Experiments on oil displacement from homogeneous porous media have shown that the component of fi0t4 across the layer is o~ten negilgibiy small compared with that parallel to it. This result is applied in the inspectional analysis of the equations governing the macroscopic displacement processes.
Water drive in a homogeneous porous medium with a uniform permeability distribution has been extensively studied in the past, both theoretically and experimentally. In this paper equations are derived for a two-dimensional water drive in a porous system with either a continuously or a porous system with either a continuously or a discontinuously varying permeability distribution perpendicular to the layer. The influence of perpendicular to the layer. The influence of capillary forces bas not been taken into account. A necessary condition for the validity of the equations is that the water should underrun the oil. It is shown that the permeability distribution has much influence on the oil recovery. A large difference in recovery was apparent from a comparison of three systems, in which the oil production decreased as follows:(1)permeability production decreased as follows:(1)permeability increasing in an upward direction perpendicular to the layer,(2)homogeneous, uniform permeability throughout,(3)permeability increasing in a downward direction perpendicular to the layer. Introduction The recovery from a homogeneous, two-dimensional system in response to a normal water drive can be calculated with the help of theories developed by Beckers. He describes segregated flow of oil and water in which the water underruns the oil due to gravity and viscous forces. In his approach it is impossible to include capillarity, which means that the system does not describe a transition zone. However, we have a great deal of scaled experimental evidence which shows that moderate initial transition zones disappear during the displacement process where gravity and/or viscous tonguing effects occur. The experiments then show a sharp interface, and a transition zone is only found in the top of the water tongue. Neglect of this small zone affects breakthrough-time calculations, but on the other hand, gives the advantage of being able to treat the problem with the end-point permeabilities only. Although not immediately recognizable, there is a form of crossflow involved in this concept. It can be found from the material balance if the layer is divided into two sections parallel to the bedding plane. The theory describes experiments with a maximum initial transition zone of about one-third of the layer thickness. There are no restrictions on the mobility ratio. The production curve predicts too early a breakthrough, but shortly thereafter very satisfactory agreement is found. For many practical cases, these theories can be reduced to the simplified formulation given by Dietz. Experimental verification shows that his theory describes horizontal scaled-model experiments satisfactorily for mobility ratios larger than 6. Although gravity forces are completely neglected in the theory but not in the experiments, only the viscous forces are now responsible for tongue forming. Neglect of gravity delays breakthrough in comparison with predictions from the Beckers theory, but generally gives a somewhat better though not correct prediction of the moment of breakthrough. These findings have encouraged us to apply the same principles to inhomogeneous systems. To delay the theoretical breakthrough, gravity forces parallel to the bedding plane have been included, parallel to the bedding plane have been included, which results in a in a better fit with the over-all production curve for tilted layers. production curve for tilted layers. The equations derived in this paper can be applied to systems with either a continuous or a discontinuouspermeabilitydistributionperpendicular to the layer They are therefore applicable to a great number of inhomogeneous systems. Areal extension can be effected with sweep efficiency factors or by applying stream-tube models. THEORETICAL RESULTS AND DISCUSSION In order to arrive at an analytical expression for the oil production from an inhomogeneous system, the following assumptions have been introduced. 1. Water flows underneath the oil. SPEJ P. 211
This paper describes a method for increasing the axial capacity of friction piles embedded in clay soils. The proposed method consists of increasing the shear strength, and consequently the soil-pile adhesion, of the soil around a pile. This is accomplished by draining water from the surrounding soil into the pile. Equations are developed to predict the maximum pile capacity, and Terzaghi's theory of radial consolidation is used to predict the variation with time of the bearing capacity during the drainage process. Results from preliminary laboratory tests that demonstrate the feasibility of the drainage pile concept are described, and practical considerations that need to be investigated in greater detail are discussed. Introduction This paper introduces an unconventional method for increasing the load carrying capacity of offshore platform piles. The basic concept consists of increasing the axial capacity of friction piles embedded in clay soils by facilitating drainage of water from the soil formation into the pile. In this system, the drainage pile is analogous to a well point. The reduction in water content due to drainage causes the soil to consolidate around the pile, resulting in an increase in the soil shear strength. This leads to an increase in the soil-pile adhesion, and consequently in the axial pile capacity. The principle of driving water out of a soil layer in order to increase the soil strength locally is already a familiar one in the area of soil stabilization, and is the basis of sand drain technology and electro-osmosis. The conventional method of increasing the axial capacity of friction piles is to increase their diameter or embedded length. The pile dimensions, however, can only be increased until the penetration resistance equals the driving capacity of the largest pile driving hammers available. If additional bearing capacity is required to support the platform, the designer has to modify the design by either altering the platform configuration, changing the pile dimensions or resorting to the use of additional piles. Regardless of the alternative chosen, the overall cost of the platform can be expected to increase substantially. In such instances, the use of drainage piles to increase the bearing capacity without altering the design may prove to be an economically attractive alternative. Drainage piles may also find application in helping to increase the load-carrying capacity of existing platforms that fail to satisfy new or revised design criteria. In such platforms, the existing conventional piles could conceivably be converted into drainage piles, thereby increasing the load carrying capacity of the platform without increasing the pile dimensions.
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