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By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By X. Gu

Mining operations, especially surface coal mines, have great impacts on the local ecosystem and the environment. However, it has been a common practice in mine design that the economic evaluation considers only the operating and capital costs, while the costs incurred due to ecological damage are left out. Such practice underestimates the total cost of mining and ignores the difference in ecological impacts between different mine design alternatives. With growing interest in sustainable development, the mining industry is under increasing pressure to operate not only based on economic and engineering principles but also on principles of sustainability. Therefore, estimating ecological costs of mining and considering such costs in the mine design process is an important step towards reducing ecological impacts at the design stage. The objective of this paper is to quantify the ecological costs of open pit coal mining and to demonstrate the influence of such costs on the ultimate pit design. The ecological costs of mining are estimated based on the areas and types of land damaged by mining activities and the carbon emission from energy consumption. Four major components of ecological cost are identified, namely, lost value of direct eco-services, lost value of indirect eco-services, prevention and restoration costs, and the cost of carbon emission from energy consumption. Necessary equations are given for estimating these costs. An algorithm is described for ultimate pit optimization in coal deposits with near-horizontal coal seams. A case study is presented in which the ultimate pits with and without ecological costs are optimized and compared to show the influence of ecological costs on the pit design outcome.

Aug 1, 2013

By Moonkyung Chung

Static pile load tests were performed in order to evaluate bearing capacities and mechanical behaviors of three different pile types: (1) steel-concrete composite drilled shaft with rebar reinforcements inside the concrete, (2) steel-concrete composite drilled shaft without rebar, and (3) conventional drilled shaft (reinforcement concrete pile). The material elastic moduli obtained from pile load tests of steel-concrete composite drilled shafts with and without rebar reinforcement were found out to be similar. On the other hand, the elastic modulus of steel-concrete composite drilled shafts is almost twice as high as that of the conventional drilled shaft. The ultimate strengths of the steel-concrete composite drilled shaft with rebar, the steel-concrete composite drilled shaft without rebar, and the conventional drilled shaft were 9,810, 7,848, and 4,414kN, respectively. The results of these load tests reveal that the ultimate strengths of the steel-concrete composite drilled shaft with reinforcement and that without reinforcement are 2.22 times and 1.78 times greater that that of the drilled shaft. The structural failures of the steel-concrete composite drilled shafts occurred either at the boundary between tip of steel casing and rock-socketed concrete.

Jan 1, 2010

By Kjell Karlsrud

"Abstract New semi-empirical design procedures for the determination of ultimate shaft friction and load-displacement response of axially loaded piles in clay are proposed. Hereunder also prediction of how the capacity will build up with time following the pile installation, primarily as result of reconsolidation. A main basis for developing the new procedures was detailed review and re-assessment of results from a series pile load test programs published over the past 30 years on piles well instrumented to monitor soil- and pore pressures as well as load distribution along the pile shafts. Two new alternative procedures are proposed for predicting the ultimate shaft friction; a-approach using the normalised undrained strength based on direct simple shear tests as a main correlation parameter, and ß-approach using the overconsolidation ratio, OCR. Both approaches include the effects of the plasticity index of the clay, Ip, which is shown to have an especially large impact on the correlations when Ip<25. It is recommended to use both methods in design practice, and select design values for the ultimate shaft friction that represents an average for the two methods. Pile diameter, length or stiffness, or whether the pile is open- or closed-ended seem to have little impact on the shaft friction. However, a moderate effect of pile length or flexibility on the total ultimate pile capacity comes out of the proposed t-z curves, which include some post-peak reduction. The proposed procedure for predicting the time for set-up is based on linear radial consolidation theory. The main input parameters are the insitu permeability and virgin modulus number (or virgin compression index) of the undisturbed clay. The same basic formula and correlations are applicable to both open and closed-ended or partially plugging piles.IntroductionThe design procedures presented herein are primarily based on observations and data collected in connection with “fully instrumented” pile testing programs that the author has been responsible for or has become involved with over the past 40 years, or that have been found in the literature.It was a pre-requisite for the test programs included that there were sufficient high quality soil data available to give a reliable determination of the true in-situ strength and compressibility characteristics of the clay deposits. The soil conditions range from soft NC clays with undrained shear strength down to about 15 kPa, to very stiff clays with undrained shear strength up to about 500 kPa and OCR up to 25. The plasticity index of the clays mostly lies in range 12 to 60 %."

