非饱和带水气二相渗流动力学模型

非饱和带地下水运动实质上是一个水气二相渗流过程。本文以多相渗流理论为基础,从水气二相渗流的连续性方程和达西定律出发,推导了非饱和带水气二相渗流的耦合动力学模型,讨论了模型的IMPES和全隐式联立求解方法的原理和步骤,认为IMPES求解方法由于达西系数项的处理,饱和度的计算均采用显式,因此该解法具有稳定性差、精度低且要求计算时间步长小的局限性;而全隐式联立求解方法是联立求解气相、水相方程,同时求出压力和饱和度值,因此压力和饱和度值都是隐式求出,具有较高精度,且无条件稳定,应是今后模型求解的重点研究内容      

煤层气运移产出气水固三相耦合模型

根据达西渗流理论 ,结合Langmuir等温吸附定律和Fick第一定律描述了煤层气由煤基质解吸经扩散进入煤层裂隙系统 ,由裂隙运移至生产井筒产出的气水二相渗流过程 ,又将其和由渗流作用引起的煤体变形场耦合起来 ,形成了煤层气运移产出的气水固三相耦合模型 ,并采用全隐式联立求解方法同时隐式求出了气、水产量和饱和度值 ,实现了模型求解的无条件稳定。在沁水盆地 3 # 煤层气井开采潜能的评价预测中 ,应用该方法分别预测了将该井的动液面置于 3 # 煤底和 15 # 煤底的气、水产量 ,效果良好。     

水气二相渗流耦合模型及其应用

本文建立了非饱和带水气二相渗流的耦合模型,并采用IMPES(隐式求解压力方程,显式求解饱和度)求解方法对该模型进行了求解。在此基础上,将该模型应用于沁水盆地TL煤层气井水气运移、产出的模拟计算,利用该井1999年2月9日～5月6日的水气排采资料,通过历史拟合计算,对影响该井水气产量的主要参数(如渗透率、表皮系数、相对渗透率等)进行了校正、识别,预测了该井未来20年的水气产量动态变化特征。     

解二维抛物型方程初边值问题的交替方向隐式方法

详细地研究了各种情形的求解二维抛物型方程初边值问题的交替方向隐式差分法。这种方法可以将二维隐式方法归结为求解三对角线性方程组。与一维情况类似,可以继续利用追赶 法求解。它具有运算速度快,存储量小,无条件稳定等优点。该方法是求解二维物型方程的有效方法,必将得到更广泛的应用。     

非饱和土二维固结简化计算的研究

针对较高饱和度的非饱和土二维固结问题展开研究。对于较高饱和度的非饱和土,如饱和度 时,将孔隙中气、水近似地看作可压缩的气、水混合流体后,非饱和土近似为土骨架和混合流体的二相土。考虑混合流体的压缩性,建立混合流体的连续方程。联立平衡方程和混合流体的连续方程,求出应力-应变和混合流体压力;再建立水连续方程求解水压力,继而求出气压力、吸力等。算例表明：加载和消散过程中,混合流体与水压力变化基本一致,气压的作用并不大;地基变形过程与高速公路填筑过程中地基变形发生规律一致。说明该简化方法是合理的,并促进了非饱和土固结变形计算走向实用化。     

声波方程隐式高阶有限差分数值模拟

推导了声波方程空间二阶导数的隐式求解公式及差分系数的求解方法,讨论了该方法的数值频散特征。利用该方法分别对均匀介质及Marmousi模型进行了数值模拟,将其结果与传统的显式差分格式的模拟结果进行了对比分析。结果表明:该方法较传统的显式求解方法具有更低的数值频散、更高的计算精度。      

大牛地低产气井产气剖面测井资料解释方法探讨

当气井产量较低时,由于气相速度不足以将地层产水带出井筒,随着开发的时间推移,井筒内积液将不断增多,最终造成气井水淹,影响气井产能。文中建立了气携水状态下的力学模型,用于计算气携水流动状态下的气相流量,并根据井筒中上、中、下三段流型特征,提出了三段式气相流量计算方法。将该解释方法用于大牛地低产气井产气剖面测井资料的解释,结果表明新方法的解释结果和实际生产状况更吻合,提高了解释精度。     

无时间差分变量的非饱和土渗透计算

在得出理查兹渗透方程近似精确解基础上，建立无时间差分变量的隐式差分计算格式。在该差分方程中，将渗透深度分为传导渗透与扩散渗透两部分深度。为了减少直接计算岩土含水量系数所产生的误差，将上述的两部分渗透深度函数表达式代入隐式差分格式，在节省大量计算时间的基础上，求得较为精确的计算结果。文中给出了该方法与普通隐式有限差分法对粘土、壤土渗透深度曲线计算结果的对比。     

下边界条件为水位流量关系的扩散波洪水演算方法研究

经大量的理论分析和实际洪水演算表明,扩散波可较好地反映洪水波的运动特点。本文基于河道下断面的水位流量关系和连续方程的联立求解,导出了水位流量关系型的下边界条件。利用Laplace变换,得到了扩散波方程在该边界条件下的解析解。文中的求解过程表明,可利用该法进行洪水演算,关键在于如何与实际洪水结合,这个问题有待进一步地分析研究。     

计算给水度和导水系数的一种新方法

本文介绍的求给水度μ值和导水系数T值的方法,是以水量平衡原理为基础,在计算区内分别建立地下水开采阶段和水位恢复阶段水量平衡方程,然后用联立求解的方法得出给水度μ值和导水系数T值     

