CN1386200A - 有限元模型中的特征建模方法 - Google Patents
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Abstract
一种使用有限元技术仿真物理系统的方法,其中求解对应于被建模的系统内不同区域两个或多个不同的模型,每一模型带有对应的鉴别程序。位于模型之间的边界上的结点可以具有对应于不同模型的不同值。当求解特定的特征模型时,使用用于该模型的鉴别程序,以便对于每一这些公共结点获得适当的值。在一个实施例中,定义了第一模型,然后从其分割出对应于系统内特定特征的区域。然后对应于该特征的有限元模型被插入到该区域。有限元可被适应性修改以共享它们之间边界上的结点。
Description
相关的申请
本申请按35 U.S.C.§-119(e)要求给予美国专利申请No.60/215,697,标题为储油层仿真与建模的方法和系统”的优先权,该申请由Stephen R.Kennon,Kok Thye Lim,Scott A.Canaan,Steven B.Ward,Stuart W.Pond,Jr.及Edward J.Barragy于2000年6月29日提交,该文献按其提交的整体在此结合以资对比。
本发明的技术领域
本发明一般地涉及使用有限元分析对物理系统建模的方法,并特别涉及用于对物理系统的特征,诸如地质构造中的特征建模的方法,其中在这些特征之间的边界和物理系统周围区域一个或多个性质有变化。
本发明的背景
在一定条件下可在数学上对物理系统建模,以便对其行为进行仿真。对这些系统进行建模,从很简单到极为复杂有各种各样的方法。对物理系统建模比较复杂的方法之一是通过使用有限元分析。顾名思义,有限元分析涉及物理系统在数学模型中的分开的有限个元素的表示,以及这种模型在存在一组预定的边界条件下的解法。
在有限元建模中,把被分析的区域划分为称为单元的子区域,划分区域为子区域的这一过程,可称之为离散化或网格的产生。区域由在每一单元上所定义的函数表示。这产生了若干局部的函数,这些函数比表示整个区域所需要的函数要简单得多。下一步是分析每一单元的响应。这是通过建立定义区域内各单元的性质的一个矩阵,以及定义结构中对每一单元的作用力的向量而实现的。一旦所有单元的矩阵和向量已经生成,则它们被组合到一个结构矩阵方程式中。这一方程式涉及整个结构对结点力的结点响应。在分析边界条件之后,可对结构矩阵方程式求解,以获得未知的结点响应。使用在每一单元上所定义的函数,能够从结点值内推出单元内响应。
有限元模型常用来确定在一定条件下诸如储油层等地质构造的行为。有限元模型能够仿真通过油层特定区域的油流对钻井等各种采油操作的响应。所得的信息在油层的分析和采油操作的管理中是有用的。
然而传统的有限元模型有一定的限制,这妨碍了模型精确仿真模型的物理系统的行为。例如,在储油层的情形下,有限元模型可以使用根据在油层中的位置逐渐变化的数学函数表示油层特定的性质。很难迫使这些函数逼近由于油层内地质特征的结果突然发生的性质上的变化。例如,储油层可能有两个不同的层面,每一层在这两层之间的边界对于给定的性质(例如孔隙度)有很不相同的值,因而表示该性质的值的数学函数在层之间的边界处必须作出立即从一个值向领域值的过渡。即使数学函数能够适用于表示两层之间的边界处性质的各个值,这种函数通常是非常复杂的,并需要大量的计算资源。
因而希望能够提供一种方法,用于更精确地表示有限元模型内一定性质的值,特别是跨越模型内性质迅速变化或不连续的特征的边界,同时要求比较小的计算资源量。
本发明的概述
