physical metallurgy few have a wider significance than that of diffusion in solid metals. The phenomena of diffusion are intimately related to many basic problems of the metallic state, but in addition to this, the process of diffu-sion is of first importance practically. The formation of alloys by the annealing of mixed powders, first practiced by Faraday and Stodart81 in 1820 and in more recent years investigated by Masing187,189 and others, has led to the development of special alloys like Carboloy, Vascoloy-Ramet, Genelite, Elcon68, and has recently been applied to the production of noble-metal alloys for electrical contacts"'.

Jan 1, 1936

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By William Alden

A GREAT landslide occurred on June 23, 1925, in the valley of Gros Ventre River, about 35 miles south of Yellowstone National Park (Fig. 1). The relations of the north-easterly dipping rock formations of the slide scarp and of the dam formed by the slide are shown in the diagrammatic cross-section of the valley (Fig. 2). This generalized section is based on unpublished maps and notes by Eliot Blackwelder, in the files of the U. S. Geological Survey. FIG. 1.-MAP SHOWING SCARP AND DAM (LARGE DOTS) AND LAKE (CROSS-LINED) FORMED BY LANDSLIDE BLOCKING GROS VENTRE RIVER. (Scale 1, in. = 1 mile; contour interval 100 ft. From Grand Teton and Mt. Leidy topographic maps). Heavy rains and melting snow in the Gros Ventre Mountains had saturated clay layers in the Carboniferous strata, which dip toward the valley at angles of 18° to 21°, consequently an enormous mass of rock at the end of the north spur of Sheep Mountain became loosened and, on the afternoon of June 23, slid suddenly down into the valley. Within a few minutes this mass of debris-estimated as 50,000,000 cu. yd.-carrying

Jan 1, 1928

By Howard A. Meyerhoff

AS a source of mineral wealth, the larger islands of the West Indies have never had an enviable reputation. The Spaniards took possession of them in the sixteenth century hopeful that they would yield gold; but it was not long before they knew the rather rigid limitations of Antillean gold production and were seeking-and finding ---richer deposits of the precious metals in Mexico and on the west coast of South America. Although a great deal of wealth changed hands in the West Indian islands in subsequent years, the fact may be laid to the abundance of pirates and privateers and not to the richness of local ore bodies.

Jan 1, 1941

By George C. Branner

STATE geological surveys have had an interesting development in this country. They first appeared more than a hundred years ago. The fact that they have persisted and are now an important part of most state governments indicates the basic need for state departments con-cerned with mineral problems. The number of state surveys in 1941 (43) is at an all-time high, as is the aggre¬gate appropriation for their support for the fiscal year 1940-'41 ($1,600,708). The first surveys, those of North and South Carolina (see Fig. 1), made their appearance in 1820-'30, but neither survived that period. During the next two decades surveys were created in twenty states, but only three survived. In fact, it was not until the decade 1900-'10, when eighteen surveys were created and only five abolished, that these agencies became firmly established.

Jan 1, 1941

ASHBEL WELCH, Lambertville, N. J.: Dr. Dudley has given the wear of steel rails under four different conditions. He arrives at the conclusion that the softer rails, or those that from their composition ought to be softer, wear better than the harder. But there is another condition which has an important bearing on the subject, and should not be overlooked,—the weight on a wheel. With the lighter weights of the past, the softer rails may have worn best; with the heavier weights of the future, the harder may wear best. Weights will probably be increased up to the capacity of steel to bear; then doubtless the harder steel will wear best. A leaden rail with ten pounds on a wheel might carry millions of tons, but with one hundred pounds on a wheel, it would be destfoyed by a few thousand tons. So in the days of iron rails, my experience was that the softer rails under light machinery stood better than some of the harder; but under heavy machinery the softer were muqh the most rapidly destroyed. It is doubtless the same with steel. The pounding motion of the wheels loosens or spreads the particles of a thin film of steel; the pull lengthwise on the rail de-