煤层气产出过程中气—水两相流与煤岩变形耦合数学模型研究

气－水二相流和煤岩变形耦合作用是煤层气产出过程中一种复杂的物理现象，为准确描述这一现象，本文建立了气－水二相流和煤岩变形的微分方程，并用有限元分别将它们进行离散化，然后讨论了煤岩变形模型和气－水二相流模型进行耦合数值求解的方法。     

水—气二相流及污染物运移数值模拟研究

本文通过对近些年来水－气二相流数值模拟进展情况的分析,总结了在水－气二相流模拟过程中,各个主要参数或物理过程的数学概化方法,以及近年来在求解水气二相流方程和污染运移方程的方法上的改进情况。并在此基础上提出了需进一步研究解决的问题。     

低渗透煤层气-水流固耦合数学模型及数值模拟

基于有效应力原理,结合弹塑性几何方程、本构方程及平衡方程建立了应力场控制方程。依据流体力学中的质量守恒原理建立了煤层气、水和煤岩体固体颗粒的渗流场方程;以上方程再配以辅助方程和定解条件构成了应力作用下煤层 气-水流固耦合的数学模型,并对简化模型进行了单相流流-固耦合数值模拟分析,得到了压力动态分布曲线,分析了耦合和非耦合情况对压力分布的影响,进一步为煤层气流-固耦合分析提供了一定的理论基础。     

Ordering-based nonlinear solver for fully-implicit simulation of three-phase flow

The Fully Implicit method (FIM) is often the method of choice for the temporal discretization of the partial differential equations governing multiphase flow in porous media. The FIM involves solving large coupled systems of nonlinear algebraic equations. Newton-based methods, which are employed to solve the nonlinear systems, can suffer from convergence problems—this is especially true for large time steps in the presence of highly nonlinear flow physics. To overcome such convergence problems, the time step is usually reduced, and the Newton steps are restarted from the solution of the previous (converged) time step. Recently, potential ordering and the reduced-Newton method were used to solve immiscible three-phase flow in the presence of buoyancy and capillary effects (e.g., Kwok and Tchelepi, J. Comput. Phys. 227(1), 706–727 2007). Here, we improve the robustness of the potential-based ordering method in the presence of gravity. Furthermore, we also extend this nonlinear approach to interphase mass transfer. Our algorithm deals effectively with mass transfer between the liquid and gas phases, including phase disappearance (e.g., gas going back in solution) and reappearance (e.g., gas coming out of solution and forming a separate phase), as a function of pressure and composition. Detailed comparisons of the robustness and efficiency of the potential-based solver with state-of-the-art nonlinear/linear solvers are presented for immiscible two-phase (Dead-Oil), Black-Oil, and compositional problems using heterogeneous models. The results show that for large time steps, our nonlinear ordering-based solver reduces the number of nonlinear iterations significantly, which leads to gains in the overall computational cost.     

Ordering-based nonlinear solver for fully-implicit simulation of three-phase flow

The Fully Implicit Method (FIM) is often the method of choice for the temporal discretization of the partial differential equations governing multiphase flow in porous media. The FIM involves solving large coupled systems of nonlinear algebraic equations. Newton-based methods, which are employed to solve the nonlinear systems, can suffer from convergence problems—this is especially true for large time steps in the presence of highly nonlinear flow physics. To overcome such convergence problems, the time step is usually reduced, and the Newton steps are restarted from the solution of the previous (converged) time step. Recently, potential ordering and the reduced-Newton method were used to solve immiscible three-phase flow in the presence of buoyancy and capillary effects (e.g., Kwok and Tchelepi, J. Comput. Phys. 227(1), 706–727 9). Here, we improve the robustness of the potential-based ordering method in the presence of gravity. Furthermore, we also extend this nonlinear approach to interphase mass transfer. Our algorithm deals effectively with mass transfer between the liquid and gas phases, including phase disappearance (e.g., gas going back in solution) and reappearance (e.g., gas coming out of solution and forming a separate phase), as a function of pressure and composition. Detailed comparisons of the robustness and efficiency of the potential-based solver with state-of-the-art nonlinear/linear solvers are presented for immiscible two-phase (Dead-Oil), Black-Oil, and compositional problems using heterogeneous models. The results show that for large time steps, our nonlinear ordering-based solver reduces the number of nonlinear iterations significantly, which leads to gains in the overall computational cost.     

非饱和土中水流入渗和气体排出过程的求解

采用孔隙介质力学分析方法,把土体骨架、孔隙水和孔隙气分别作为独立的研究对象,结合孔隙水和孔隙气在气液交界面上满足的力学条件建立耦合方程,求解非饱和土中孔隙水的入渗和孔隙气体的排出过程。对标准砂进行的一维有压水流入渗试验和计算表明,孔隙气的排出过程影响孔隙水的渗流运动。数值计算与试验结果拟合较好。     

Numerical approximation of water–air two-phase flow by the mixed finite element method

A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems.     

水流入渗和气体驱替过程二维问题的耦合求解

采用孔隙介质力学分析方法,把土体骨架、孔隙水和孔隙气体分别作为独立的研究对象,结合孔隙水和孔隙气体在气、液交界面上的力学条件建立耦合方程,研究非饱和土中孔隙水的入渗和孔隙气体的排出过程,为水流入渗问题的求解提供了一种新的方法。将此种方法应用于二维水流入渗问题的数值求解,利用简单的工况校验了这种计算方法的可靠性。通过对砂体和粉煤灰断面进行的二维水流入渗计算表明,孔隙气体的排出过程影响孔隙水的入渗运动。