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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Convergence analysis of the nonlinear iterative method for two-phase flow in porous media associated with nanoparticle injection
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Convergence analysis of the nonlinear iterative method for two-phase flow in porous media associated with nanoparticle injection

机译：与纳米粒子注入相关的多孔介质中两相流非线性迭代方法的收敛性分析

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Purpose - This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles' transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles' concentration, deposited nanoparticles' concentration on the pore-walls and entrapped nanoparticles concentration in porethroats. Design/methodology/approach - A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation-IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated. Findings - Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant-Friedrichs-Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size. Research limitations/implications - The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters. Originality/value - The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.
机译：目的-本文旨在介绍多孔介质中两相流携带的纳米颗粒传输问题的建模，数值模拟和收敛性分析。该模型由压力，饱和度，纳米颗粒浓度，孔壁上沉积的纳米颗粒浓度以及孔喉中截留的纳米颗粒浓度等式组成。设计/方法/方法-非线性迭代IMPES-IMC（隐式压力显式饱和-隐式浓度）方案用于解决所考虑的问题。控制方程使用单元中心有限差分法（CCFD）离散化。压力和饱和度方程耦合以计算压力，然后显式更新饱和度。因此，隐式计算了纳米颗粒浓度，在孔壁上沉积的纳米颗粒浓度和在孔喉中截留的纳米颗粒浓度的方程式。然后，更新孔隙率和渗透率变化。发现-陈述并证明了自然条件下迭代方法收敛的三个引理和一个定理，并给出了证明和证明。该定理由归纳状态证明，经过多次迭代，诸如饱和度和浓度之类的因变量序列在下一时间步接近解。此外，根据Courant-Friedrichs-Lewy（CFL）条件和松弛因子，通过收敛测试引入了两个数值示例。诸如压力，饱和度，浓度，沉积浓度，孔隙率和渗透率之类的因变量在图中以等高线的形式绘制，而误差估计值则以时间步长，迭代次数和网格尺寸的不同值显示在表格中。研究局限/含义-计算范围相对较小；但是，通过保持CFL数和其他物理参数的相似定义，可以将此方法扩展到油藏（大）域，这很简单。创意/价值-所考虑的问题的模型之前尚未研究过。同样，此模型之前未使用求解技术和收敛分析。

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