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地球科学进展, 2018, 33(4): 416-424
doi: 10.11867/j.issn.1001-8166.2018.04.0416
致密砂岩储层岩石物理模型的优化建立
Optimization of the Rock Physical Model in Tight Sandstone Reservoir
贾凌云1,, 李琳1, 王千遥2, 马劲风1, 王大兴3
1.西北大学地质学系,二氧化碳捕集与封存技术国家地方联合工程研究中心,陕西 西安 710069
2.中煤科工集团西安研究院有限公司,陕西 西安 710077
3.中国石油长庆油田公司勘探开发研究院,陕西 西安 710018
Jia Lingyun1,, Li Lin1, Wang Qianyao2, Ma Jinfeng1, Wang Daxing3
1.National & Local Joint Engineering Research Center of Carbon Capture and Storage Technology, Department of Geology of Northwest University, Xi’an 710069, China;
2.China Coal Technology Engineering Group Xi’an Research Institute, Xi’an 710077, China;
3.Research Institute of Exploration and Development, Changqing Oil Field Company, PetroChina, Xi’an 710018,China;
 引用本文:
贾凌云, 李琳, 王千遥, 马劲风, 王大兴. 致密砂岩储层岩石物理模型的优化建立[J]. 地球科学进展, 2018, 33(4): 416-424, doi:10.11867/j.issn.1001-8166.2018.04.0416
Jia Lingyun, Li Lin, Wang Qianyao, Ma Jinfeng, Wang Daxing. Optimization of the Rock Physical Model in Tight Sandstone Reservoir[J]. Advances in Earth Science, 2018, 33(4): 416-424, doi:10.11867/j.issn.1001-8166.2018.04.0416

摘要:

Krief模型、Nur模型和Pride-Lee模型通常被用于计算砂岩储层干岩石模量,但对于致密砂岩储层却效果不佳。基于Krief模型和Nur模型,在满足纵波或横波预测值与实测值差值最小的条件下,通过Gassmann方程求出模型中的岩性指数m或临界孔隙度Øc,进而将模型中通常采用的经验参数表示成随采样点变化的值,提高了Krief模型和Nur模型估算纵横波速的精度,称为变参数Krief模型和变参数Nur模型。此外,对比不同约束条件下纵横波预测精度,可知在致密砂岩储层中3种模型的剪切模量公式的精度更高、适用性更好。Han提出的Kdryudry关系式不受孔隙度、岩性等因素的影响,将该关系式与上述3种模型中任意一种剪切模量公式结合建立干岩石模型,应用到Gassmann方程中对鄂尔多斯盆地苏里格气藏盒8致密砂岩储层横波速度进行预测,提高了预测横波速度的精度,同时获得了3种模型中每个采样点对应的岩性指数m、临界孔隙度Øc和固结参数c的值,这些参数值可以反映出储层的岩性差异、孔隙结构、压实程度等特征,映射了储层的地质特征。

关键词: 致密砂岩储层 ; 体积模量 ; 岩石物理模型 ; Kdryudry的关系

Abstract:

Krief model, Nur model and Pride-Lee model are usually used to calculate dry rock modulus of sandstone reservoirs, but they are not effective for tight sandstone reservoirs. Based on Krief model and Nur model, and minimizing the difference between predicted P-wave or S-wave velocities and measured velocities, we acquireed lithologic index m in Krief model and critical porosity Øc in Nur model by Gassmann relationship. The empirical parameters used in the models are expressed as the values changing with depth, so the accuracy of Krief and Nur models to estimate the P-wave and S-wave velocities was improved, and these two models are called as the variable parameter Krief model and the variable parameter Nur model. In addition, comparing with prediction accuracy of P-wave and S-wave velocities under different constraints, we can see that the shear modulus formulas in the three models are more accurate and more suitable in the tight sandstone reservoir. Han’s relationship about Kdry and udry is not affected by porosity, lithology and other factors, and the paper established dry rock model by Han’s relationship and any one of the above three models. The new dry rock model was applied in the Gassmann relationship to predict S-wave velocity of H8 tight sandstone reservoir in Sulige Gas Filed, Ordos Basin, which improved the accuracy of predicting S-wave velocity. At the same time, lithology index m in Krief model, critical porosity Øc in Nur model and consolidation parameters c in Pride-Lee model which are corresponding to each sample can be obtained. The values of these parameters can reflect lithology difference, pore structure, compaction degree and other characteristics, which indicate the geological characteristics of the reservoir.