Jan 1, 2014

By T. M. Yegulalp

A short review of the current practice and recent developments is followed by a description of a newly developed approach for the solution of the optimum ultimate pit limit problem. The new approach utilizes the network modeling of the problem for solution by maximum flow algorithm. The latest developments in the implementation of maximum flow algorithm present significant time and memory savings as compared to initial development due to Ford and Fulkerson. Results of a series of computational tests are presented to demonstrate how this approach performs as compared to the well-known Lerchs Grossman algorithm. It is also shown that the solution by the new method will automatically include several optimal solutions based on predetermined number of benches to be included in the analysis.

Jan 1, 1993

By Thys B. Johnson

A three-dimensional dynamic programing method is presented for determining the optimal ultimate open pit limit. The method given is based on the block concept and is an extention of the two-dimensional Lerchs-Grossmann approach. The three-dimensional technique presented herein is fast and simple and may be used for an initial open pit evaluation when only limited data are available or as a more refined model when the entire deposit is well delineated. The method is illustrated by simple numerical examples and is also presented in algorithmic form. A computer program was written in Fortran IV which implements the three-dimensional algorithm and some computational aspects are discussed.

Jan 1, 1971

By L. F. Miao

Studies were carried out to investigate the ultimate soil pressure acting on pile(s) undergoing lateral soil movement in soft clay. A special apparatus has been designed to apply a uniform rectangular profile of lateral soil movement on the rigid pile(s) with pinned head and tip conditions to obtain the ultimate soil pressure. The piles were 16 mm (5/8 in) in diameter. For the pile group tests, the behavior of different number of piles (2, 3, 4, 6 and 9), pile arrangements and center-to-center spacings (3 and 6 diameters) were investigated. In this paper, the group factors of 11 combinations of number of piles, pile arrangements and pile spacings are presented. The group factors are given for individual piles in a pile group as well as for the entire group. Generally, the group factors of individual piles in a group varied significantly according to pile spacing in both directions, and pile arrangement; the group factor of the whole group reduced with an increasing number of piles, and increased with increasing pile spacing. For a pile group with the same number of piles but different pile arrangement, no significant difference was found in the group factors for the entire group.

Jan 1, 2008

By R. W. Drier

THE conductivity of copper wire is of prime importance to the electrical industry and consequently to the copper refiner and wire manufacturer. Annealed copper wire has a higher conductivity than hard-drawn wire, but, on the other hand, its tensile strength is lower. In an attempt to explain the reasons for these changes in property or at least to study the conditions existing in these two types of copper wire, the experiments described here were carried on in the Department of Metallurgy of the Michigan College of Mining and Technology. This is only a partial and preliminary report on some of the work done to date on a research program of which the object is an intensive study of copper. It is offered with the hope that, though it is not an exposition of the most rigorous of conclusions, the general trend of inferences which may be drawn will be of value and interest.

Jan 1, 1929

By John Ward Smith

This paper describes and evaluates a method that the Federal Bureau of Mines used to determine the ultimate composition of the organic material in 10 samples of oil shale from the Mahogany zone of the Green River formation in Colorado and Utah. Since interest has centered on the Mahogany zone, the richest section of the deposit, these 10 samples were chosen to provide a broad representation of this zone with the objective of obtaining generally valid ultimate composition values. The most probable organic composition for the Mahogany zone and the 95-percent confidence limits for each component average (in weight-percent of organic material) are: Carbon 80.5 ± .4 Hydrogen 10.3 ± .1 Nitrogen 2.4 ± .1 Sulfur 1.0 ± .1 Oxygen 5.8 ± .5 As only minor variations in composition were observed, the organic material of this particular bed is quite similar over a wide geographic area.

