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| 储层流固耦合的数学模型和非线性有限元方程 | |
| 引用本文： | 张广明,刘合,张劲,吴恒安,王秀喜.储层流固耦合的数学模型和非线性有限元方程[J].岩土力学,2010,31(5):1657-1662. |
| 作者姓名： | 张广明 刘合 张劲 吴恒安 王秀喜 |
| 作者单位： | 1. 中国科学技术大学,近代力学系,合肥,230026 2. 中国科学技术大学,近代力学系,合肥,230026;中国石油勘探开发研究院,北京,100083 3. 中国石油大学(北京)石油和天然气工程学院,北京,102200 |
| 摘 要： | 根据饱和多孔介质固体骨架的平衡方程和多孔介质中流体的连续性方程，建立了储层流固耦合数学模型。模型中引入了Jaumann应力速率公式描述多孔介质固体骨架的大变形效应，并考虑了地应力、初始孔隙压力、初始流体密度和初始孔隙度对耦合模型的影响。基于与微分方程等价的加权余量公式，在空间域采用有限元离散，对时间域进行隐式差分格式离散，导出了以单元节点位移和单元节点孔隙压力为未知量的储层流固耦合的非线性有限元增量方程。该模型在石油工程中有广泛的应用，为储层流固耦合的数值模拟奠定了理论基础。 |
| 关 键 词： | 储层 流固耦合 数学模型 非线性有限元 多孔介质 |
| 收稿时间： | 2008-11-28 |
Mathematical model and nonlinear finite element equation for reservoir fluid-solid coupling |
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| ZHANG Guang-ming,LIU He,ZHANG Jin,WU Heng-an,WANG Xiu-xi.Mathematical model and nonlinear finite element equation for reservoir fluid-solid coupling[J].Rock and Soil Mechanics,2010,31(5):1657-1662. | |
| Authors: | ZHANG Guang-ming LIU He ZHANG Jin WU Heng-an WANG Xiu-xi |
| Institution: | 1. Department of Modern Mechanics, Hefei 230026, China; 2.Research Institute of Petroleum Exploration Development, Petro China, Beijing 163453, China; 3. School of Petroleum and Gas Engineering, China University of Petroleum, Beijing 102200, China |
| Abstract: | A mathematical model for fluid-solid coupling in reservoir was constructed based on the equilibrium equation of solid skeleton and continuity equation of wetting liquid in porous medium. Jaumann stress rate formula was adopted to describe the finite deformation behavior. The effects such as in situ stress, initial pore pressure, initial fluid density and initial porosity of the medium was also taken into account in the mathematical model. Finite element discretization was carried out on the mathematical model to get a fully coupled finite element equation with the parameters of element nodal displacement and element nodal pore pressure as unknown variables. Finally, the transient nonlinear finite element equation in incremental form for reservoir fluid-solid coupling is obtained by means of time discretization in implicit difference scheme. The resulted finite element formulation can simulate the reservoir behavior comprehensively and would have wide applications in petroleum engineering. |
| Keywords: | reservoir fluid-solid coupling mathematical model nonlinear finite elements porous medium |
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