CN1291240C - 获取多相介质中物理特性的优化模型的方法 - Google Patents
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Abstract
本发明的方法可以通过变换,借助与介质中观测或测量的数据结构一致的更为定量的变换参数特性(例如标准偏差和相关长度)获得物理量的优化模型,该物理量代表了分层多相介质(该介质的阻抗与例如在其中传播的波有关)。通过定义这些参数的内在依赖性,有利于指导解释者选择用于参数所考虑的数值。最终的模型相对借助于纯粹经验选择而言得到了改进。
Description
技术领域
本发明涉及获取多相介质中物理特性的优化模型的方法。按照本发明的方法可以对波传播涉及的地下区域的阻抗建模,并且由此获取底土图像,从而更加精确地对产生这些阻抗变化的非连续性进行定位。本发明适于对碳氢化合物储层定位。
背景技术
现在众所周知的是,储层模型的精度和可靠性很大程度上取决于具有不同性质的兼容数据的综合作用,这或多或少地与所研究储层的性质相关。许多调查表明,地震数据能用于把储层的图象约束在钻井之间的空间中。
将地震数据整合到储层模型中的一般方法是,根据地震振幅估计声波或弹性波的阻抗,并将它们转换为储层性质。
在各种变换算法中,利用先验模型的技术要求选择对数据和先验模型在优化中的各种影响的进行加权的参数。
本申请人提交的专利EP-354,112(US-4,972,383)和EP-889,331描述了一种称为Interwell方法的方法,它可以获取代表地下区域声波阻抗变化的至少二维模型,它与观测或测量得到的数据(地质数据、堆积后地震数据或其他通过钻井获得的数据)匹配最好。它包括通过将钻井数据与已知结构或地层数据结合构造先验阻抗模型。特别是沿着地层单元内的相关表面沿着钻井Kriging已知的阻抗。地震层给出了地层单元的几何结构,并且通过根据沉积模式跟随限定的表面完成相关性(平行于顶层或地面的协调)。随后,通过考虑测得的地震振幅,更新钻井间的初始阻抗分布。为此,这可以用迭代的方式,通过使下述两项代价函数最小来完成:
F=Fs+Fg,这里
Fs为地震项,该指标代表从模型获得的合成轨迹与实际地震轨迹(堆积前轨迹、堆积后轨迹)之振幅的差值;而
Fg为地理项,它测量了先验模型与标准模型的差值。
优化阻抗模型是根据相应权重在这两项之间进行折衷的结果。这些权重与变换参数有关,即Fs与信噪比有关,而Fg与相关长度λ和关于先验模型的误差的方差σ2有关,这里假定所述误差是随机变量,其平稳指数协方差为σ2,相关长度为λ。
Fs的权重通常根据实际振幅估计。相反,相关长度为λ和标准偏差σ由用户根据他对先验模型的置信度而定义。但是由于对先验模型的置信度取决于数据的质量、钻井的数量和位置以及阻抗场的空间性态,所以不应太过于由经验估计。
发明内容
依照本发明提供了一种用于获得代表一分层多相介质的物理量的优化模型的方法。该方法包含以下步骤:
通过在所述介质的一定数量的参考点上进行测量、记录或观测,获得已知数据,用kriging方法从所述获得已知数据中构造一先验模型,其中在沿分层方向的所有点上,所述先验模型中物理量值的不确定性与所述介质中的相应值有关,它由一平稳协方差模型Cz描述,所述平稳协方差模型Cz依赖于各点之间的距离矢量
通过考虑所述先验模型,以迭代方式使一代价函数最小化,来构造一个通过变换优化的模型,所述代价函数依赖于当前模型与已知数据之间的偏差,
所述方法的特征在于,根据一误差协方差模型确定变换参数(λ,σ),所述误差协方差模型是:
这里x和y为介质距离为
的任意两点,K为所述kriging矩阵,β(x)和
分别为点x和点y上的所述kring权重,所述误差协方差模型包括对应于所述平稳协方差模型
的第一项,以及依赖于kriging矩阵和kriging权重的非平稳协方差项。
本发明的方法可以通过变换,借助与介质中观测或测量的数据结构一致的更为定量的变换参数特性(例如标准偏差和相关长度)获得物理量的优化模型,该物理量代表了分层多相介质(该介质的阻抗与例如在其中传播的波有关)。通过定义这些参数的内在依赖性,有利于指导解释者选择用于参数所考虑的数值。最终的模型相对借助纯粹靠经验选择而言得到了改进。
它包含:从一定数量介质点测量、记录或观测获得的已知数据构造先验模型;以及通过考虑先验模型,根据要寻求的模型与已知数据之间的差值使代价函数最小化而构造优化模型。
本方法的特征在于先验模型的构造包括通过用krging方法处理沿不连续性(分层方向)方向不同介质点物理量已知值之间的协方差(Cz)得到相关性,先验模型中物理量值的不确定性与介质中沿这些方向的各点相应的值有关,按照控制变换参数的协方差模型(Cε),所述模型包括平稳协方差项(Cz),它仅仅依赖于该点与非平稳协方差项之间的距离矢量
非平稳协方差项取决于点的位置和分别与其他点之间的距离。
按照第一实施例,为了比普通先验模型更为精确地定义变换参数,平均协方差(Cε)被确定和调整至(已知类型的)平稳指数协方差模型。
按照第二实施例,为了获得变换参数的局部值(λx,σx),在所有点上将协方差项(
Cε)调整至平稳指数模型。
附图说明
通过以下结合附图对本发明的描述,可以理解本发明的其他特征和优点,其中:
图1A、1B示出了三口钻井W1、W2和W3附近相关平面内kriging误差的两个协方差栅格,分别对应两种不同的距离矢量
表示不确定协方差的非平稳性质;
图2示出了用介质标准变换参数获得的阻抗模型的实例;以及
图3示出了借助本发明方法获得的阻抗模型实例,其变换参数被更好调整至不确定协方差的性态。
具体实施方式
由于通过kriging法构造了先验模型,所以我们研究了用于主要控制地质项Fg之权重的kriging误差的理论协方差。在普通kriging法中,如果Z为阻抗场,而Z先验为kriging化的阻抗场Z*,则所述误差可以表示如下:
ε(x)=Z(x)-Z*(x)
如果x和y表示介质内距离为h的两个点,则误差ε(x)的协方差Cε(x,y)表示如下:
