油水运移聚集数值模拟和分析

油资源的运移聚集数值模拟是描述在盆地发育中油水运移聚集演化的历史,它对于油田的勘探和合理开发有着重要的价值.本文提出问题的数学模型和修正交替方向隐式迭式格式.对于着名的二次运移聚集的水动力学实验(剖面和平面问题),进行了数值模拟,模拟结果和实验结果是完全吻合的.     

滩海地区运移聚集的精细数值模拟和分析

对滩海地区三层油资源运移聚集进行高精度精细平行数值模拟,提出数学模型和精细平行算子分裂隐式迭代格式,设计了并行计算程序,提出了并行计算的信息传递和交替方向网格剖分方法. 并对不同的CPU组合进行并行计算和分析,对滩海地区数值模拟结果和实际情况吻合.对模型问题进行数值分析,得到最佳阶误差估计,成功地解决了这一困难问题．     

三维盆地发育史的数值模拟

盆地数值模拟方法就是在计算机上重建盆地发育的地史和热史，并将这些地质信息进一步定量化地导出石油生成、运移和聚集的历史。其中地史和热史的数学模型是一组非线性偏微分方程初边值问题。本文给出了三维问题的数值解法，模型问题的稳定性分析以及计算实例的数值结果，计算得到的超压和古温度合理，有很强的物理特性。     

油、水两相渗流驱动问题的离散算子法及其数值分析

本文应用离散算子法解决油、水两相渗流驱动问题的数值模拟并进行了理论分析.最后我们根据油田的实际地质参数进行了模型试算,并对结果进行分析.对于单相渗流数值模拟的理论分析我们已有工作.对于不考虑毛细管力的弹性驱动问题的有限元方法我们已有工作.     

油资源二次运移大规模并行数值模拟及其在胜利油田应用

从生产实际出发,开展了多层问题的石油地质和渗流力学特征研究,提出了新的数学模型,构造了适合并行计算的耦合算子分裂隐式迭代格式,并成功地对胜利油田东营凹陷（四层）和滩海地区（三层）的实际问题进行了大规模并行计算的数值模拟,计算结果在油藏位置等方面和实际情况相吻合．成功地解决了这一计算渗流力学和石油地质的重要问题．     

注采比方法在油田精细注水中的应用——以牛心坨油田为例

在低渗透油田合理配注量研究的基础之上,建立了油藏数值模型,进行了历史生产数据不同含水阶段注采比合理性分析.根据牛心坨油层上层系矿场实际资料,建立牛心坨油层综合含水与水油比、综合含水与耗水量的数学模型,并推导出不同含水率的注采比模型,对油田注采比进行了预测;为研究单一因素对注采比的影响,建立理想模型,应用数值模拟方法以定液量生产制度预测不同含水时期不同注采比条件下开发指标变化,并与油藏工程方法结合得出最优注采比.目的在于直接得出注采比与含水率的关系,对于低渗透油田预测注采比具有很好的推广应用价值.     

三维动边值问题的迎风差分方法

可压缩可混溶油、水三维渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值, 其数学模型是一组非线性耦合偏微分方程组的动边值问题. 该文对有界域的动边值问题提出一类新的二阶修正迎风差分格式, 应用区域变换、 变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧, 得到了最佳 $l^2$ 误差估计结果. 该方法已成功应用到油资评估的数值模拟中. 它对这一领域的模型分析, 数值方法和软件研制均有重要的价值.     

油水渗流动边值问题的迎风差分方法

可压缩可混溶油、水渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值,其数学模型是一组非线性耦合偏微分方程组的动边值问题.对二维有界域的动边值问题提出一类新的迎风差分格式,应用区域变换、变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到了最佳误差估计结果.该方法已成功应用到油资评估的数值模拟中.它对这一领域的模型分析,数值方法和软件研制均有重要的价值.     

三维渗流耦合系统动边值问题迎风差分方法的理论和应用

对多层渗流方程耦合系统动边值问题,提出适合并行计算的两类迎风差分格式,利用区域变换、变分形式、能量方法、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,得到收敛性的l~2误差估计.该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中,得到了很好的数值模拟结果.     

多层油资源运移聚集的数值模拟和实际应用

研究了三维问题的石油地质和渗流力学特征。提出了数学模型,构造了新的算子分裂隐式迭代格式,并成功地对胜利油田东营凹陷(厚层)和惠民凹陷(多层)带断层和通道的实际问题进行了大规的数值模拟计算。计算结果在油藏位置等方面和实际情况相吻合,完整地解决了这一石油地质和渗流力学的国际着名问题。     

The upwind finite difference fractional steps method for nonlinear coupled systems

For nonlinear coupled system of multilayer dynamics of fluids in porous media, a second‐order upwind finite‐difference fractional‐steps scheme applicable to parallel arithmetic are put forward, and two‐ and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators, and prior estimates are adopted. Optimal order estimates in l² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of migration‐accumulation of oil resources. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

The second‐order upwind finite difference fractional steps method for moving boundary value problem of oil‐water percolation

The research of the three‐dimensional (3D) compressible miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil‐gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil‐gas resources, and numerical simulation of seawater intrusion. The mathematical model can be described as a 3D‐coupled system of nonlinear partial differential equations with moving boundary values. For a generic case of 3D‐bounded region, a kind of second‐order upwind finite difference fractional steps schemes applicable to parallel arithmetic is put forward. Some techniques, such as the change of variables, calculus of variations, and the theory of a priori estimates, are adopted. Optimal order estimates in l² norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development. Thus, the well‐known problem has been solved.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1103–1129, 2014     

The upwind finite difference fractional steps methods for two‐phase compressible flow in porous media

The upwind finite difference fractional steps methods are put forward for the two‐phase compressible displacement problem. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators, and prior estimates, are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration‐accumulation of oil resources. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 67–88, 2003     

三维非线性对流扩散问题的数值方法在渗流力学的应用

对三维非线性对流扩散问题提出一类适合并行计算的二阶迎风分数步差分格式,采用分数步技术,将三维问题化为连续解3个一维问题计算．利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到收敛性的最佳阶的误差估计．该方法已成功的应用油资源运移聚集渗流力学数值模拟计算、海水入侵预测和防治的工程实践中．     

Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application

For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L ² norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.