Jan 1, 1961

By Glen Mann, H. G. Vestberg, Robert D. Holtz

"Underpinning of residential and commercial structures is often accomplished using a number of driven-in-place small diameter steel pipe piles. These piles, at least in the Seattle area, are typically described as pin-piles and are driven with an air compressor operated jack hammer to a refusal criterion developed from an empirical basis. Over the past twenty years or so, the materials have improved in quality and strength, and the driving equipment has improved in efficiency and capability. These improvements have resulted in damage to the pin-piles during driving as well as to the driving equipment. The primary objectives of this load testing study were to develop a relationship between the driving penetration resistance of 2-inch diameter pin-piles and the ultimate bearing capacity when piles were driven at different penetration rates and, based on the load test results, to develop an opinion regarding an increase in the allowable axial load capacity [ultimate load capacity divided by a factor of safety] of a 2-inch diameter pin-pile over the currently used permissible load capacity of 4 kips in the Seattle area. Also, if feasible, a reduction in the present driving penetration rate was to be recommended to help reduce the rate and magnitude of pile and equipment damage whilst maintaining the allowable load capacity. The recorded ultimate bearing capacities were also compared with the Tagnent-line and the Davisson analytical methods in an effort to determine if either of these provided a reasonable determination of the pile load capacity.IntroductionThis paper describes the results of a series of load tests performed on small diameter, 2-inch, driven-in-place steel pin (pipe) piles and based on these results, provides the support for a modification to the presently used allowable axial pin-pile capacities.The intent of the load testing program was to determine how much influence the penetration resistance might have on the individual piles' ability to support the allowable axial load without undergoing any significant vertical deformation. For the purposes of this paper the ""allowable load capacity"" is considered to be the ultimate pile load capacity divided by a minimum factor of safety, typically considered to be 2.0 in this area. A pin (pipe) pile comprises an open or closed ended, schedule 80 steel tube which is driven-in-place, usually with an air compressor operated 90 pound pneumatic jack hammer. These jack hammers typically operate at a rate of about 1,200 blows per minute, (Haggard, Holtz and Mann, 2001 )."

Jan 1, 2005

By Heinrich Ries

In another place,* the writer has called attention to the modern methods of the laboratory investigation of clay, and it is desired here simply to discuss one branch of the subject, which, though of considerable importance, has heretofore received little attention in this country, viz., the rational analysis of clay. In order, however, the better to point out the bearings and advantages of this procedure, it is necessary to refer briefly to the ultimate analysis as well. The remarks in this paper refer only to the use of clay for the manufacture of clay-products. Pure clay or kaolin-f is extremely refractory, possesses little plasticity, and usually shrinks aud warps considerably in burning. Even the smallest proportion of impurities changes these properties, so that the kaolin exhibits variations in shrinkage, plasticity, tensile strength, fusibility, and often color when burned. The majority of nearly pure kaolins consist of kaolinite (A1,O2 2SiO,, 2H20), undecomposed feldspar, and quartz. The kaolinite generally forms the finest particles of the clay and is known as the clay-substance, while the rest of the clay-particles are collectively spoken of as sand. In the ordinary or ultimate analysis, the substances generally determined are silica, alumina, ferric oxide, lime, magnesia, alkalies and water. An analysis of this type simply regards the clay as a mixture of elements or oxides, but gives no clue as to the actual condition in which these substances exist, i.e., whether as silicates, oxides or carbonates, etc., a point which it is of the highest importance to know; for the individual components of the clay influence its properties not only according

Jan 1, 1899

By James A. Schneider

Selection of resistance factors within Load and Resistance Factor Design (LRFD) requires accurate assessment of uncertainty and bias in load and resistance. To date, many studies have focused predominantly on the assessment of uncertainty, while the potential for bias appears to be the dominant factor in design for consistent levels of reliability under a variety of situations. Bias comes from factors which have been ignored in design method development but significantly influence resistance when extrapolating from conditions typical of databases to those at a given site. Uncertainty and bias can be quantified as the coefficient of variation and mean (or median) of a data set, respectively, for statistical assessment of load and resistance factors. This paper first presents an overview of statistical assessment of resistance factors, and then discusses factors that influence uncertainty and bias when extrapolating to situations outside of conventional databases of driven pile axial capacity.

Jan 1, 2009

By C. Garcia, H. Arias, J. D. Miller, C. L. Lin

The question of ultimate recovery in heap leaching operations is always of particular concern with respect to economic considerations. Of course the particle size distribution is a critical factor which determines ultimate recovery and which must be established based on a balance between the extent of mineral exposure and transport phenomena. Now it seems that the ultimate recovery for a given particle size distribution can be established from mineral exposure analysis by x-ray microtomography (XMT). Using recently developed software, micro-CT data can be used to determine the fraction of mineral exposed and thus the ultimate recovery. Examples of mineral exposure analysis are given for the copper heap leaching operation at Zaldivar, Chile.