两点x与y之间的理论误差协方差Cε(x,y)以允许构造所述先验模型的初始kriging协方差
的形式出现,该协方差通常是各向同性的,并且依赖于距离
再由依赖于距离
和所考虑点x位置的非平稳项
来修正。在远离钻井处,以初始协方差
为主,而随着靠近某一钻井时,第二项变得越来越重要。
以下以三口竖井的实际场为例子,描述这种性态。对于储层的分层单元,沿基部的平行表面,借助一普通的指数模型(相关长度为750米,阻抗标准偏差为1122g/cm3.m/s),对阻抗作kriging化处理。如图1A和1B所示,为两个距离矢量计算了相关误差的协方差。
本方法包括选择与包含变换过程中的可用数据定量兼容的变换参数。最简单的途径无需进行变换算法修正,而是计算用于调整一平稳指数协方差(其具有专家已知的类型)的平均误差协方差
以自动获取平均变换参数 和
因此,本方法容易使解释者采用kriging误差的空间性态,来调整分配给地质项Fg的权重。
在上述实例中,本方法用于建模与传播的波(弹性波、电磁波等)有关的阻抗形式。显然本方法也可以用于建模其他形式的物理量,例如孔隙度、渗透率、饱和度等或与钻井测试有关的量。广义而言,本方法可以用于专家熟知的贝叶斯型变换模型。
Claims (3)
1.一种用于获得代表一分层多相介质的物理量的优化模型的方法,所述方法包含以下步骤:
通过在所述介质的一定数量的参考点上进行测量、记录或观测,获得已知数据,用kriging方法从所述获得已知数据中构造一先验模型,其中在沿分层方向的所有点上,所述先验模型中物理量值的不确定性与所述介质中的相应值有关,它由一平稳协方差模型Cz描述,所述平稳协方差模型Cz依赖于各点之间的距离矢量
通过考虑所述先验模型,以迭代方式使一代价函数最小化,来构造一个通过变换优化的模型,所述代价函数依赖于当前模型与已知数据之间的偏差,
所述方法的特征在于,根据一误差协方差模型确定变换参数(λ,σ),所述误差协方差模型是:
3.如权利要求1所述的方法,其特征在于,在所有点上,在一平稳指数模型中调整协方差项(Cε),以便定义所述变换参数的局部值(λx,σx)。
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FR9905288A FR2792419B1 (fr) | 1999-04-16 | 1999-04-16 | Methode pour obtenir un modele optimal d'une caracteristique physique dans un milieu heterogene, tel que le sous-sol |
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FR2635197B1 (fr) * | 1988-08-05 | 1990-09-28 | Inst Francais Du Petrole | Methode pour obtenir un modele representatif d'un milieu heterogene et notamment du sous-sol |
US5321613A (en) * | 1992-11-12 | 1994-06-14 | Coleman Research Corporation | Data fusion workstation |
US5416750A (en) * | 1994-03-25 | 1995-05-16 | Western Atlas International, Inc. | Bayesian sequential indicator simulation of lithology from seismic data |
US5838634A (en) * | 1996-04-04 | 1998-11-17 | Exxon Production Research Company | Method of generating 3-D geologic models incorporating geologic and geophysical constraints |
FR2765692B1 (fr) * | 1997-07-04 | 1999-09-10 | Inst Francais Du Petrole | Methode pour modeliser en 3d l'impedance d'un milieu heterogene |
US5995906A (en) * | 1997-10-03 | 1999-11-30 | Western Atlas International, Inc. | Method for reconciling data at seismic and well-log scales in 3-D earth modeling |
FR2772138B1 (fr) * | 1997-12-10 | 1999-12-31 | Inst Francais Du Petrole | Methode statistique multivariable pour caracteriser des images que l'on a formees d'un milieu complexe tel que le sous-sol |
US6302221B1 (en) * | 2000-05-31 | 2001-10-16 | Marathon Oil Company | Method for predicting quantitative values of a rock or fluid property in a reservoir using seismic data |
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