Jan 1, 1881

By George R. Ensminger, E. Heaton Hemingway

During the past year, the Watertown Arsenal has been interested in the occluded gas and oxide content of certain ordnance steels in order to determine, if possible, whether some of the peculiar failures in their physical properties might not be traced to these causes. For the purpose of best accomplishing a study of this nature, it was decided to heat the various samples of steel in a vacuum for definite periods of time at high temperatures and carefully examine the quantity and composition of the gases evolved. By the use of a fused quartz tube fitted with a water-cooled, ground-glass stopper, it was possible to maintain a vacuum at a temperature of 1000" C. for 10 hr. without perceptible leakage being evidenced as measured by a McLeod gage. The silica tube was connected with an evacuating system so constructed that the volatilized gases could be removed from time to time and a low vacuum of 0.0002 to 0.0010 mm. of mercury continuously maintained. At no time during the period of heating or in the removal of the gases did the evacuated system come in contact with rubber stoppers or any rubber connections, making contamination from such a source, impossible. In other words, the only volatile products that could be: obtained must necessarily have come from the steel itself or from the glass and fused quartz system or from the mercury used as a sealing agent. In the carlier experiments, the steel treated was in the form of turnings, but this practice was discarded because the weight's of the turnings before and after being heated were widely inconsistent,, even when taken from the same piece of steel. This discrepancy developed largely through variation in the amount of metal volatilized with the gases; this metal could always be seen in the form of a ring where it condensed in the cooler portion of the tube in either the amorphous or crystalline condition. Because of the frequency in occurrence and the variation in the manner of deposition, this material was roughly analyzed and found to consist for the most part of iron. At the same time two samples of steel that had been

Jan 1, 1922

By E. Heaton Hemingway, George R. Ensminger

During the past year, the Watertown Arsenal has been interested in the occluded gas and oxide content of certain ordnance steels in order to determine, if possible, whether some of the peculiar failures in their physical properties might not be traced to these causes. For the purpose of best accomplishing a study of this nature, it was decided to heat the various samples of steel in a vacuum for definite periods of time at high temperatures and carefully examine the quantity and composition of the gases evolved. By the use of a fused quartz tube fitted with a water-cooled, ground-glass stopper, it was possible to maintain a vacuum at a temperature of 1000" C. for 10 hr. without perceptible leakage being evidenced as measured by a McLeod gage. The silica tube was connected with an evacuating system so constructed that the volatilized gases could be removed from time to time and a low vacuum of 0.0002 to 0.0010 mm. of mercury continuously maintained. At no time during the period of heating or in the removal of the gases did the evacuated system come in contact with rubber stoppers or any rubber connections, making contamination from such a source, impossible. In other words, the only volatile products that could be: obtained must necessarily have come from the steel itself or from the glass and fused quartz system or from the mercury used as a sealing agent. In the carlier experiments, the steel treated was in the form of turnings, but this practice was discarded because the weight's of the turnings before and after being heated were widely inconsistent,, even when taken from the same piece of steel. This discrepancy developed largely through variation in the amount of metal volatilized with the gases; this metal could always be seen in the form of a ring where it condensed in the cooler portion of the tube in either the amorphous or crystalline condition. Because of the frequency in occurrence and the variation in the manner of deposition, this material was roughly analyzed and found to consist for the most part of iron. At the same time two samples of steel that had been

Jan 1, 1922

By D. M. Milne, R. F. Stoner, W. Bakiewicz

The Lower Indus Basin deposits form a substantial unconfined alluvial aquifer of excellent quality. This aquifer contains basically highly saline groundwater, overlain in places by considerable amounts of fresh water whose origin can be traced to the present and historical courses of the River Indus. In the past, the main source of groundwater recharge has been direct river seepage and water tables were generally deep. Since the establishment of a perennial irrigation regime however, deep percolation from the increased irrigation supplies has predominated and the water table has risen to within a few feet of the surface. The river system itself is being progressively devel-oped for irrigation and very shortly a situation will arise where the entire low winter flow will be utilized. Fresh groundwater will then be exploited to supplement the surface supplies, and at the same time a drainage system, mainly based on wells will be used to stabilize the water table at safe depths. This paper discusses some of the methods used to ensure optimum economic development of the fresh groundwater and describes the general design philosophy evolved by the authors' firms for both irrigation and drainage wells, with respect to both well configuration and operation. Water quality standards are discussed insofar as they affect subsequent use of the groundwater. A few particular aspects are considered, including the values of the relevant aquifer constants, the construction of wells, and the determination of screen losses. A major problem solved during the Lower Indus Project investigations has been the design of wells to produce fresh water from layers overlying saline water. This solution is also discussed. The recent interest in the groundwater of the Lower Indus Plains of West Pakistan has two main aspects. Firstly, soil waterlogging and the associated salinity hazards caused by rising water tables are a serious problem in agriculture, and the ease with which drainage requirements can be met by aquifer pumping makes this an obvious solution. The second interest stems from the rapid intensification of irrigation agriculture and the growing shortage of water supplies. In the areas where the groundwater is of suitable quality it can be used immediately for irrigation at relatively small cost and with large financial returns. In addition, the aquifer forms a potential storage reservoir which could be recharged from high river flows and depleted by pumping at times of scarcity. SOURCE OF GROUNDWATER The Lower Indus plain is a relatively long and narrow alluvial basin on a north-south axis, some 23,000 sq miles in area, bounded by higher land to the east and west. One hypothesis to explain the distribution and quality of groundwater in the region1 presupposes a river system considerably larger than, but very similar to the present river. This is characterized by a single mainstream, with subsidiary overspill channels in times of flood, running along the crest of a self-deposited ridge and with an extensive advancing delta. Sea water is contained in the alluvial pores of the advancing delta, forming the native groundwater. This has been partially displaced from two sources, namely direct seepage of fresh water from the river channel in meander flood plain areas and percolation from flood spillage in cover flood plain areas. Percolation has been subject to much re-evaporation and is thus slightly saline even as it reaches the groundwater. The whole complex has been further affected by two main influences: evapotranspiration from the land surface that tends to salinize the groundwater and down-valley flow that tends to bring fresher water