Jan 1, 2002

By E. O. Bennett

When oil is takcn from a subsurface structure it is generally accompanied by gas. The gas thus produced represents the 1ighter hydrocarbons present in the original petroleurn accurnulation, which arc, insoluble at the reduced pressures created around a well when it is producing. In some cases the gas accompanying the oil may come from a gas-bearing stratum not in immediate contact with the oil. The amount of gas from the formation accompanying each barrel of oil is called the natural gas factor. Energy Causing Well to Flow The force causing the flow of fluid into a well when it is drilled into an oil-bearing structure is the pressure differential between the well bore and the formation. A pressure differential between the formation and the well may be set up in three different ways, as follows: (1) pressure due to gas in solution or in contact with the oil, (2) hydrostatic pressure due to water in contact with the oil (it may be either bottom or edge water); (3) pressure difference due to forcc of gravity. The greatest source of energy for producing oil from most oil fields, and the one over which the greatest control can be exerted, is the poten-tial energy in the gas under pressure in the formation. In any pool there is but a definite amount of gas available. Part of this gas may be in solution and a part in contact with oil. The amount of gas in solution in each bard of oil depends on the pressure and temperature in the formation and the characteristics of the oil. Whether the gas is in solution or in contact with the oil it is necessary to use the energy it, contains as efficiently as possible in order to obtain the greatest ultimate recovery from the pool. Bush1 states: Gas being the most efficient aid in moving the oil, it is important to prevent more of it from escaping than is necessary to remove the maximum amount of oil from the sands. The conservation of this energy is far more important to the producer of oil than his returns from sales of gas to distributing companies. The flowing life of the well is the most profitable period, and keeping the gas-oil ratio low, or keeping the

Jan 1, 1928

By Z. Jin, D. DePaoli, P. Zhang

"Phosphate beneficiation in Florida generates more than one tonne of phosphatic clay, or slime, per tonne of phosphate rock produced. Since the start of the practice of large-scale washing and desliming for phosphate beneficiation, more than 2 Gt of slime has accumulated, containing approximately 600 Mt of phosphate rock, 600 kt of rare earth elements (REEs) and 80 million kilograms of uranium. The recovery of these valuable elements from the phosphatic clay is one of the most challenging endeavors in mineral processing, because the clay is extremely dilute, with an average solids concentration of 3 percent, and fine in size, with more than 50 percent having particle size smaller than 2 µm, and it contains nearly 50 percent clay minerals as well as large amounts of magnesium, iron and aluminum. With industry support and under funding from the Critical Materials Institute, the Florida Industrial and Phosphate Research Institute in conjunction with the Oak Ridge National Laboratory undertook the task to recover phosphorus, rare earths and uranium from Florida phosphatic clay. This paper presents the results from the preliminary testing of two approaches. The first approach involves three-stage cycloning using cyclones with diameters of 12.4 cm (5 in.), 5.08 cm (2 in.) and 2.54 cm (1 in.), respectively, to remove clay minerals followed by flotation and leaching. The second approach is a two-step leaching process. In the first step, selective leaching was conducted to remove magnesium, thus allowing the production of phosphoric acid suitable for the manufacture of diammonium phosphate (DAP) in the second leaching step. The results showed that multistage cycloning with small cyclones is necessary to remove clay minerals. Selective leaching at about pH 3.2 using sulfuric acid was found to be effective for removing more than 80 percent of magnesium from the feed with minimal loss of phosphorus.IntroductionFlorida phosphate ore, or “matrix,” as it is called locally, contains three different mineral groups that have to be separated from each other: (1) phosphate minerals, (2) clay minerals and (3) quartz, or sand. As mined, the phosphate and sand particles are embedded in compacted mud, or clay-balls. Before separation can begin, all of the particles must be liberated from the matrix of mud. The very first unit operation in the beneficiation process is to disaggregate the various particles. This actually starts while the matrix is flowing through the multimile pipeline from the mine to the beneficiation plant. While in the pipeline, the matrix is exposed to shear forces as it passes through the various centrifugal pumps along the pipeline. These intense shear forces cause a significant percentage of the sand and phosphate particles to be liberated from the clay-balls by the time they arrive at the plant. Once they reach the plant, the first goal is to finish disaggregating the clay, and follow that by making a size separation at 1 mm. This processing is conducted in the washer, consisting of a large rotating trammel screen and a few stages of log washer, screens and hydrocyclones. In all of the currently operating beneficiation plants, the washer is a large structure that receives the matrix, screens it and then discharges a pebble phosphate product sized larger than 1.0 mm and a slurry of liberated clay, sand and phosphate particles that are smaller than 1.0 mm."