上述问题的一个或多个可由本发明的各个实施例解决。一般来说,本发明包括使用有限元模型仿真物理系统的方法,该模型包含对应于被建模的系统内不同区域的至少两个不同的模型。
在本发明的一个实施例中,一种方法包括定义对应于储油层的有限元模型。还定义了对应于在储油层内发现的特征的第二个有限元模型。特征模型的边界用来特征化储油层模型的部分。虽然它们表示同一储油层模型的部分,但能够独立地定义对应于两个有限元模型的性质。在某些情形下,存在两个某些共同的结点,因而必须对一定的性质根据该值用于储油层模型还是特征模型的解而取不同的值。因而与每一模型相关联一个鉴别程序。鉴别程序判断性质的值是由储油层模型还是由特征模型控制。当求解一个模型时,使用对应的的鉴别程序,以便根据特定模型的定义鉴别两个模型共用的结点。
在本发明的一个实施例中,在一维(例如垂直方向)有相对不变特征的储油层或其它系统,按三维建模,这是通过对系统每一不同特征生成二维有限元模型并在第三维延伸这一模型。该二维模型可通过产生第一模型并然后分割这一模型的一部分以提供第二模型而被定义。第二模型对应于第一模型系统内的特征。第一模型适应分割的边界,使得两个模型的每一个扩展到它们之间的边界。多个结点对于两个模型是共用的。这些共用的结点对于给定的性质可以具有两个不同的值,其每一个与一个模型相关。然后联合的模型的单元被延伸并被细分为三维单纯形单元。鉴别程序与每一所得的三维有限元模型相关联。当产生这些模型的每一个的解时,对应的鉴别程序控制与每一共用结点相关联的值(以便使用与对应的模型相关联的值)。
在另一实施例中,构成了一种软件应用程序以实现上述的方法。该软件应用程序包括所构成的用来引起计算机执行所述方法的指令。这些指令可以存储在任何类型的计算机可读介质上。这些介质可以无限制地包括CD-ROM,软盘,磁带,固态存储器等。
附图的简要说明
通过参照附图阅读以下详细说明,本发明的其它目的和优点将变得显而易见,其中:
图1是表示二维和三维中的单纯形的图示。
图2是表示储油层内几个特征之间的边界的图示。
图3是表示对应于储油层一部分的二维有限元网格。
图4是图3中所示的二维有限元网格的展开图。
图5是表示根据本发明方法的流程图。
图6是表示通过延伸图4的二维网格所产生的三维有限元网格的图示。
图7是表示二维网格被延伸而形成三维网格的方式的图示。
图8是表示二维单纯形被适应修改而形成位于交叉边界任一侧的新的单纯形。
虽然本发明可以有各种变形和修改,但是其特定的实施例在附图和伴随的详细说明中是通过例子的方式表示的。然而应当理解,附图和详细的说明并不是要限制本发明为所述特定的实施例。本公开是要覆盖所有属于所附权利要求定义的本发明的精神和范围的变形,等价物和改型。
优选实施例的详细说明
以下将说明本发明的优选实施例。应当注意,以下所述的这一和任何其它实施例是示例性的并是要说明本发明,而不是限制。
一般来说,本发明包括使用有限元建模仿真系统的方法,以及实施该方法的计算机应用程序与设置为执行该方法的计算机。该方法涉及表示对应于被建模的系统内的区域的多个不同的有限元模型的定义。这些有限只模型的每一个包括一组对各种性质定义了值的结点。对于位于模型之间的边界的结点,有对应于给定性质的多个值,其中每一个值对应于不同的模型之一。使用对应于该模型的每一性质的值,对每一个模型分别求解。
如上所述,本发明在储油层仿真中可能是有用的,储油层有这样的特征,即引起一定的性质作为储油层中位置的函数而迅速变化。这些特征可能包括不同的地质层状的,裂痕,完井带,破损带,或任何其它可能引起储油层内强烈的非均质性特征。应当注意,虽然这里所述的本发明的实施例本来目的只是对诸如储油层这种地质构造建模,但它们也可用于其它系统的建模。
