﻿ 钻井液在致密砂岩中裂缝的侵入深度模型
 西南石油大学学报(自然科学版)  2018, Vol. 40 Issue (4): 97-104

“油气藏地质及开发工程”国家重点实验室·西南石油大学, 四川 成都 610500

Invasion Depth Model for Drilling Fluids in Fractures in Dense Sandstones
LEI Qiang , TANG Hongming, ZHANG Liehui, ZHU Boyu
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China
Abstract: The pore structure and fractures of the reservoir in the Keshen site of the Kelasu Gas Field cause significant leakage of drilling fluids while drilling. In particular, solid particles block the fractures, leading to low or even zero productivity for some wells after completion. In the field, acid fracturing is mainly employed to remove blockage. The variations in the invasion depth of the drilling fluid in fractures can reflect the performance of acid fracturing. Concerning this issue, according to the flow mechanism of Newtonian fluids in fractures, fracture aperture variations, and filtration losses of fracture walls, a dynamic model for drilling fluid leakage in a single fracture is established. The invasion depth of the drilling fluid is quantitatively described based on the distribution of the drilling fluid pressure inside the fracture. The relationship between the invasion depth and invasion time and that between the pressure difference and fracture aperture are considered and analyzed. Finally, using the established model, the relationship between the invasion depths of the acid and drilling fluid is predicted. The results are compared with the actual values obtained from the Keshen C well, indirectly validating the model.
Key words: fractured reservoir     drilling fluid     leakage     dense sandstones     invasion depth

1 钻井液漏失动力学模型

(1) 所有钻井液都沿着一条裂缝漏失，且漏失过程中主要是钻井液沿裂缝发生漏失。

(2) 地层基质渗透率不能忽略，钻井液沿裂缝壁面滤失，同时地层压力不变。

(3) 地层基质渗透率不能忽略，钻井液沿裂缝壁面滤失，同时地层压力不变。

(4) 钻井液假设为牛顿流体，且钻井液在裂缝中流动不发生堵塞，流体为层流流动。

Liu等在研究单相不可压缩钻井液在双重介质中的漏失动力模型时，分别在裂缝和基质中使用连续性方程[28]

 ${{\phi }_{{\rm f}}}{{C}_{{\rm f}}}\dfrac{\partial {{p}_{{\rm f}}}}{\partial t}=\dfrac{{{K}_{{\rm f}}}}{\mu }\dfrac{{{\partial }^{2}}{{p}_{{\rm f}}}}{\partial {{x}^{2}}}-\alpha \dfrac{{{K}_{{\rm m}}}}{\mu }\left( {{p}_{{\rm f}}}-{{p}_{{\rm m}}} \right)$ (1)

 ${{\phi }_{{\rm m}}}{{C}_{{\rm m}}}\dfrac{\partial {{p}_{{\rm m}}}}{\partial t}=\dfrac{{{K}_{{\rm m}}}}{\mu }\dfrac{{{\partial }^{2}}{{p}_{{\rm m}}}}{\partial {{x}^{2}}}+\alpha \dfrac{{{K}_{{\rm m}}}}{\mu }\left( {{p}_{{\rm f}}}-{{p}_{{\rm m}}} \right)$ (2)

$\phi _{\rm f}$—裂缝孔隙度，%；

$C_{{\rm f}}$—裂缝压缩系数，Pa$^{{\rm -1}}$

$p_{{\rm f}}$—裂缝内的压力，Pa；

$t$—时间，s；

$x$—横坐标，m

$p_{{\rm m}}$—基质内的压力，Pa；

$\mu$—流体黏度，Pa.s；

$\alpha$—形状因子，无因次；

$K_{{\rm f}}$—裂缝渗透率，D；

$K_{{\rm m}}$—基质渗透率，D；

${{\phi }_{{\rm m}}}$—基质孔隙度，%

$C_{{\rm m}}$—基质压缩系数，Pa$^{{\rm -1}}$

 $q=\alpha \dfrac{{{K}_{{\rm m}}}}{\mu }\left( p-{{p}_{{\rm m}}} \right)$ (3)

$q$—流体串流量，m$^{{\rm 3}}$/s；

$p$—裂缝内的压力，Pa。

 图1 900 mm长裂缝在不同正压差情况缝宽增量 Fig. 1 The increment of fracture width with different positive pressure differential of 900 mm fracture

