利用多点地质统计学方法模拟岩相分布

JournalofXicanShiyouUniversity(NaturalScienceEdition)Sep.2005Vol.20No.5

文章编号:1673-0X(2005)05-0009-03

利用多点地质统计学方法模拟岩相分布

Stochasticsimulationoflithofaciesdistributionusingmulti-pointgeostatistics

冯国庆1,陈浩2,张烈辉1,李允1

(1.西南石油学院油气藏地质及开发工程国家重点实验室,四川成都610500;

2.油田分公司陆梁油田作业区,克拉玛依834000)

摘要:文中介绍了多点地质统计学的基本原理,并利用该算法模拟了我国东部某砂岩油藏的岩相分布.通过对储层非均质性模拟研究,揭示储层在岩性、物性和含油气性的各向异性或非均质性,揭示

砂体展布、连通程度以及在横向、纵向上的变化规律,有利于开发方案的制定及注采井网的布署.模拟结果表明,多点地质统计学模拟方法可以很好地再现砂体局部的变异性和非均质性.由此可得出以下结论:snesim模拟算法可以快速灵活地进行多点地质统计模拟,多点地质统计学比两点地质统计学更具有优势.

关键词:多点地质统计学;随机模拟;训练图像中图分类号:TE19;TE121.1+5 文献标识码:A 传统的地质统计学是利用变差函数描述地质变量的相关性和变异性,通过建立在某个方向上两点之间的地质变量的变化关系来描述空间的变化特性.但是,建立在两点统计关系上的变差函数本身在描述储层非均质性上有很大的不足,它反映的仅仅是空间两点之间的相关性,不能充分描述复杂几何形状砂体如河道砂体和冲积扇砂体空间的连续性和变异性.当井资料较少时,用于计算实验变差函数的点对很少,它也就不能正确反应空间两点之间的相关性.建立在两点基础上的变差函数在储层地质建模中存在一定的不足,而多点地质统计学是建立在多个点的相关关系上,所以它在解决描述空间变量的连续性和变异性方面得到越来越广泛的应用.斯坦福大学的Journel教授曾指出多点地质统计学是今后地质统计学发展的方向,它的优势已越来越显著.

[1-4]

1 多点地质统计学的原理

在阐述多点地质统计学之前,首先回顾一下变

差函数的地质统计学方法是如何模拟储层岩相分布的,以序贯指示模拟算法为例进行说明.该方法的基本原理[5]简述如下:

假设在模拟区域有k种岩相s1,s2,,sk,对于模拟目标区域内的每一相,定义指示变量:

,

0 Z(u)|sk

对于任一待模拟点,其出现第k种相的概率为:P(Ik=1|Z(uA)=sA,PA),A为待估点所包括的条件区域,利用两点地质统计学方法计算该概率是采用克里格方法:

P(Ik=1|Z(uA)=sA,PA)=E(Ik)+

A=1

I(u)=

1 Z(u)Isk

A[1-EK

n

E(Ik)].

收稿日期:2005-01-18

基金项目:国家教育部高等学校优秀青年教师教学科研奖励计划(TRAPOYT)资助作者简介:冯国庆(1974-),男,山东荷泽人,博士,主要从事油藏描述和油藏数值模拟研究.

)10)

西安石油大学学报(自然科学版)

其中,KA为克里格方法确定的权系数,它通过求解由变差函数或协方差函数建立的克里格方程组来确定.

多点地质统计学与两点地质统计学的主要区别在于上面的概率的确定方法不同,它首先引入一训练图像,通过在训练图像中寻找与待估点内条件数据分布完全相同的事件的个数来确定概率分布,因此它可以反映出多个位置的联合变异性.

例如,计算图1(a)中u点的概率时,相应的条件数据场为dn={z(u1),z(u2),z(u3),z(u4)},其基本方法是首先要在训练图像(b)中寻找与图(a)中数据分布完全相同的事件的个数,即要在训练图像中找出与图(a)几何完全相同的区域,同时在该区域中相同的位置处z(u1),z(u2),z(u3),z(u4)的值完全相同.在训练图像中一共找到4个既能满足条件数据u1,u2,u3,u4数值,同时又能满足它们分空间几何形状的事件,在这4个事件中,3个事件的u点的值为0,只有1个事件中u点值为1,因此u点岩相为1的条件概率为P{u=1|dn}=1/4,而P{u=0|dn}=3/4,这样便可求出了u点的条件概率.