以下将陈述优选实施例的细节。首先定义几个术语可能是有宜的。
结点是空间中的一点。在有限元建模中,结点形成被建模的单元的顶点。结点还形成结点与边的网格的部分,边定义被建模的空间中单元之间的边界。
边是两个形成单元顶点的结点之间的线,边形成定义被建模的空间中单元之间的边界的网格的部分。
单纯形是由维数等于或大于n的空间中n+1个点确定的一个n维的空间构形。换言之,一个单纯形是在给定的维数下具有封闭一空间所必须的最小边界点数的几何空间单元。例如,在二维空间中,单纯形包括一个三角形并同时包括以三角形为边界的内部区域(见图1)。两个点不足以形成二维空间中的单纯形,因为没有区域能以两个点(以及互相连接这两点的线)为边界。虽然四个点足以范围一个二维区域,但是它们包括的不是二维区域被范围的最小数的边界点。在三维中,一个单纯形包括由四个顶点所范围的一个四面体(见图1)。在四维中,一个单纯形包括有五个顶点的超四面体(有时称为hypertet)。
网格是填充一个空间的单元的一个集合。这些单元是存在于该空间中的一个系统的一种表示。由于每一单元可由多个结点和/或这些结点之间的边定义,因而网格又可认为是结点和/或它们之间的边的集合。在本公开各处,视术语所使用的上下文,“网格”将交替用来指单元或结点/边的集合。这里网格还可以指称有限元模型或简单地就是模型。
参见图2,其中示出表示储油层内几个特征之间的边界的图示。该图是被建模的储油层的剖视图。图2描绘出包含具有对应的性质集合的第一材料(例如页岩)的第一层11。还示出第二层12。层12包含具有对应的性质集合的材料(例如白垩)。一般来说,为了对储油层建模的目的,同一性质(例如渗透性或多孔性)将对两个层都作标识。然而每一层中这些性质的值可能本质上不同。例如,一个层的渗透性可能高而另一层的渗透性可能低。图2还描绘出通过两层11和层12延伸的裂痕13。裂痕还能够由每一标识的性质对应的值特征化。例如,虽然通常不用作为裂痕(即空的空间)的标识特性,但可向裂痕指定渗透性值(显然将是很高的)。
当构成图2所示对于储油层的有限元模型时,它可以包括三个子模型:一个对应于层11;一个对应于层12;一个对应于裂痕13。每一子模型将包含位于它与另一子模型之间边界上的结点。一般来说,这些边界之一上的每一结点将对于共享该边界的所有子模型是共用的(虽然不总是这样)。因为对一个以上的子模型共用的结点对于特定的性质与被鉴别的子模型相关,将必须具有不同的值,因而必须提供一种机制保证使用适当的值。
在一个优选实施例中,一种鉴别程序与每一子模型相关联。鉴别程序控制对模型之间边界上每一结点的参数值。这样,根据正在对其求解的子模型对每一结点定义参数。在计算特定子模型的解时,对应于该子模型的鉴别程序用于共用的结点,使得对应于该子模型的参数用于共用结点。这样,位于两个子模型之间边界上单一的结点被视为具有来自第一个子模型的第一参数集合,但也被视为具有来自第二个子模型的第二参数集合。
本方法中,能够对储油层内所选择的结构生成子模型(例如地质层状,裂痕)。使用这些子模型,唯一的值或函数可用于仿真每一构造中性质的变化。因为子模型是不同的,性质差别悬殊的单元之间的边界可被精确地表示。
参见图3和4,示出对应于储油层一部分的二维有限元网格,以便举例表示使用不同的子模型表示储油层内不同区域。图3是网格较大的视图,而图4是同一网格近看的视图。图4所示网格的范围由图3中的虚线23指示。
图3所示的网格包括表示储油层内不同特征的两个子模型。第一个模型21对应于一局部完全区域和裂痕。第二模型对应于完全区域和裂痕毗邻的分开的,相对均匀的构造。(“均匀”这里用来指称变化相对慢而不是简单地不变的性质)。模型21被加上小点,以便更清楚地描绘出其范围。
图3和4中网格的单元由表示单元的边的线界定。每一个边在切割对应的的两个结点之间延伸。二维网格能够被拉伸为三维而形成三维有限元网格,以下将对此详细说明。
因为模型22的单元表示相对均匀的区域,它们能够通过对应的性质值(或数学函数)相对容易地生成。模型21的单元在模型内也充分均匀,能够通过指定值或数学函数对在模型中结点的性质建模。因为它们是通过不同的值和/或函数被建模的,因而两模型中相邻单元的性质(每一模型的一个)在单元之间的边界处可能有悬殊的变化或不连续性.。
参见图4,容易看见,某些定义了模型21的单元的结点也用于定义模型22的单元。例如,结点26,27和28位于两个模型之间的边界上,并用于定义每一模型的结点。于是,这些结点根据它们被鉴别为是相对于一个模型或另一模型,对于给定的性质可能必须取不同的值。在优选实施例中,这是通过使唯一的鉴别程序与每一模型相关联而实现的。当对于特定的模型求解时,与该模型相关的鉴别程序用来确定每一边界结点的适当的值。
应当注意,可能有结点位于两个模型之间的边界上,但是它们不是两个模型共用的。因为这些结点只定义了模型之一中的单元,它们对每一性质只有一个值/函数,于是不必对其结点用来计算解的模型进行识别。
参见图5,示出表示根据本发明一个实施例的方法的流程图。虽然这一图示将把储油层作为被建模的系统,但是同样的方法论能够也适用于其它系统。在这一方法中,产生对应于整个储油层的最初的有限元网格,并然后对应于储油层内特征的分开的有限元网格被插入到第一网格。这第一网格被适应性修改而适用于新的第二级网格。换言之,由第二级网格占据的区域是从第一网格分割出来的,使得没有两个网格占据相同的空间。
最初的有限元网格,由于被修改而适应其它网格,将适于作为储油层区域之一的模型。(虽然这区域某些情形下可能比其它区域简单,但是它一般表示储油层的主体)。这网格能够通过有限元建模技术业内专业人员所知道的任何适当的方法产生。最好是单纯形单元的未构成的网格。在产生第一网格之后,定义特征并然后从第一网格分割出第二级区域,以适应第二级区域。在对于特征定义边界内产生一网格。该网格可以在第二级区域从第一网格分割出来之前构成,或者也可以在此后产生。在每一种情形下,生成对应于被建模的系统不同区域的两个不同的有限元模型。这些模型彼此直接相邻(即它们直接有一共用的边界)。可对被建模的系统中另外的特征(以及第一有限元网格内另外的第二级区域)重复这一过程。
在优选实施例中,这一过程实际上是在二维中进行的,以产生然后延伸到三维的网格。例如,如果假设由图4中的模型21表示的完全带和裂痕表示水平面中的特征,则该图所示的二维网格能够被垂直延伸而产生三维网格。这是在图6中示出的。
图6从倾斜角度示出图4的二维网格。这个二维网格被垂直延伸(如虚线所示),形成多个三维棱柱。在优选实施例中,这些棱柱被细分为三维单纯形(四面体)。三维网格按这种方式的产生,可以减少通过限制适应修改过程在二维并然后把精细化的二维网格延伸这样的网格产生的计算需求。这有效地免除了要在三维中不同点几次分别精细化同一个二维网格。
虽然本公开中将不详细描述延伸过程,这里还是提供了图7说明实现从二维向三维延伸的方式。图7示出单一的二维单纯形(一个三角形),该三角形被延伸而形成三维棱柱。然后这棱柱被细分为三个三维单纯形(四面体)。应当注意,这同一过程可用于在第四维空间(即时间)中延伸三维网格。