Key words: Tight sandstone reservoir ; Bulk modulus ; Rock physical model ; The relationship of Kdry and udry.
1 引 言

岩石物理模型是在一定的假设条件下,采用基质模量、干岩石模量、流体体积模量等弹性参数和压力、温度、声波、频率等环境参数对岩石进行表达。致密砂岩储层具有低孔隙度和低渗透率的特点,常常包含一些封闭孔隙,与常规高孔隙度、高渗透率储层的地质特征差异较大[1,2],因此,两者的岩石物理模型也有一定的差异。常规储层的岩石物理模型在致密砂岩储层中一般不适用,需要针对致密砂岩储层提出新的岩石物理建模方法或对常规岩石物理模型进行优化。Gassmann方程[3]基于孔隙受力均衡、孔隙之间相互连通的假设条件,建立了孔隙度、流体饱和度等物性参数与各项弹性参数的关系[4,5],用来研究流体对岩石弹性参数响应特征的影响,但致密砂岩储层中的封闭孔隙使得Gassmann方程的应用有一定的局限性。许多学者对封闭孔隙的岩石物理模型进行了研究,Brown等[6]提出了不连通孔隙岩石体积模量计算的通用公式,其中包含的参数有流体体积模量、连通孔隙中不随流体压力变化的岩石体积模量、孔隙度及2种基质体积模量(连通与不连通状态下的基质体积模量)。Mavko等[7]将压实地层干岩石体积模量表示为基质体积模量、孔隙度和孔隙体积模量的关系,其中孔隙体积模量是在孔隙压力不变的情况下与围压和孔隙度有关。在实际研究区中,我们难以获得这些公式中所有参数的准确值。

固结较好的砂岩储层干岩石物理模型一般采用Krief模型、Nur临界孔隙度模型和Pride模型。Krief等[8]提出的体积模量和剪切模量为Biot系数[9]的模型,指数为一个经验公式。Nur等[10,11]根据每一种岩石都存在临界孔隙度,提出了线性的干岩石模型。Pride[12]引入固结参数的概念,指出干岩石体积模量和剪切模量与孔隙度和固结参数有关,Lee[13]对Pride模型进行了修改,将剪切模量公式中固定值1.5修改为固结参数的函数,结合Gassmann方程预测纵波速度,用预测纵波波速与实测纵波速度之差最小为约束条件,求出固结参数的值,进而预测横波速度。Knackstedt等[14]将Krief和Nur的体积模量和剪切模量公式估算的数据与实验测得的数据对比分析,认为2种剪切模量公式与实验数据匹配度都较高,而2种体积模量公式都具有较大误差。同时他们采用大量的实验数据对Arns等[15]提出的泊松比经验公式进行研究,发现该经验公式精度很高,与Krief和Nur剪切模量公式结合使用,提高了各项参数的预测精度,但泊松比经验公式为分段函数,以泊松比0.2为界分为2个不同的公式,在缺乏横波速度的测井资料中泊松比难以获得,同时公式中包含随岩性和孔隙结构等变化的临界孔隙度,一般采用经验值,准确值也难以获得。张佳佳等[16]对Krief模型、Nur模型和Pride-Lee模型研究,得出Pride-Lee模型包含了随岩石变化的固结参数,更加准确地描述了干岩石和基质之间的关系。

本文对Krief模型、Nur模型和Pride-Lee模型进行了深入研究,采用随采样点变化的参数代替经验参数对Krief模型和Nur模型进行优化,通过致密砂岩储层的实际应用可知优化后模型的剪切模量公式比体积模量公式精度更高。然后,采用Han提出的Kdryudry关系式与3种模型的剪切模量公式相结合的方式来建立致密砂岩储层的干岩石模型,应用到Gassmann方程中,对横波速度进行预测。

2 岩石物理模型

2.1 3种常用岩石物理模型

Gassmann孔隙介质理论中,干岩石模量是不确定的,通常采用实验室测量和理论预测的方法,实验室测量数据一般较少甚至缺乏,常用的方法是通过干岩石模量与基质模量的关系进行预测。为了获得这种关系,前人提出了一些干岩石模型,如Krief模型、Nur模型和Pride模型等。每一种模型都有其应用前提及实用性。

