﻿ 油气藏多孔岩石鼓胀压缩特性表征方法探讨

1. 燕山大学石油工程研究所, 河北秦皇岛 066004;
2. 中国石油华北油田分公司第三采油厂, 河北河间 062450

Discussion on a New Methods for the Characterization of the Swelling and Compression in Porous Rocks in Oil and Gas Reservoirs
LI Zifeng1, ZHENG Yiqing2
1. Petroleum Engineering Institute of Yanshan University, Qinhuangdao, Hebei, 066004, China;
2. Third Oil Production Plant of PetroChina Huabei Oilfield Company, Hejian, Hebei, 062450, China
Abstract: It is always controversial when one discusses the best way to calculate the stress in porous media and whether the porosity of rock can only be used to correlate the rock pore swelling coefficient and skeleton compression coefficient.After summarizing and analyzing the arguments of these two problems, the authors found that the main causes of disputes were caused by confused concepts, unclear understanding of engineering and mechanics, and wrong mathematical derivation.The authors proposed that Terzaghi's formula was wrong, and it was impossible to correlate rock pore swelling coefficient and rock skeleton compression coefficient only by rock porosity.Meanwhile, the paper put forward six coefficients, including the rock swelling coefficient, the rock pore swelling coefficient, the rock permeability swelling-increase coefficient, the rock compression coefficient, the rock pore compression coefficient, and the rock permeability compression-decrease coefficient, and also given their physical meanings and expressions, which can solve the confusion of the characterization of swelling and compression features in porous rocks.
Key words: porous rock     effective stress     rock volume     pore volume     permeability

1 主要问题的讨论综述 1.1 关于Terzaghi公式的讨论

Karl Terzaghi是第一个提出土力学有效应力概念的人，并给出了计算公式[27]

 (1)

 (2)

 (3)

1.2 关于仅用岩石孔隙度关联岩石孔隙鼓胀系数与岩石骨架压缩系数的讨论

 (4)

 (5)

 (6)

 (7)

 (8)

2 存在问题的原因分析

2.1 概念混乱

1) 同一名词，不同作者表达不同意义。例如文献[13]与文献[12, 14, 17, 21]中，“岩石压缩系数”的意义不同。

2) 同一意义，不同作者用不同概念表达。例如文献[12]中的“岩石压缩系数”与文献[13]和文献[15]中的“岩石孔隙压缩系数”表达的是同一意义。

3) 文字定义与数学定义不一致。例如文献[15]中的“岩石压缩系数”的文字定义与数学定义(即原文中的式(2))不一致。

2.2 对工程、力学和数学问题认识不清

1) “岩石颗粒不可压缩”的假设不合理。若岩石颗粒不可压缩则岩石不可压缩，即岩石为刚体，则其体积、孔隙度和渗透率不会随孔隙压力和环境压力的变化而变化，永远是个常数。如果是岩石颗粒体积不可压缩的误写，则孔隙体积变化量等于岩石外观体积的变化量，在研究孔隙度极高(接近于1)的多孔介质的孔隙度随孔隙压力和环境压力的变化时尚有一定精度；在研究孔隙度极低的多孔介质(例如页岩)的孔隙度随孔隙压力和环境压力的变化时误差太大。

2) “岩石骨架与孔隙等比例胀缩”的假设不合理。无论是孔隙压力变化还是围压变化引起的孔隙胀缩率都要远大于岩石骨架的胀缩率，这才符合最小势能原理。例如吹气球，气球是个弹性体，大气压强是个常数，当人们吹气球时，气球的断面并不是等比例变化，而是空腔直径不断变大，球壁越变越薄。

3) “孔隙度是常数”的假设不合理。孔隙度是变量，不是常数。岩石力学中有一个压实的概念，即孔隙度减小。孔隙压力变化导致孔隙体积、骨架体积变化就是压实或反压实过程。文献[12]在对式(2)进行微分时得到的公式：

 (9)

 (10)

4) “岩石的平均压应力为常数”的假设，在油藏内一般不严格成立。在实验室条件下，可以控制围压，使岩石的平均压应力为常数。但是，在油藏内，局部注液体必然引起注入部位及周围的平均压应力增高，所以，在油藏内“岩石的平均压应力为常数”不严格成立。

2.3 不能仅用岩石孔隙度关联岩石压缩系数与岩石骨架压缩系数

 (11)

3 解决问题的措施探讨

3.1 岩石鼓胀系数

 (12)

Cbp(σbc, ppc)来表示岩石鼓胀系数，不是表示围压和孔隙压力都一直为常数，而是因为Cbpσbcppc的函数，一般不是常数。这种表达就像数学中的 一样。其他5个系数均采用同样的表达方式。

3.2 岩石孔隙鼓胀系数

 (13)

3.3 岩石渗透率鼓增系数

 (14)

3.4 岩石压缩系数

 (15)

3.5 岩石孔隙压缩系数

 (16)

3.6 岩石渗透率压减系数

 (17)

