油藏数值模拟中动边值问题的特征差分方法

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对于合理评估油气资源的勘探和开发有重要的价值。其数学模型是一组非线性偶合偏微分方程组的动边值问题。通过一类特征差分格式,得到了最佳阶的l~2误差估计结果。对这一领域的模型分析、数值方法和软件研制均有重要的理论和实用价值。     

三维动边值问题的特征混合元方法和分析 *

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对于评估油气资源的勘探和开发有重要的价值.其数学模型是三维空间非线性偶合偏微分方程组的动边值问题.从实际出发,考虑了重力、毛管力和浮力作用的二类边值问题,提出一类特征混合元格式,应用区域变换,处理边界条件的时间变步长技巧,负模估计和先验估计理论,得到最佳阶L²估计。     

动边值问题的混合元方法和数值分析

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史。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。本文对二维、有界区域的一般情况，提出一类特征混合元逼近并得到了逼近解的最佳Ｌ＾２模误差估计。     

二维可压缩油水两相渗流动边值问题的特征差分方法

可压缩可混溶油、水两相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偶合偏微分方程组的动边值问题．本文对二维有界域的两类边值问题提出一类新的特征差分格式,应用区域变换、时间的变步长、粗细网格配套、变分形式、先验估计的理论和技巧,得到了最佳阶l2误差估计结果．将J．Douglas,Jr．提出的著名方法,成功地拓广到这一新领域,并得到实质性进展．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.     

油藏盆地发育数值模拟中的偏微分方程组的差分方法和数值分析

近年来石油科学在石油有机地球化学,石油的生成,运移,聚集理论的研究方面取得了重大的进展,在评价一个盆地的含油气资源时,对于盆地发育史,尤其是对受热变化的历史了解是非常重要的。 本文研究盆地发育史模型所提出的耦合抛物型偏微分方程组的初、边值问题,第一个     

三维油资源运移聚集的模拟和应用

盆地发育的运移聚集史数值模拟,其功能是重建油气盆地的运移聚集演化史,它对于油资源的勘探,确定油藏位置和计算油藏贮量,寻找新的油田,具有极其重要的价值.本文从地质科学实际出发,研究了三维问题的地质和渗流力学特征,提出二阶修正算子分裂隐式迭代格式,对着名油水运移聚集实验进行了数值模拟,结果基本吻合,并对胜利油田东营凹陷的实际问题进行数值模拟试验,结果和实际地质情况(油田位置等)基本吻合,成功解决了这一着名问题.     

具有活动边界的油藏盆地发育史的数值模拟方法

近年来,石油科学在石油有机地球化学,石油的生成、运移和聚集的理论等方面的研究都取得了重大进展。在评估一个含油气盆地的油气资源时,对于盆地的发育史,尤其是温度变化的历史的了解是极其重要的。由于含油气盆地是经过一个漫长的复杂过程形成的,因而以往的研究都是在油气盆地具有固定边界的假设下进行的,而实际上盆地是随时间不断变     

油气资源数值模拟的变网格交替方向特征有限元格式和分析

石油科学在有机地球化学、石油的生成、运移、聚集研究取得重大进展,在评价油气资源时,对盆地发育史尤其对流体流动规律和受热变化历史的计算是非常重要的.其数学模型是三维空间非线性偶合偏微分方程组的初边值问题.从实际出发,考虑了流体的压缩性和三维问题大规模科学与工程计算的特征, 提出了一类变网格交替方向特征有限元格式,应用变分形式、算子分裂、广义$L^2$投影、能量方法、负模估计、微分方程先验估计的理论和技巧,得到最佳阶$L^2$误差估计. 此方法已成功应用到油气资源评估数值模拟的生产实践中,成功解决了这一重要问题.     

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference 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 change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.     

三维油水运移聚集数值模拟的交替方向格式和分析

研究油气运移聚集史的数值模拟,其数学模型是三维非线性偏微分方程组的初进值问题．我们从实际出发,考虑了重力、毛管力和浮力的作用,同时考虑到三维问题大规模科学和工程计算的特征,提出对流动方程采用大步长的混合元法,而对三维饱和度方程的计算,采用一类交替方向特征有限元法．将其化为连续解三个一维问题,使工程数值计算成为可能．应用张量积计算．负模估计和先验估计理论,得到最佳阶Ｌ~２误差估计．     

CHARACTERISTIC FINITE DIFFERENCEALTERNATING-DIRECTION METHOD AND ANALYSIS FOR NUMERICAL RESERVOIR SIMULATION

1IntroductionInrecentyears,petroleun1sciellcel1asll1aderemarkableprogressillorgallicgeochell1istryandtheresearchil1totl1etl1eoriesofpetroleumorigin,itstrallsportalldaccllmulatiol1.Inestil11ati1lgtheoil-gasresourcesofabasin,thek11owledgeofitsevolutiollaryhistoryandcs-peciallytl1ellun1ericaJcolllputatiolloffluidflowa11dthehistoryofitscl1al1gesll1lderl1eatarevital.Nu111ericalsinmlationforevolutiol1aryl1istoryofthebasillistousell1oder11con1putersandcalculatingtechniquestorepeattheproccssofbasi1lcv…     

THE CHARACTERISTIC FINITE ELEMENT ALTERNATING-DIRECTION METHOD AND ANALYSIS FOR THREE-DIMENSIONAL NUMERICAL RESERVOIR SIMULATION

Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L~2 norm for the error in the approximate assumption.     

凝析气藏段塞流动的初—边值问题及褶积理论的应用

推出凝析油－气两相渗流方程,引入凝析油－气两相拟压力－时间函数,使渗流方程线性化,针对低渗凝析气藏的钻杆测试问题,在研究凝析油－气的段塞流动特征的基础上,建立了描述凝析气段塞流动的初－边值问题,求出这一问题解,并把褶积理论引入凝析气段塞流动资料分析模型中,建立了短时段塞流动资料解释的新理论与新方法,作为理论的应用文中给出了分析实例。     

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 67–84, 2006.     

Reduced order fully coupled structural–acoustic analysis via implicit moment matching

A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS.