One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise line...One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.展开更多
为实现多组分复杂流体流动与扩散耦合过程的准确预测,提出一种耦合多组分Shan-Chen格子玻尔兹曼法(lattice Boltzmann method,LBM)、Maxwell-Stefan扩散通量方程及4参数(临界温度、临界压力、偏心因子和体积修正因子)Peng-Robinson状态...为实现多组分复杂流体流动与扩散耦合过程的准确预测,提出一种耦合多组分Shan-Chen格子玻尔兹曼法(lattice Boltzmann method,LBM)、Maxwell-Stefan扩散通量方程及4参数(临界温度、临界压力、偏心因子和体积修正因子)Peng-Robinson状态方程(equation of state,EOS)的多组分流体流动与扩散耦合模型(equation of state Maxwell-Stefan force model,EOS-MS模型).通过Peng-Robinson EOS计算混合流体整体的流体间作用力,结合多组分LBM中流体间作用力与压力的关系,构建组分流速与流体间作用力的关联,并代入Maxwell-Stefan方程,推导得到各组分受力的代数方程组.利用精确差分法(exact difference method,EDM)将计算得到的组分间作用力引入多组分LBM.分别模拟甲烷、乙烷纯物质及其混合物的气液两相共存问题,计算结果与标准参考数据及逸度平衡法的计算结果一致,验证了模型在预测混合流体热力学平衡态方面的准确性.通过模拟氢气、氮气和二氧化碳的三元扩散动态过程,发现模型结果与有限体积法预测高度吻合,并成功复现了多组分流体中逆扩散等实际扩散现象,证明模型在多组分流体流动与扩散耦合模拟中的有效性.本研究构建的EoS-MS力模型可准确预测多组分流动与扩散耦合过程,避免了在组分受力计算中引入人为假设带来的误差,为解决地热资源利用等领域中存在的多组分复杂流动问题提供了新方法.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(Grant 2015XKMS014)
文摘One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.
文摘为实现多组分复杂流体流动与扩散耦合过程的准确预测,提出一种耦合多组分Shan-Chen格子玻尔兹曼法(lattice Boltzmann method,LBM)、Maxwell-Stefan扩散通量方程及4参数(临界温度、临界压力、偏心因子和体积修正因子)Peng-Robinson状态方程(equation of state,EOS)的多组分流体流动与扩散耦合模型(equation of state Maxwell-Stefan force model,EOS-MS模型).通过Peng-Robinson EOS计算混合流体整体的流体间作用力,结合多组分LBM中流体间作用力与压力的关系,构建组分流速与流体间作用力的关联,并代入Maxwell-Stefan方程,推导得到各组分受力的代数方程组.利用精确差分法(exact difference method,EDM)将计算得到的组分间作用力引入多组分LBM.分别模拟甲烷、乙烷纯物质及其混合物的气液两相共存问题,计算结果与标准参考数据及逸度平衡法的计算结果一致,验证了模型在预测混合流体热力学平衡态方面的准确性.通过模拟氢气、氮气和二氧化碳的三元扩散动态过程,发现模型结果与有限体积法预测高度吻合,并成功复现了多组分流体中逆扩散等实际扩散现象,证明模型在多组分流体流动与扩散耦合模拟中的有效性.本研究构建的EoS-MS力模型可准确预测多组分流动与扩散耦合过程,避免了在组分受力计算中引入人为假设带来的误差,为解决地热资源利用等领域中存在的多组分复杂流动问题提供了新方法.