4 结论

1) Terzaghi公式是错误的。

2) 不可仅用岩石孔隙度关联岩石孔隙鼓胀系数与岩石骨架压缩系数，且测量岩石骨架压缩系数比测量岩石孔隙鼓胀系数更难。

3) 在研究岩石的外观体积、孔隙度和渗透率随孔隙压力和环境压力的变化规律时，既不可假设基质岩石颗粒尺寸不可压缩，也不可假设基质岩石颗粒体积不可压缩，还不可假设基质岩石颗粒与孔隙等比例变形。否则，会产生逻辑问题或难以置信的误差。

4) 提出的岩石鼓胀系数、岩石孔隙鼓胀系数、岩石渗透率鼓增系数、岩石压缩系数、岩石孔隙压缩系数和岩石渗透率压减系数等6个概念可以解决多孔岩石鼓胀压缩特性表征方面出现的混乱现象。

 [1] 李传亮. 岩石压缩系数测量方法的理论研究[J]. 石油与天然气地质, 1998, 19(4): 280–285. LI Chuanliang. A theoretical study on measurement of rock compacting factors[J]. Oil & Gas Geology, 1998, 19(4): 280–285. DOI:10.11743/ogg19980403 [2] 李传亮, 孔祥言, 徐献芝, 等. 多孔介质的双重有效应力[J]. 自然杂志, 1999, 21(5): 288–291. LI Chuanliang, KONG Xiangyan, XU Xianzhi, et al. Double effective stresses of porous media[J]. Chinese Journal of Nature, 1999, 21(5): 288–291. [3] 李传亮. 多孔介质的应力关系方程:答周大晨先生[J]. 新疆石油地质, 2002, 23(2): 163–164. LI Chuanliang. Equations for stress relations in porous medium:in reply to Mr.Zhou Dachen[J]. Xinjiang Petroleum Geology, 2002, 23(2): 163–164. [4] 李敬元, 李子丰. 渗流作用下井筒周围岩石内的弹塑性应力分布规律及井壁稳定条件[J]. 工程力学, 1997, 14(1): 131–137. LI Jingyuan, LI Zifeng. Rock elastic-plastic stresses around a wellbore and wellbore stability under permeation osmosis[J]. Engineering Mechanics, 1997, 14(1): 131–137. [5] 李子丰. 基岩应力公式的探讨[J]. 石油钻采工艺, 2001, 23(3): 41. LI Zifeng. Discussion on the matrix stress formula[J]. Oil Drilling & Production Technology, 2001, 23(3): 41. [6] 陈庭根, 管志川. 钻井工程理论与技术[M]. 东营: 石油大学出版社, 2000: 8. CHEN Tinggen, GUAN Zhichuan. Drilling engineering theory and technology[M]. Dongying: Petroleum University Press, 2000: 8. [7] 窦宏恩. 油田开发中岩石压缩系数和孔隙度相关问题探讨[J]. 新疆石油地质, 2012, 33(5): 617–622. DOU Hongen. Discussion about rock compressibility and porosity applied in oilfield development[J]. Xinjiang Petroleum Geology, 2012, 33(5): 617–622. [8] 张睿, 宁正福, 杨峰, 等. 页岩应力敏感实验研究及影响因素分析[J]. 岩石力学与工程学报, 2015, 34(增刊1): 2617–2622. ZHANG Rui, NING Zhengfu, YANG Feng, et al. Experimental study of stress sensitivity of shale reservoirs[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(supplement 1): 2617–2622. [9] ZHANG Rui, NING Zhengfu, YANG Feng, et al. Impacts of nanopore structure and elastic properties on stress-dependent permeability of gas shales[J]. Journal of Natural Gas Science and Engineering, 2015, 26: 1663–1672. DOI:10.1016/j.jngse.2015.02.001 [10] 蔡新树, 陈勉, 金衍, 等. 各向异性多重孔隙介质有效应力定律[J]. 工程力学, 2009, 26(4): 57–60. CAI Xinshu, CHEN Mian, JIN Yan, et al. An effective stress law for anisotropic multi-porosity media[J]. Engineering Mechanics, 2009, 26(4): 57–60. [11] 陈茜, 骆亚生, 程大伟. 非饱和土有效应力及其参数的确定[J]. 工程力学, 2013, 30(6): 340–345. CHEN Xi, LUO Yasheng, CHENG Dawei. Effective stress and parameters of unsaturated loess[J]. Engineering Mechanics, 2013, 30(6): 340–345. [12] 李传亮. 岩石压缩系数与孔隙度的关系[J]. 中国海上油气(地质), 2003, 17(5): 355–358. LI Chuanliang. The relationship between rock compressibility and porosity[J]. China Offshore Oil and Gas(Geology), 2003, 17(5): 355–358. [13] 罗瑞兰. 对"低渗透储层不存在强应力敏感"观点的质疑[J]. 石油钻采工艺, 2006, 28(2): 78–80. LUO Ruilan. Queries to the viewpoint low permeability reservoirs have not the characteristics of strong stress sensitivity[J]. Oil Drilling & Production Technology, 2006, 28(2): 78–80. [14] 李传亮. 储层岩石的应力敏感问题:答罗瑞兰女士[J]. 石油钻采工艺, 2006, 28(6): 86–88. LI Chuanliang. Discussion on the stress sensitivity of reservoir rocks:reply to Ms.Luo Ruilan[J]. Oil Drilling & Production Technology, 2006, 28(6): 86–88. [15] 窦宏恩. 