Jan 1, 1970

Jan 1, 1925

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,' who first dealt with the coning problem; (2) Chaney, et al,' who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.' Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,' and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy's law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

By William Hurst

Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This nietkod of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined tern? for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and sec-ondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. INTRODUCTION The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent move- ment of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation. The type of depletion performance equation chosen for predicting the future performance of a reservoir depends on the amount of past history available. When the reservoir is somewhere past the halfway mark in depletion, some form of decline curve is often used. With less past history, material balance equations which incorporate empirical factors based on the past performance are often used. When, however, the amount of past history is small, the Muskat depletion performance equation will usually be used. The distinguishing feature of this type of equation is that empirical factors based on the over-all or macroscopic reservoir behavior are almost or entirely absent. Each parameter affecting the reservoir performance is ascribed an independent set of values based on measurements made on laboratory samples; that is, incorporating microscopic empirical factors. In establishing Muskat-type depletion performance equations, it is necessary to consider the reservoir as consisting of a number of associated blocks, in each of which the saturations and pressures may be considered uniform, and in each of which all substances have uniform pressure-volume characteristics. Thus, a primary gas cap can usually be considered as one block and an aquifer as another. Gravity segregation may be negligible for practical purposes when the rock and oil properties are adverse and/or the dip or thickness of the reservoir is too small. In this case the whole oil leg may be considered as one block, except in very large reservoirs. In very large reservoirs the fluid and rock properties may vary enough, particularly in the dip direction, for it to be necessary to divide the oil leg into a number of blocks, in each of which the relevant quantities may be considered uniform. When gravity segregation of the oil and free gas is not negligible, it is necessary to consider the space occupied by the initial oil leg as divided into two blocks, a secondary gas cap and an effective oil leg, in each of which saturations may be considered to be uniform. The total volume of these two blocks is thus constant, but the secondary gas cap grows continuously at the expense of the oil leg. Muskat1 derived depletion performance equations for the basic case of an oil reservoir with closed boundaries and without segregation, and for the case of an oil

By Charles Wraith

THE property of the Roan Antelope Copper Mines, Ltd., is situated at Luanshya, north-central part of Northern Rhodesia, and is connected with the main line of the Rhodesia Railways, Ltd., by a 24-mile branch line from N'dola. Most of the material and supplies that are not available in Africa are shipped into the country via Beira, on the East Coast of Africa, a distance of 1473 miles from Luanshya and the nearest ocean port. The output of copper is shipped by rail to Beira and thence by boat to the market. Passenger travel is mostly via Cape Town, a distance of 2162 miles from Luanshya. Excellent passenger trains operate on regular schedules between Cape Town and Northern Rhodesia. Luanshya is 13° south of the equator at an elevation of 4000 ft. above sea level, and has a mild healthful climate. During the rainy season, from October to March, the rainfall averages 53 in. The area is pro-fusely covered with vegetation. An ample supply of water for industrial and domestic purposes is available throughout the year. The more important supplies for smelting purposes, such as wood, coal, limestone, silica, quartzite, and clay for "dolly" mud, are con-veniently available. Excellent grades of coal, coke and firebrick are obtained from the Wankie Colliery Co., Ltd., Southern Rhodesia. The Wankie colliery has just completed the erection of equipment for the manufacture of silica brick. An ample supply of quartzite of good grade is available for this purpose. Silica brick is also obtained from the Belgian Congo and from India. Limestone is quarried from a large deposit a few miles from Bwana Mkubwa, which is 30 miles by rail from the smelter. An abundant supply of clay for "dolly" mud and for lining launders is available within a short distance of the smelter.

Jan 1, 1933