Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible,three-phase flow with gravity

Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model). Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation). The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities. The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/ sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of nonlinear compressible multiphase flow in strongly heterogeneous formations.     

Investigation of splitting gas and aqueous operators in atmospheric multiphase box models

Operator splitting techniques are widely used in atmospheric modeling in order to reduce the cost of time integration and allow more flexibility by treating each operator separately. However, this is not error free and the magnitude of the error depends on whether the splitted operators commute or not and the magnitude of the splitting time step. In multiphase models, the gas and the aqueous phase chemistries are related through the gas-droplet mass transfer processes. In the present paper, we show that splitting the gas chemistry operator from the aqueous chemistry and mass transfer operator is not appropriate and leads to errors beyond the tolerated thresholds. Analytical expressions for the splitting errors are derived and numerical experiments are conducted. The LAMP chemical mechanism is employed. Time integration is performed with LSODE.     

一种新的基于连通成分的边缘评价方法

考虑到边缘局部相关性的特点，提出了一种新的边缘评价方法，该方法不需要标准边缘图，对边缘图直接求取总的边缘点数(A)、4一连通成分数(B)、8一连通成分(C)数以及C／A、C／B的比值，然后进行综合评价。实验结果表明，该评价方法具有很强的现实意义和参考价值。     

常系数非齐次微分方程特解的算子解法和注释

本文对常系数非齐次微分方程特解的算子解法进行了比较系统地论证和归纳,并对某些问题作了必要的注释。     

Groundwater transport modeling with nonlinear sorption and intraparticle diffusion

Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of “dual mode” sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including “dual mode” and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.     

湿大气方程组解的渐近性质

研究无穷维Ｈｉｌｂｅｒｔ空间中,湿大气运动系统解的长期行为,在导得了湿大气运动方程是Ｈｉｌｂｅｒｔ空间中一个非常特殊的算子方程之后,利用算子的性质讨论了全局吸收集和全局吸引子的存在性,揭示出系统解的渐近行为表现在吸引子的结构上及系统向非绝热加热的非线性适应过程。最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同,从而给出长期天气或气候研究中简化方程组必须遵循的原则。     

地震反演成像中的Hessian算子研究

总结了牛顿类地震反演方法中Hessian算子的作用,对其在地震反演成像中的数学物理含义进行了分析.Hessian算子是误差泛函对模型参数的二阶导数,反映了误差泛函对模型变化的二次型特征.分析声波方程下的Hessian算子的格林函数表达形式,发现其表达了整个观测系统和子波频带等因素对地震数据空间到模型空间投影过程的影响.提出了两种分别适用于最小二乘偏移和全波形反演的Hessian算子简化格式.平面波Hessian算子应用于最小二乘偏移能够得到相对保真的成像结果,改善了地震偏移成像的精度.地下偏移距Hessian算子应用于全波形反演能够加快反演迭代的计算效率.最后,对Hessian算子在地震反演成像中的价值进行了讨论和评价.     

Computer simulation of deep sulfate reduction in sediments of the Amazon Fan

 Pore water concentration profiles of sediments at a site on the Amazon Fan were investigated and simulated with the numerical model CoTReM (column transport and reaction model) to reveal the biogeochemical processes involved. The pore water profiles for gravity core GeoB 4417-7 showed a distinct sulfate–methane transition zone in which deep sulfate reduction occurs. Only a small sulfide peak could be observed at the reaction zone. Due to high amounts of iron minerals, the produced sulfide is instantaneously precipitated in form of iron sulfides. We present a simulation which starts from a steady state system with respect to pore water profiles for methane and sulfate. Furthermore, sulfide, iron, pH, pE, calcium and total inorganic carbon (TIC) were included in the simulation. The program calculated mineral equilibria to mackinawite, iron sulfides (more stable than mackinawite), iron hydroxides and calcite via saturation indices (SI) by a module incorporating the program PHREEQC (Parkhurst 1995). The measured sulfide and iron profiles are obtained in the simulation output by using a constant SI (=0) for mackinawite and calcite, while a depth dependent SI distribution is applied for the PHREEQC phases “Pyrite” and “Fe(OH)3(a)”, representing a composition and the kinetics of different iron sulfides and iron hydroxides. These SI distributions control the results of sulfide and iron pore water profiles, especially conserving the sulfide profile at the reaction zone during the simulation. The results suggest that phases of iron hydroxides are dissolved, mackinawite is precipitated within, and other iron sulfides are precipitated below the reaction zone. The chemical reactivity of iron hydroxides corresponds to the rate of sulfide production. The system H₂O–CO₂–CaCO₃ is generally successfully maintained during the simulation. Deviations to the measured pH profile suggest that further processes are active which are not included in the simulation yet. Received: 9 November 1998 / Accepted: 26 October 1999     

两种变时间步长的显式差分算法

针对一类大气、海洋问题，从算子方程出发，在显式完全平方守恒差分格式的基础上提出两种变时间步长的差分算法，使数值计算更加有效。在人工调节时间步长法中，通过人为控制方程中算子能量变化的办法调整时间步长；在自动调节时间步长法中，通过数值试验自动比较出所构造差分格式稳定性的好坏，将它与泰勒展开法及分解算法进行混合应用，验明了自动调节时间步长法具有综合判断差分格式好坏的功能，并得出一些有意义的结论。     

等价观测与GPS差分法定位

本文首先利用空间和投影算子的概念证明了等价观测中的部分等价性定理，然后从该定理出发讨论了各种GPS差分定位法的等价性问题并给出了其相应的等价条件。