Krief等[8]认为干岩石的纵横波速度比与孔隙度无关,但与基质的纵横波速度比相等,将Raymer等[17]实验获得的砂岩数据拟合为一个关于Biot系数β的表达式:

K dry = K 0 ( 1 - β ) , (1)

u dry = u 0 ( 1 - β ) , (2)

式中:Kdry,udry分别为干岩石的体积模量和剪切模量;K0,u0为基质的体积模量和剪切模量。进而推导出干岩石的体积模量和剪切模量表达式为[8]:

K dry = K 0 ( 1 - Ø ) m ( Ø ) , (3)

u dry = u 0 ( 1 - Ø ) m ( Ø ) , (4)

提出的经验公式为m(Ø)=3/(1-Ø),其中Ø为孔隙度。

Nur等[11]认为大部分岩石都有一个临界孔隙度,用Øc表示,当Biot系数β=Ø/Øc时,上述干岩石模型称为临界孔隙度模型,孔隙度满足0<Ø<Øc,当岩石的孔隙度超过临界孔隙度时,即Ø>Øc,岩石矿物颗粒会相互分离,处于悬浮状态。Nur模型的具体公式为[11]:

K dry = K 0 ( 1 - Ø / Ø c ) , (5)

u dry = u 0 ( 1 - Ø / Ø c ) , (6)

纯砂岩临界孔隙度Øc约为0.4。

Pride[12]引入固结参数c,将干岩石模量简化为:

K dry = K 0 1 - Ø 1 + , (7)

u dry = u 0 1 - Ø 1 + 1.5 , (8)

固结参数c的范围一般为2<c<20,在较固结岩石中c为2,在固结较差时c为20,剪切模型中1.5不是固定不变的,也可为5/3或2。Lee[13]将剪切模量公式改写为:

u dry = u 0 1 - Ø 1 + γc Ø , (9)

式中:γ= 1 + 2 c 1 + c ,当c=1时,γ=1.5;当c=2时,γ=5/3;当c逐渐增大时,γ接近2,包含了Pride提出的所有情况。在预测纵波速度与实测纵波速度相比误差最小的约束下,求出固结参数c的值,进而预测出横波速度。

2.2 Krief和Nur模型优化

Krief模型与张金钟[18,19]提出的地层因数公式Vp=Vm(1-Ø)x形式类似,其中VpVm为岩石和基质的纵波速度,x被称为岩性指数,张金钟对美国岩心分析家协会公布的实验数据和Han等[20]的实验数据进行研究,发现指数x值与孔隙度、压力、温度和泥质含量有关。本文将Krief模型中的m也称为岩性指数,并认为指数mx的变化规律类似,也与孔隙度、压力、温度和泥质含量等因素有关。m值一般分布范围为010[21],由于致密砂岩储层地质特征的特殊性,使得影响m值的因素更为复杂,因此认为m值是一个多因素综合的变量。

Nur等[11]通过实验数据获得了多种常用纯矿物岩石的临界孔隙度值,指出临界孔隙度的大小取决于岩石的岩性及内部结构,并发现裂隙的存在会导致岩石有一个很低的临界孔隙度。Blangy等[22]通过研究Yin等[23]和Han等[20]的数据指出沉积砂岩临界孔隙度随着泥质含量的多少变化。张佳佳等[16]指出岩石的临界孔隙度是孔隙形状的函数。因此,可知临界孔隙度是与岩石成分、孔隙形状、胶结程度和裂隙发育程度等多种因素有关的物理量。临界孔隙度Øc分布范围为01。

综上,Krief模型和Nur模型与Pride-Lee模型类似,也可以表示为一个未知参数的函数,Krief模型表示为岩性指数 m 的函数 : K dry = f 1 ( m ) , u dry = f 2 ( m ) ; Nur 模型表示为临界孔隙度 Ø c 的函数 : K dry = f 3 ( Ø c ) , u dry = f 4 ( Ø c ) 。将它们应用到Gassmann方程中,在预测纵波速度与实测纵波速度相比误差最小约束下,求出Krief模型中的岩性指数m值或Nur模型中的临界孔隙度Øc值,进而预测横波速度。本文将这种计算方法求得的模型称为变参数模型,即变参数Krief模型和变参数Nur模型,Pride-Lee模型的应用方法与变参数模型的一致,也属于变参数模型之一。

2.3 采用Han关系式优化岩石物理模型

Knackstedt等[14]研究发现Krief和Nur剪切模量公式的精度较高,而体积模量公式误差相对较大,针对致密砂岩储层的复杂地质特征,需要建立更精确的岩石物理模型才能达到储层预测的要求。许多学者研究发现纯砂岩的干岩石纵横波速度比(Vp/Vs)dry是一个固定值[21,24,25],根据Gassmann方程可推出干岩石体积模量Kdry和剪切模量udry的比值Kdry/udry=(Vp/Vs ) dry 2 -4/3,也是一个固定值。Han[26]通过大量实验数据研究提出某一个采样点的体积模量和剪切模量比Kdry/udry随孔隙度、有效压力和基质性质的变化接近一个固定值,但不同采样点的Kdry/udry值不同,主要因为其与岩石的结构有关,并证实干岩石的体积模量和剪切模量有非常好的相关性,这个相关性对纯砂岩、泥质砂岩、不胶结或胶结的砂岩都实用,其受压力的影响较小,不予考虑。本文采用研究区获得的Kdryudry数据对Han公式[26]重新拟合,具体公式为:

M dry = ρ dry V p_ dry 2 = K dry + 4 / 3 u dry , (10)

u dry = 0.0009 × M dry 2 + 0.3186 × M dry + 1.6888 , (11)

式中:Mdry为干岩石的纵波模量,ρdry为干岩石密度,Vp_dry为干岩石的纵波速度。

采用Han公式建立干岩石模型,并预测横波速度的具体步骤为:

(1)采用Voigt-Reuss-Hill模型计算岩石基质的剪切模量u0

(2)采用Brie经验公式计算流体的体积模量,其中各相流体的体积模量采用Batzle等[27]方程计算。

(3)在变参数Krief模型、变参数Nur模型或Pride-Lee模型中,选取任意一个剪切模量公式,将其与 Han[26]提出的Kdryudry关系式相结合,计算出干岩石的体积模量和剪切模量。

(4)将干岩石模量应用到Gassmann方程中,在预测纵波速度和实测纵波速度相比误差最小约束条件下,计算出岩性指数m值、临界孔隙度Øc值或胶结参数c值,再根据udry=usat=ρ V s 2 预测出横波速度,其中usat为饱和岩石剪切模量;ρ为岩石密度;Vs为横波速度。

3 模型的应用

苏里格气田位于鄂尔多斯盆地西北部,主力产气层为上古生界二叠系石盒子组盒8段,是低孔、特低渗致密砂岩储层,孔隙度范围为2.2%14.1%,平均值为7.4%,渗透率为0.22 mD。储层以砂岩为主,包含少量的泥岩,成藏过程中压实作用和胶结作用较强,孔隙类型多样,非均质性强,导致气、水分布复杂。致密储层与常规储层的地质特征差异较大,岩石物理模型也与常规储层的不同。

3.1 变参数模型的应用

采用变参数Krief模型、变参数Nur模型和Pride-Lee模型对苏里格致密气藏盒8储层的纵横波速度预测,选用王大兴[28]实测的304个岩样数据。在岩性指数(0<m<10),临界孔隙度(0<Øc<1)和固结参数(2<c<20)范围中估算纵横波速度(图1图2),可知3种模型在速度较高处误差都较大,且变参数Krief模型和变参数Nur模型的预测误差较小,Pride-Lee模型预测误差较大。变参数Krief模型、变参数Nur模型和Pride-Lee模型预测横波速度的平均误差分别为7.1%,7.2%和16.3%。将实测纵横波速度及3种岩石物理模型带入到Gassmann方程中反推出3种未知参数(图3-5),每种参数都存在一些异常点,超出了参数的值域范围。这是由于致密砂岩储层连通性差,受力不均衡,存在微孔隙等地质特征[29,30],导致这3种岩石物理模型的应用具有一定的局限性。


图1

预测纵波速度对比

Fig.1

Comparison of predicted P-wave velocity

为了验证变参数Krief、变参数Nur和Pride-Lee体积模量公式与剪切模量公式各自在致密砂岩储层中应用的误差大小,在每种参数的值域范围内,对3种模型再分别采用预测横波速度与实测横波速度相比误差最小约束下,应用Gassmann方程求取3种参数,并预测纵横波速度。横波速度误差最小约束下预测的横波速度(图6)与纵波速度误差最小约束下预测的纵波速度(图1)对比,可知前者预测精度更高,推出致密砂岩储层中3种模型的剪切模量公式比体积模量公式更合理。


图2

预测横波速度对比

Fig.2

Comparison of predicted S-wave velocity


图3

岩性指数与孔隙度交汇

Fig.3

Cross plot of lithological index and porosity


图4

临界孔隙度与孔隙度交汇

Fig.4

Cross plot of critical porosity and porosity


图5

固结参数与孔隙度交汇

Fig.5

Cross plot of consolidation parameters and porosity


图6

预测横波速度对比

Fig.6

Comparison of predicted S-wave velocity

3.2 采用Han关系优化模型的应用

一般测井资料缺乏横波速度[31],致密砂岩储层中岩石物理模型选择的合理性决定着横波速度的预测精度。本文采用变参数Krief、变参数Nur和Pride-Lee的剪切模量公式和Han公式(公式(10)和(11))结合,建立干岩石模型,对王大兴实验的304个致密岩样数据进行纵横波速度预测(图7,图8),与图1图2比较,提高了纵横波速度预测精度,预测横波速度的平均误差分别为2.63%,2.62%和2.63%。


图7

预测纵波速度对比

Fig.7

Comparison of predicted P-wave velocity


图8

预测横波速度对比

Fig.8

Comparison of predicted S-wave velocity

因此可知,采用Han公式建立岩石物理模型对致密砂岩储层更合理。并且获得了较准确的岩性指数m、临界孔隙度Øc和固结参数c的值(图9-11),这些参数值定性的反映了地质储层特征。


图9

岩性指数与孔隙度交汇

Fig.9

Cross plot of lithological index and porosity


图10

临界孔隙度Øc与孔隙度交汇

Fig.10

Cross plot of critical porosity Øc and porosity


图11

固结参数与孔隙度交汇

Fig.11

Cross plot of consolidation parameters and porosity

选用3组岩石物理模型对苏里格致密气藏苏46井盒8段纵横波速度进行预测(图12),分别是:①经验参数模型:常规Krief模型和常规Nur模型,预测的横波速度平均误差分别为8.35%和10.42%;②变参数模型:变参数Krief模型、变参数Nur模型和Pride-Lee模型,预测的横波速度平均误差分别为2.96%,2.95和5.82%;③Han公式改进模型:变参数Krief模型、变参数Nur模型和Pride-Lee模型中的剪切模量公式和Han公式结合建立的干岩石模型,预测的横波速度平均误差分别为2.75%,2.73%和2.74%。


图12

苏46井盒8段纵横波速度预测对比

Fig.12

Comparison of prediction velocity methods of He 8 formation of well Su 46

对比分析可知,变参数模型预测纵横波速度精度比经验参数模型高,但在地层A段和B段纵横波速度预测产生了突变值,表明这2组模型在致密砂岩储层中的应用具有一定的局限性,而采用Han公式优化后的模型预测纵横波速度,没有出现突变值,与实测数据相比误差较小,是适合致密砂岩储层的岩石物理模型。

4 结 论

本文将研究的岩石物理模型分成了3组,分别是经验参数模型、变参数模型和Han公式改进模型,由于每一组中的几个模型预测横波速度的误差相近,所以本文以组的形式对比模型的预测误差。以苏46井为例,预测横波速度的平均误差分别为:经验参数模型9.39%(常规Krief模型和常规Nur模型预测误差的平均值),变参数模型3.91%(变参数Krief模型、变参数Nur模型和Pride-Lee模型预测误差的平均值)和Han公式改进模型2.74%(Han关系优化的3种模型预测误差的平均值)。Han公式改进模型明显提高了预测精度,可以有效地预测致密砂岩储层的横波速度。