(3)对随机路径中的任意待估点l(=1,2,,,l):¹定义查找范围内的条件数据;º保留邻区的数据点;»在训练图像中寻找与该区域内条件数据完全相同的事件,计算该点岩相的分布概率.¼由MontoCarlo法得到位置处的一个模拟值;½将模拟结果归入条件指示数据集中.

(4)重复上一步模拟,直到所有的点全被模拟.训练图像既可以通过非条件模拟求出,也可以通过该地区的地质露头资料分析得出.对训练图像的条件非模拟可以选择非条件的布尔模拟方法,其方法和原理参见文献[6].

2 实例分析

对于开发中后期的砂岩油藏储层参数模拟采用两阶段模拟方法可以较为准确地反映储层的非均质性,而/两步建模0的第一步就是要建立储层结构或流动单元模型,模拟沉积体在空间排列的复杂性;利用多点统计学模拟方法可以较好地完成砂体骨架模拟.

模拟区域选择我国东部某砂岩油藏第15小层,在该层一共有口井,测井资料解释结果表明有26口井钻遇砂体,另外38口井钻遇泥岩,砂体比例为40%.对岩相进行编码,砂岩为1,泥岩为0,图2为该层井位分布图.

图1 多点统计方法估计条件概率的原理

上述方法不仅考虑了区域内条件数据的值,而且也考虑了条件数据的几何形状.而两点地质统计学只是依靠z(u1),z(u2),z(u3),z(u4)的值及各点与u点距离通过求解克里格方程组来确定u点的概率,并没有考虑dn的几何形状和各条件数据的配位关系.

基于上述原理,SebastienStrebelle提出了snes-im模拟算法

[2]

图2 第15小层井位和井点岩相图

采用上述方法模拟砂体的分布.首先建立训练图像,运用布尔模拟方法,把砂体比例40%输入,为保证训练图像数据充足,网格划分为250@250@1,

一共由62500个模拟数据组成,布尔模拟结果见图3.

把条件数据和布尔模拟生成的训练图像,输入到snesim模拟算法中进行模拟.根据该区域的特点,椭圆最大搜索半径选为300m,搜索半径内最多

,利用该算法可以快速、灵活地模拟

岩相分布.该方法的具体步骤为:

(1)利用非条件模拟建立三维训练图像;

(2)定义通过所有待估结点的随机路径;

冯国庆等:利用多点地质统计学方法模拟岩相分布

)11)

的条件数据设为30,搜索主方向选择物源方向5b,得到该层的砂泥岩分布(图4).从模拟结果看出,它很好地满足了条件数据,即在各井点处的模拟结果与数据相一致,这表明该方法为条件模拟.同时,模拟的砂体展布方向和趋势与依靠地质经验手工绘制的砂体展布图(图5)比较吻合,在模拟的左下角与左上角砂体的展布与手工勾绘的几乎完全一致,但该方法在局部区域表现出砂体展布的非均质性和不确定性,与手工勾画砂体展布的平滑而唯一的表现是具有一定差别的,它充分体现了砂体局部的变异性和非均质性.

图5 手工绘制的该小层的砂体展布图

3 结 论

(1)多点地质统计学是今后地质统计学发展的主要方向,它可以联合反映空间多个位置点的几何形状和相互配位关系;在模拟具有复杂形状地质体分布时,它比两点地质统计学方法具有更大的优势.(2)利用snesim模拟算法可以快速灵活地进行多点地质统计模拟,模拟的岩相展布图具有一定的真实性,它为储层参数的两阶段模拟奠定了基础.参考文献:

图3 布尔模拟生成的训练图像

[1] StrebelleS.Conditionalsimulationofcomplexgeological

structuresusingmultiplepointstatistics[J].MathematicalGeology,2002,34(1):1-22.

[2] StrebelleS,JournelAG.Reservoirmodelingusingmult-iple-pointstatistics[C].SPE71324,2001.

[3] JefCaers.StochasticReservoirCharacterizationUsing

Multiple-pointstatistics[A].In:ProceedingsoftheIAMG99,FifthAnnualConferenceoftheInternationalAssociationforMathematicalGeology[C].LipparsSG,etal,1999.467-472.[4] JefCaers.Geostatisticalhistorymatchingundertraining-imagebasedgeologicalmodelconstraints[A].SPE

图4 多点地质统计方法模拟的砂泥岩展布图

77429,2002.

[5] 冯国庆,李允.应用序贯指示模拟方法模拟沉积微相[J].西南石油学院学报,2001,23(2):1-4.

[6] Deutsch,Journel.GSLIB:GeostatisticalSoftwareLibrary

andUser.sGuide,2nded[M].NewYork:OxfordUn-i

versityPress,1998.104-109.

编辑:国伍玲

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