Jan 1, 2017

By C. Roldan, C. Garcia, J. D. Miller, C. L. Lin

The ultimate recovery in a heap leaching operation is related to the degree of exposure of the valuable minerals in comminuted particles. Recently, high-resolution cone beam x-ray microtomography (XMT) has been used to determine this parameter. XMT technology consists of examining the extent of mineral exposure for each size fraction of ore in 3D, then, by algebraic calculations, the ultimate recovery can be estimated for different particle size distributions (PSD). To confirm the usefulness of the XMT technology for mineral exposure analysis, column tests were performed to determine ultimate recovery using three PSDs for two composites obtained from the copper heap leaching operation at Zaldivar-Chile.

Jan 1, 2003

By L. C. Reese

The ultimate resistance against a rigid cylinder which is moved laterally in a cohesionless soil is a function of the geometry of the cylinder and the properties of the soil. An approximate method is developed for computing this resistance and is tested against results of laboratory experiments. Satisfactory agreement between the method and experiment was obtained. Not only was the ultimate resistance against the cylinder measured, but measurements were made of the shape of the rupture surfaces. These measurements should allow the development of a more rigorous computation procedure. INTRODUCTION A critical aspect in the design of offshore drilling platforms is assuring the stability of the platform during a hurricane. The large horizontal loads from waves and wind make a severe loading condition. Piles are generally employed as the foundation since they can be effective in resisting both horizontal and vertical loads. Spuds are sometimes used with a mat foundation, where the spuds are designed principally to resist horizontal loads and the mat designed principally to resist vertical loads. The research reported in this paper is related to one aspect of the problem of laterally loaded piles or spuds in sand. The complete solution to the problem of the laterally loaded pile in sand would require the prediction of soil resistance against the pile as a function of pile deflection; only the ultimate resistance against short piles is considered in this paper. A considerable amount of additional research will be necessary in order to obtain a complete solution to the problem of the laterally loaded pile in sand; however, the work reported here should be useful as a guide in the performance of some of the additional research. ULTIMATE LATERAL RESISTANCE AGAINST A LONG FALL IN SAND To aid in the understanding of the theory which is developed for a cylinder, the theory for earth pressure against a wall is reviewed. In Fig. l(a), a long wall of height H is shown embedded in soil. Soil resistance will develop as the wall is deflected, and the soil resistance will increase with deflection until some limiting value is reached. In this discussion, and those following, it is assumed that all points on the wall deflect equal amounts. A possible shape of the real curve which relates soil resistance to deflection is shown by the dashed line in Fig. l(b); however, as a means of simplifying the discussion, an idealized curve (shown by the unbroken lines) is drawn. If such a wall as this were furnishing the horizontal support for an offshore structure, the dashed curve in Fig. 1 would be the information needed in performing a foundation analysis, with the idealized curve possibly being an acceptable substitute. For the idealized curve, the soil resistance is linear with deflection for the early portion of the curve such that

By W. F. Kieschnick, C. C. Miller, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By C. C. Miller, W. F. Kieschnick, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By M. Deutsch, E. González, M. Williams

"Uncertainty exists in ultimate-pit limits due to geologic variation and unpredictable economic landscapes. In this work, we show how this uncertainty affects the ultimate pit and how it can be analyzed to improve the mine planning process. A stochastic framework using geostatistical simulation and parametric analysis was used to model the effects of geologic and economic variations on ultimate-pit limits and overall project economics. This analysis was made possible by a new pit optimization implementation that can be automated and set up to calculate ultimate pits for hundreds of different scenarios in a matter of hours. Quantifying ultimate-pit uncertainty early in the mine planning process allows mining engineers to make informed decisions regarding infrastructure placement and to mitigate the possibility of incurring substantial costs to relocate critical mine facilities. Resumen ¦ Existen dudas sobre los límites del pit final por causa de la variación geológica y lo impredecible de los paisajes económicos. En este trabajo les mostramos como esta incertidumbre afecta el pit final y como puede ser analizada para mejorar el proceso de planificación de la mina. Se usó un marco estocástico con simulación geoestadística de análisis paramétrico con el fin de poder hace la modelación de los efectos de las variaciones geológicas y económicas en los límites de pit finales y proyectos económicos en general. Este análisis fue posible gracias a una nueva implementación de optimización de pits que puede ser automatizada y configurada para calcular pits finales para cientos de escenarios diferentes en cuestión de horas. La cuantificación temprana de la falta de certeza en pits finales durante el proceso de planificación permite a los ingenieros de minas tomar decisiones informadas en lo que respecta a la ubicación de infraestructura y en la mitigación de posibles costos sustanciales por causa de la reubicación de instalaciones clave de la mina."

Jan 1, 2015