 $w={{w}_{o}}+\dfrac{p-{{p}_{\rm o}}}{{{k}_{\rm n}}}$ (4)

$w$—裂缝宽度，μm；

$w_{{\rm o}}$—初始裂缝宽度，μm；

$p_{{\rm o}}$—地层压力，Pa；

$k_{{\rm n}}$—裂缝法向刚度，Pa/m。

 $-\dfrac{\partial }{\partial x}\left( wv \right)=q+\dfrac{\partial w}{\partial t}$ (5)

$v$—钻井液在裂缝中的流速，m/s。

 $v=\dfrac{{{w}^{2}}}{12\mu }\left( -\dfrac{\partial p}{\partial x} \right)$ (6)

 $\dfrac{{{w}^{3}}}{12\mu }\dfrac{{{\partial }^{2}}p}{\partial {{x}^{2}}}+\dfrac{3{{w}^{2}}}{12\mu {{k}_{\rm n}}}{{\left( \dfrac{\partial p}{\partial x} \right)}^{2}}=\dfrac{1}{{{k}_{\rm n}}}\dfrac{\partial p}{\partial t}{\rm +}\dfrac{\alpha {{K}_{\rm m}}}{\mu }\left( p-{{p}_{\rm o}} \right)$ (7)

2 漏失模型钻井液侵入深度影响因素

 图2 不同初始裂缝宽度下钻井液侵入深度与裂缝内的压力间的关系 Fig. 2 Invasion depth of drilling fluid vs. fracture pressure at different width of initial fracture
 图3 不同压差下钻井液侵入深度与裂缝内的压力间的关系 Fig. 3 Invasion depth of drilling fluid vs. fracture pressure at different pressure differential
 图4 不同漏失时间钻井液侵入深度与裂缝内的压力间的关系 Fig. 4 Invasion depth of drilling fluid vs. fracture pressure at different leakage time

3 钻井液侵入深度模型在现场的应用

 图5 克深A，B，C井在单一裂缝中钻井液钻井液侵入深度与裂缝内的压力间的关系 Fig. 5 Invasion depth of drilling fluid vs. fracture pressure at single fracture in Well Keshen A, Keshen B, Keshen C

 图6 克深C井钻井液侵入深度和酸液侵入裂缝压力/酸液侵入裂缝压力间的关系 Fig. 6 Invasion depth of drilling fluid vs. fracture pressure/acid liquor pressure in Well Keshen C

4 结语

(1) 利用牛顿流体在裂缝中的流动机理，考虑裂缝宽度的变化以及裂缝壁面的滤失等建立了单一裂缝钻井液漏失动力模型，根据裂缝中的压力分布来定量描述钻井液的侵入深度。考虑并分析了钻井液漏失模型的侵入深度与侵入时间，压差和裂缝宽度之间的关系。