质疑不存在启动压力之观点[J]. 特种油气藏, 2009, 16(1): 53–57. DOU Hongen. The viewpoint of there isn't threshold pressure is doubted[J]. Special Oil and Gas Reservoirs, 2009, 16(1): 53–57. [16] 窦宏恩, 白喜俊. 低渗透和高渗透储层都存在应力敏感性[J]. 石油钻采工艺, 2009, 31(2): 121–124. DOU Hongen, BAI Xijun. Stress sensitivity consists in low permeability and middle-high permeability reservoirs[J]. Oil Drilling & Production Technology, 2009, 31(2): 121–124. [17] 李传亮. 低渗透储层很特殊吗:回应窦宏恩先生[J]. 特种油气藏, 2011, 18(5): 131–134. LI Chuanliang. Are low permeability reservoirs very special:reply to Mr.Dou Hongen[J]. Special Oil and Gas Reservoirs, 2011, 18(5): 131–134. [18] 窦宏恩. 岩石孔隙体积压缩系数表达式推导:兼答《低渗透储层很特殊吗》一文作者[J]. 特种油气藏, 2012, 19(4): 149–150. DOU Hongen. Derivation of equations of rock pore volume compressibility:a reply to the author of is low permeability reservoir very special?[J]. Special Oil and Gas Reservoirs, 2012, 19(4): 149–150. [19] 贾碧霞, 徐予勖. 岩石压缩系数的新求解方法:对"岩石压缩系数对油藏动态储量计算结果的影响"中压缩系数求解方法的质疑[J]. 青海石油, 2010, 28(2): 29–31. JIA Bixia, XU Yuxu. A new method to solve rock compressibility[J]. Qinghai Oil, 2010, 28(2): 29–31. [20] 王厉强, 李正科, 申红, 等. 实测岩石孔隙压缩系数偏高原因再分析:与李传亮教授商榷[J]. 新疆石油地质, 2011, 32(1): 102–103. WANG Liqiang, LI Zhengke, SHEN Hong, et al. A discussion on results interpretation again of higher measured rock compressibility[J]. Xinjiang Petroleum Geology, 2011, 32(1): 102–103. [21] 李传亮. 储集层岩石的压缩系数公式:回应王厉强博士[J]. 新疆石油地质, 2012, 33(1): 125–126. LI Chuanliang. The formulae of rock compressibility of reservoirs:reply to Dr.Wang Liqiang[J]. Xinjiang Petroleum Geology, 2012, 33(1): 125–126. [22] 王厉强, 李正科, 袁昭, 等. 再论储集层岩石的压缩问题:对《储集层岩石的压缩问题》一文的不同看法[J]. 新疆石油地质, 2012, 33(6): 379–381. WANG Liqiang, LI Zhengke, YUAN Zhao, et al. Re-discussion on the compression of reservoir rocks[J]. Xinjiang Petroleum Geology, 2012, 33(6): 379–381. [23] 李传亮. 岩石的压缩系数问题:再与王厉强博士商榷[J]. 新疆石油地质, 2013, 34(3): 354–356, 360. LI Chuanliang. Compressibility of reservoir rocks:re-discussion with Dr.Wang Liqiang[J]. Xinjiang Petroleum Geology, 2013, 34(3): 354–356, 360. [24] 陈元千, 邹存友. 三种岩石压缩系数关系的推导与对比[J]. 新疆石油地质, 2012, 33(4): 459–460. CHEN Yuanqian, ZOU Cunyou. Deduction and comparison of relationships among three kinds of rock compressibility factors[J]. Xinjiang Petroleum Geology, 2012, 33(4): 459–460. [25] 张睿, 宁正福, 杨峰, 等. 页岩应力敏感实验与机理[J]. 石油学报, 2015, 36(2): 224–231, 237. ZHANG Rui, NING Zhengfu, YANG Feng, et al. Shale stress sensitivity experiment and mechanism[J]. Acta Petrolei Sinica, 2015, 36(2): 224–231, 237. DOI:10.7623/syxb201502012 [26] ZHANG Rui, NING Zhengfu, YANG Feng, et al. A laboratory study of the porosity-permeability relationships of shale and sandstone under effective stress[J]. International Journal of Rock Mechanics & Mining Sciences, 2016, 81: 19–27. [27] TERZAGHI K. Theoretical soil mechanics[M]. New York: John Wiley & Sons, 1943: 11-13. [28] LI Zifeng, LI Xuejiao. Semantic issues with the word "anti" in particle physics[J]. Physics Essays, 2012, 25(3): 347–348. DOI:10.4006/0836-1398-25.3.347

#### 文章信息

LI Zifeng, ZHENG Yiqing

Discussion on a New Methods for the Characterization of the Swelling and Compression in Porous Rocks in Oil and Gas Reservoirs

Petroleum Drilling Techniques, 2018, 46(3): 1-6.
http://dx.doi.org/10.11911/syztjs.2018066