在一个实施例中,在产生任何网格之前确定不同区域的边界。当定义了不同的区域时,在每一区域内构成网格。每一网格是这样构成的,使其扩展到由网格共享的边界(以及整个被建模系统的外部范围)。网格的产生可以任何适当的方式进行。能够定义任何所希望的区域数,并能够在这些区域中产生对应的网格。
在另一实施例中,第一网格这样产生,使其填充被建模系统的整个空间。然后定义边界以分开系统的区域。由于这一边界可以把现有的单元分割为两个部分,每一区域中的网格被适应性精细化以形成有效的单纯形而代替交叉的单元。其结果是获得对应于系统的两个区域的两个网格。
虽然将不会详细说明适应性精细化过程,但是展示了图8以提供该过程的表示。图8包括一个二维单纯形(三角形)的三个视图,该单纯形被适应性精细化以形成边界的每一侧的单纯形。在第一个图示中,示出单纯形由一边界曲线交叉。单纯形的边在两点处被交叉。在每一交叉处生成一个新的结点。然后在新的结点之一和单纯形相对的顶点之间定义了一个新的边,形成两个新的单纯形。然后在其余新的结点与新的单纯形相对顶点之间定义了一个新的边。这一过程的结果是生成三个新的单纯形-一个在边界上面,两个在其下面。
在三维单纯形的情形下基本上能够执行相同的过程。所得到的单纯形将基本上位于边界的一侧或另一侧。(因为可以是弯曲的,扁平表面的单纯形可能不完全位于边界上)。由于适应性修改过程产生几乎完全在边界一侧的单纯形,它们每一个能够被定义为第一区域或第二区域的部分,因而是第一或第二有限元模型的部分。
应当注意,描述生成对应于被建模系统的不同区域的有限元模型的以上各节适用于n维网格的情形。
以上就特定实施例说明了好处,其它的优点和对问题的解决。然而,好处,其它的优点和对问题的解决,以及可能引起任何好处,其它的优点和对问题的解决的发生或更多被宣称的因素,并不构成为任何或所有权利要求的关键的,必须的或基本特征或要素。作为这里所使用的术语“包括”,“包括”或其任何其它的变形,是要覆盖非排他性的包含,使得包括一系列要素的过程,方法,文章或设备并不仅仅包含那些要素,而是可以包含其它没有明显列出的或这种过程,方法,文章或设备固有的要素。
虽然已经参照特定的实施例对本发明进行了说明,但应当理解,实施例是示例性的,而本发明的范围不限于这些实施例。许多对所述实施例的变化,改型,附加和改进是可行的。特别地,这些变化可以包含计算机或其它数据处理装置,包含软件,固件或其它实施上述方法编程的计算机可读介质(诸如软盘,CD-ROM,DVD-ROM等)存储装置,计算机存储器等。这些变化,改型,附加和改进被认为属于在以下权利要求内所详述本发明的范围。
Claims (20)
1.使用有限元技术对系统建模的一种方法,包括:
定义多个有限元网格,其中多个结点对至少两个有限元网格是共用的;
定义与每一有限元网格相关的性质,其中对每一有限元网格,性质是通过对应的独立于其它函数的一个函数定义的;
使鉴别程序与每一有限元网格相关;以及
对每一有限元网格产生一解,其中对每一有限元网格,根据与有限元网格相关的鉴别程序选择用于定义每一共用结点处性质的值的函数。
2.权利要求1的方法,其中定义多个单元网格包括定义有限元网格之间边界上与对应的边界接触的有限元网格所共用的所有结点。
3.权利要求1的方法,其中位于有限元网格之间的一个边界上至少一个结点不是对与对应的的边界接触的所有的有限元网格共用的。
4.权利要求1的方法,其中每一函数不同于其它函数。
5.权利要求4的方法,其中至少两个函数彼此不是连续的。
6.权利要求1的方法,其中有限元网格之一对应于储油层的第一部分,而另一个有限元网格对应于储油层内的特征,且其中特征是从由裂痕;完井带;破损带;地质层;和近井区域组成的组中选择的。
