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A Finite Volume Method For Flows Of Viscoelastic Polymer Solution Through Porous Media

Posted on:2006-04-25Degree:MasterType:Thesis
Country:ChinaCandidate:H T WangFull Text:PDF
GTID:2121360155477203Subject:Oil and gas field development project
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It's well known that the finite volume element methods are widely and successfully used in solving many mathematical-physical problems due to their simplicity and local conservation properties in recent years. But the finite volume method is very few to use when we solve the flow problem of viscoelastic because that the basic theories on polymer flooding is far from complete, for the characterizing flow behavior of polymer solution still relies on empirical of simi-empirical constitutive equation. In this thesis, a great deal of work is reviewed including the status quo of basic theories on polymer flooding, model for viscoelastic fluid, model of porous media, and general research on the flow of viscoelastic fluid through complex channels. It is shown that research on the mechanism of microscopic displacement commonly bases on laboratory studies, for some oil displacement phenomena, it can only explained qualitatively, the theoretical research needs further on. So that, besides choosing proper model for viscoelastic fluid and geometric model characterizing reservoir pores, effective numerical methods should be used to solve mathematical model, so as to theoretically study viscoelasticity of polymer solution how to affect the microscopic displacement efficiency quantitatively. Therefore, we have done the following work mainly: First, in order to obtain the complete mathematic description for the flowing behaviour of viscoelastic fluid in pores, which will be convenient for understanding microscopic recovery efficiency of viscoelastic fluid in theory, we utilize two pore structure model for various existence form of residual oil : expansion channel and one-slotted (with one transverse slot) channel in this paper. The models combined with the constitutive equations for upper convected Maxwell, the momentum equations, the continuity equation and boundary conditions of two channel model, were used to building the complete mathematics model. Second, the nonlinearly coupled systems, which made up with UCM constitutive equation, the momentum equation, the continuity equation as well as boundary condition, are solved using the finite volume method (FVM). To overcome the Unreasonable pressure computation problem and accuracy of calculation, staggered grid is used in whole calculation domain. In the paper an upwind scheme is used in the constitutive equation and a hybrid scheme is used in the momentum equation and discretization form of control equation group is obtained. The last important link is solving of discretization equation. The alternating direction implicit (ADI) method is used to solve discretization equation and supplement block iteration method to quickening convergence. Ultimately, we calculate steam function field, velocity field, pressure field and stress field. Third, in order to calculate microscopic sweep efficiency in pore models, we define sweep boundary of displacement fluid, and determine it by velocity method. The calculation results show that Re, We and the shape of channel play a great role in microscopic efficiency. At low Re number, that is to say, under the reservoir situation Re<10, viscoelastic effect contributes to enhancing sweep efficiency in dead oil area most, so with We number increasing, microscopic displacement efficiency is linearly increased. At high Re number, Re>10, inertia effect is the most important. Therefore, for fluid without elasticity microscopic sweep efficiency rapidly increases. In addition, pore channel's shape affects microscopic sweep efficiency by changing the flow situation. Last, combined with analyses mentioned above, as to the microscopic displacement efficiency of viscoelastic fluid, our conclusions is: under reservoir flow situation, the internal reason why viscoelastic fluid enhances sweep efficiency in dead oil area of salient corner and "dead end" is that viscoelastic effect changes the distribution of some comprehensive stress in the whole field. Numerical results show that higher viscoelasticity, the larger microscopic sweep efficiency of the fluid.
Keywords/Search Tags:Finite volume method, staggered grid, upper-convected Maxwell model, viscoelastic fluid, microscopic displacement efficiency
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