Influence Of Capillary Forces Research Articles

円筒形油層内の水押しの挙動

In this paper equations of oil recovery and water-oil interface are derived for a water drive in a horizontal, cylindrical homogeneous oil reservoir by an extension of the Daalen and Domselaar's theory developed for a rectangular model. The influence of capillary forces are not taken into account. A necessary condition for the validity of the equations is that the water should underrun the oil. Results of the cylindrical model are compared with those of the rectangular model. It is found that oil production curves of both models agree precisely when an angle between initial water-oil interface and cap rock is only 90 degrees, and that the interfaces of both models after water invasion become different shapes, respectively.

Nonlinear capillary waves in thin films of viscous liquid and breaking of the films

A study is made of the dynamics of a thin film of viscous liquid with allowance for the influence of capillary forces and long-range van der Waals forces. Asymptotic solutions are found to problems of the dynamics of films in communication with a region of reduced pressure. It is shown that at a certain instant such a film breaks at its edge. The critical parameters that determine the instant of breaking are found and the form of the solution in the stage of breaking is given.

Water Drive in Inhomogeneous Reservoirs - Permeability Variations Perpendicular to the Layer

Abstract 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 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 discontinuous permeability distribution perpendicular 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.

Analysis of densification kinetics during the sintering of reduced chromium powder

1. Chromium powder in a deformed condition contains no substantial type II distortions; this points to a low ductility of the strating reduced chromium powder. 2. Thermodynamic calculations and experiments demonstrate that chromium oxides may be reduced under the usual sintering conditions in hydrogen with a dew point of 253–243°K (between −20 and −30°C) at 1473°K. 3. The experimentally determined energy of activation for the densification process of chromium powder at the initial instant of sintering in hydrogen in the 1373–1473°K is 134±8.3 kj/mole (32±2 kcal/mole), which is equal to 0.43 of the energy of activation for volume self-diffusion (Evol). 4. The fact that sintering durations obtained by calculation on the basis of phenomenological theory are longer than the experimental values and that the energy of activation for the shrinkage of chromium is lower than Evol indicates that the densification of active reduced chromium powder at the initial stages of sintering is not governed by the volume-viscous flow mechanism. 5. Without diminishing the role played by boundary and surface diffusion, it is necessary to note that the mechanism of activated dislocation slip under the influence of capillary forces may play an important part in the densification process of reduced chromium powder at the early stages of sintering; this is indicated by the circumstance that the value of the energy of activation for dislocation intersection is similar to that for the shrinkage of chromium powder.

Calculation of Oil Displacement by Countercurrent Water Imbibition

Abstract This paper presents numerical solutions of the equations describing the imbibition of water and the countercurrent flow of oil in porous rocks. The imbibition process is of practical importance in recovering oil from heterogeneous formations and has been studied principally by experimental means. Calculations were made for imbibition of water into both linear and radial systems. Imbibition in the linear systems was allowed to take place through one open, or permeable, face of the porous medium studied. In the radial system, water was imbibed inward from the outer radius. The effects on rate of imbibition of varying the capillary pressure and relative permeability curves, oil viscosity and the initial water saturation were computed. For each case studied, the rate of water imbibition and the saturation and pressure profiles were calculated as functions of time. The results of these calculations indicate that, for the porous medium studied, the time required to imbibe a fixed volume of water of a certain viscosity is approximately proportional to the square root of the viscosity of the reservoir oil whenever the oil viscosity is greater than the water viscosity. Results are also presented illustrating the effects on rate of imbibition of the other variables studied. Introduction The process of imbibition, or spontaneous flow of fluids in porous media under the influence of capillary pressure gradient s, occurs wherever there exist in permeable rock capillary pressure gradients which are not exactly balanced by opposing pressure gradients (such as those resulting from the influence of gravity). The importance of such capillary movement in the displacement of oil by water or gas was recognized in early investigations and described by Leverett, Lewis and True in 1942. Methods advanced by these authors for studying the process using dynamically scaled models were rendered more general and flexible by the research of later workers. The influence of capillary forces in laboratory water floods has also been discussed by several authors. While imbibition plays a very important role in the recovery of oil from normal reservoirs, Brownscombe and Dyes pointed out that imbibition might be the dominant displacement process in water flooding reservoirs characterized by drastic variations in permeability, such as in fractured- matrix reservoirs. In water-wet, fractured-matrix reservoirs, water will be imbibed from fractures into the matrix with a countercurrent expulsion of oil into the fractures. If the imbibition occurs at a sufficiently rapid rate, a very successful water flood can result; if the imbibition proceeds slowly the project might not be economically attractive. Scaled-model studies have demonstrated the vital importance of imbibition in secondary recovery in fractured reservoirs. It is therefore important in the evaluation of waterflooding prospects to develop a thorough understanding of the quantitative relationships of the factors which control the rapidity of capillary imbibition. The imbibition process serves reservoir engineers in still another important way by providing a technique for studying the wettability of reservoir core samples. Such experiments are usually conducted by observing the rate of expulsion of oil or water from core samples submerged in the appropriate fluid. Several papers have been published on the experimental techniques involved. Although Handy has recently published a method for calculating capillary pressures from experiments with gas-saturated cores, it has not yet been possible to deduce quantitative information regarding water-oil relative permeability and capillary pressure characteristics of the rock from the experimental results. Thus a technique is needed for studying the quantitative dependence of imbibition rate on oil and water viscosity, initial water saturation, relative permeability-saturation, and capillary pressure-saturation relations. The development of such information, including saturation and pressure profiles by laboratory experiments, would be very difficult. SPEJ P. 195ˆ

Influence of capillary forces upon the coefficient of contraction of a jet

Influence of capillary forces upon the coefficient of contraction of a jet