7.权利要求1的方法,其中定义多个有限元网格包括定义多个二维有限元网格,并把二维有限元网格在第三维中延伸而获得三维有限元网格。
8.权利要求1的方法,其中定义多个有限元网格包括定义第一有限元网格,以便包含对应于被建模的系统的第一区域和第二区域两个区域,精细化第一有限元网格以便分割出第二区域,并在第二区域内定义第二有限元网格。
9.权利要求8的方法,其中精细化第一有限元网格以分割出第二区域包括定义第一区域与第二区域之间的边界面,适应性修改第一有限元网格以定义具有基本上位于边界表面上的表面的单元,定义第一有限元网格作为边界面的第一侧上的单元,并定义第二有限元网格作为边界面的第二侧上的单元。
10.权利要求1的方法,其中适应性修改第一有限元网格包括识别的第一有限元网格单元的边与边界面的交叉,在识别出的交叉处定义结点,并精细化第一有限元网格的单元以结合新定义的结点。
11.使用有限元分析对储油层建模的一种方法,其中储油层具有对应于储油层和储油层内一个或多个特征的多个相邻区域,其中每一区域在对应的的有限元模型中被特征化,且其中对于所选择的储油层的性质每一有限元模型采用独立的函数表示选择的性质,其中的方法包括:
使一鉴别程序与每一有限元模型相关联;以及
对于每一有限元模型产生解;
其中产生解包括基于在有限元模型中每一结点处所选择的性质的值计算解,其中对位于被求解的有限元模型和多个有限元模型中一个或多个其它模型之间的边界上一个或多个结点的每一个,对于所选择的性质的值取决于与被求解的有限元模型相关的鉴别程序。
12.包含被设置为引起计算机执行以下方法的指令的计算机可读介质,该方法包括:
定义多个有限元网格,其中多个结点对至少两个有限元网格是共用的;
定义与每一有限元网格相关的性质,其中对每一有限元网格,性质是通过对应的独立于其它函数的一个函数定义的;
使鉴别程序与每一有限元网格相关;以及
对每一有限元网格产生一解,其中对每一有限元网格,根据与有限元网格相关的鉴别程序选择用于定义每一共用结点处性质的值的函数。
13.权利要求12的一种计算机可读介质,其中定义多个单元网格包括定义有限元网格之间边界上与对应的边界接触的有限元网格共用的所有结点。
14.权利要求12的一种计算机可读介质,其中位于有限元网格之间的一个边界上至少一个结点不是对与对应的的边界接触的所有的有限元网格共用的。
15.权利要求12的一种计算机可读介质,其中每一函数不同于其它函数。
16.权利要求15的一种计算机可读介质,其中至少两个函数彼此不是连续的。
17.权利要求12的一种计算机可读介质,其中有限元网格之一对应于储油层的第一部分,而另一个有限元网格对应于储油层内的特征,且其中特征是从由裂痕;完井带;破损带;地质层;和近井区域组成的组中选择的。
18.权利要求12的一种计算机可读介质,其中定义多个有限元网格包括定义多个二维有限元网格,并把二维有限元网格在第三维中延伸而获得三维有限元网格。
19.权利要求12的一种计算机可读介质,其中定义多个有限元网格包括定义第一有限元网格,以便包含对应于被建模的系统的第一区域和第二区域两个区域,精细化第一有限元网格以便分割出第二区域,并在第二区域内定义第二有限元网格。
20.权利要求12的一种计算机可读介质,其中精细化第一有限元网格以分割出第二区域包括定义第一区域与第二区域之间的边界面,适应性修改第一有限元网格以定义具有基本上位于边界表面上的表面的单元,定义第一有限元网格作为边界面的第一侧上的单元,并定义第二有限元网格作为边界面的第二侧上的单元。
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