在岩性指数m、临界孔隙度Øc及胶结指数c有效值变化范围内,对比分析了变参数Krief、变参数Nur和Pride-Lee模型的体积模量和剪切模量公式在致密砂岩储层中应用的精度,得出它们的体积模量公式误差较大,而它们的剪切模量公式精度较高。提出采用Han的Kdryudry关系式结合3种模型中任一种剪切模量公式来建立干岩石模型,应用于Gassmann方程中,获得了每个采样点的岩性指数m、临界孔隙度Øc及胶结指数c的值可以反映出储层的地质特征,为判断地层的岩性差异、裂隙发育程度(裂隙发育处一般Øc较小)及固结情况等提供依据。

Han虽在多种砂岩岩样的基础上提出了Kdryudry关系式,但直接应用到不同的研究区中可能会有一定的误差。在实际应用中,需要根据研究区的数据重新拟合,修改公式中的系数值,获得更准确的拟合公式。

The authors have declared that no competing interests exist.

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[付斌,李进步,陈龙,. 苏里格气田西区致密砂岩气水识别方法与应用[J]. 特种油气藏,2014,21(3):66-69.]
Fu Bin, Lin Jinbu, Chen Long, et al. The gas/water identification method and its application in tight sandstone reservoir in the west of sulige gas field[J]. Special Oil and Gas Reservoirs, 2014, 21(3): 66-69.
DOI:10.3969/j.issn.1006-6535.2014.03.015 Magsci URL
在前人研究工作的基础上,在苏里格气田西区筛选多口典型井,采用阵列感应及偶极子声波实验,获得了岩石物理参数,明确了电性特征与气水间的关系,建立了对应的交会图,并应用在三维高分辨率地震资料的解释上。基于地震、测井联合技术,预测了苏186 区块气水分布特征,有效地指导了井位部署与气藏开发,同时对其他致密砂岩气藏的气水分布识别具有一定的指导意义。
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[30]
[贾培锋,杨正明,肖前华,. 致密油藏储层综合评价新方法[J]. 特种油气藏,2015,22(4): 33-36.]
Jia Peifeng, Yang Zhengming, Xiao Qianhua, et al. A new method to evaluate tight oil reservoirs[J]. Special Oil and Gas Reservoirs, 2015,22(4): 33-36.
DOI:10.3969/j.issn.1006-6535.2015.04.009 Magsci URL
致密油藏开发需要储层评价作为指导,但尚无一套评价方法立足于致密油开发实际。通过对大庆油田和长庆油田典型致密油储层岩心进行实验研究,运用统计学方法和数值模拟方法,优选了平均喉道半径、可动流体百分数、脆性指数、地层压力系数、启动压力梯度、原油黏度6 个参数用于致密储层评价。在低渗透油藏参数评价界限基础上,补充了地层压力系数和脆性指数分类界限;提出了致密油储层综合分类评价方法,将致密储层按综合分类系数分为4类。应用结果表明,大庆油田龙西区块的扶余油层和高台子油层,长庆油田的长8、长9 储层为Ⅱ&mdash;Ⅲ类储层,有一定开发潜力。
[本文引用: 1]
[31]
Li Lin, Ma Jinfeng.Study of shear wave velocity prediction during CO2-EOR and sequestration in Gao 89 area of Shengli Oilfield[J]. Applied Geophysics, 2017,14(3): 372-380.
DOI:10.1007/s11770-017-0638-5 URL
Shear-wave velocity is a key parameter for calibrating monitoring time-lapse 4D seismic data during CO2-EOR (Enhanced Oil Recovery) and CO2 sequestration.However,actual S-wave velocity data are lacking,especially in 4D data for CO2 sequestration because wells are closed after the CO2 injection and seismic monitoring is continued but no well log data are acquired.When CO2 is injected into a reservoir,the pressure and saturation of the reservoirs change as well as the elastic parameters of the reservoir rocks.We propose a method to predict the S-wave velocity in reservoirs at different pressures and porosities based on the Hertz-Mindlin and Gassmann equations.Because the coordination number is unknown in the Hertz-Mindlin equation,we propose a new method to predict it.Thus,we use data at different CO2 injection stages in the Gao89 well block,Shengli Oilfield.First,the sand and mud beds are separated based on the structural characteristics of the thin sand beds and then the S-wave velocity as a function of reservoir pressure and porosity is calculated.Finally,synthetic seismic seismograms are generated based on the predicted P-and S-wave velocities at different stages of CO2 injection.
[本文引用: 1]
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