(2) 裂缝性致密砂岩储层基质的渗透率非常小，这使得裂缝壁面的滤失量较小，滤失造成的钻井液压力损失也很小，导致了钻井液在在裂缝中的滤失受钻井液压力的影响很大。

(3) 裂缝性致密砂岩储层而言，虽然裂缝壁面的滤失很小，但是裂缝壁面的滤失任然对地层基质压力有一定的影响，不过影响很小，本文为简化模型没有给予考虑。

(4) 模型仅考虑了牛顿流体在壁面光滑的水平裂缝中的漏失动力模型，对于不同流体，在壁面粗糙的弯曲裂缝中的侵入深度问题还有待于进一步研究。

 [1] DUPRIEST F E. Fracture closure stress(FCS) and lost returns practices[C]. SPE 92192-MS, 2005. doi: 10.2118/-92192-MS [2] 蒋官澄, 张弘, 吴晓波, 等. 致密砂岩气藏润湿性对液相圈闭损害的影响[J]. 石油钻采工艺, 2014, 36(6): 50-54. JIANG Guancheng, ZHANG Hong, WU Xiaobo, et al. Effect of tight sandstone gas reservoir wettability on liquid traps damage[J]. Oil Drilling & Production Technology, 2014, 36(6): 50-54. doi: 10.13639/j.odpt.2014.06.013 [3] 王俊鹏, 张荣虎, 赵继龙, 等. 超深层致密砂岩储层裂缝定量评价及预测研究——以塔里木盆地克深气田为例[J]. 天然气地球科学, 2014, 25(11): 1735-1745. WANG Junpeng, ZHANG Ronghu, ZHAO Jilong, et al. Characteristics and evaluation of fractures in ultra-deep tight sandstone reservoir:Taking Keshen Gas Field in Tarim Basin, NW China as an example[J]. Natural Gas Geoscience, 2014, 25(11): 1735-1745. doi: 10.11764/j.-issn.1672-1926.2014.11.1735 [4] QUTOB H, BYRNE M. Formation damage in tight gas reservoirs[C]. SPE 174237-MS, 2015. doi: 10.2118/-174237-MS [5] 张惠良, 张荣虎, 杨海军, 等. 超深层裂缝孔隙型致密砂岩储集层表征与评价——以库车前陆盆地克拉苏构造带白垩系巴什基奇克组为例[J]. 石油勘探与开发, 2014, 41(2): 158-167. ZHANG Huiliang, ZHANG Ronghu, YANG Haijun, et al. Characterization and evaluation ofultra-deep fracturepore tight sandstone reservoirs:A case study of Cretaceous Bashijiqike Formation in Kelasu tectonic zone in Kuqa foreland Basin, Tarim, NW China[J]. Petroleum Exploration and Development, 2014, 41(2): 158-167. doi: 10.-11698/PED.2014.0204 [6] 曾义金, 刘建立. 深井超深井钻井技术现状和发展趋势[J]. 石油钻探技术, 2005, 33(5): 1-5. ZENG Yijin, LIU Jianli. Technical status and developmental trend of drilling techniques in deep and ultra-deep wells[J]. Petroleum Drilling Techniques, 2005, 33(5): 1-5. doi: 10.3969/j.issn.1001-0890.2005.05.001 [7] 李永平, 程兴生, 张福祥, 等. 异常高压深井裂缝性厚层砂岩储层"酸化+酸压"技术[J]. 石油钻采工艺, 2007, 32(3): 76-80. LI Yongping, CHENG Xingsheng, ZHANG Fuxiang, et al. Acid fracturing technology for thick fractured sandstone reservoir of deep wells with abnormal high pressure[J]. Oil Driling & Production Technology, 2007, 32(3): 76-80. doi: 10.13639/j.odpt.2010.03.018 [8] 肖鑫, 王建民, 刘兆龙, 等. 库车坳陷克深9气藏储层特征及成岩作用研究[J]. 石油地质与工程, 2017, 31(1): 26-29. XIAO Xin, WANG Jianming, LIU Zhaolong, et al. Study on reservoir characteristics and diagenesis of Keshen 9 gas reservoir in Kuqa Depression[J]. Petroleum Geology and Engineering, 2017, 31(1): 26-29. [9] 张荣虎, 张惠良, 寿建峰, 等. 库车坳陷大北地区下白垩统巴什基奇克组储层成因地质分析[J]. 地质科学, 2008, 43(3): 507-517. ZHANG Ronghu, ZHANG Huiliang, SHOU Jianfeng, et al. Geological analysis on reservoir mechanism of the Lower Cretaceous Bashijiqike Formation in Dabei Area of the Kuqa Depression[J]. Chinese Journal of Geology, 2008, 43(3): 507-517. doi: 10.3321/j.issn:0563-5020.-2008.03.006 [10] 屈海洲, 张福祥, 王振宇, 等. 基于岩心电成像测井的裂缝定量表征方法——以库车坳陷ks2区块白垩系巴什基奇克组砂岩为例[J]. 石油勘探与开发, 2016, 43(3): 425-432. QU Haizhou, ZHANG Fuxiang, WANG Zhenyu, et al. Quantitative fracture evaluation method based on coreimage logging:A case study of Cretaceous Bashijiqike Formation in ks2 well area, Kuqa Depression, Tarim Basin, NW China[J]. Petroleum Exploration and Development, 2016, 43(3): 425-432. doi: 10.11696/PED.2016.-03.13 [11] 张荣虎, 张惠良, 马玉杰, 等. 特低孔特低渗高产储层成因机制——以库车坳陷大北1气田巴什基奇克组储层为例[J]. 天然气地球科学, 2008, 19(1): 75-82. ZHANG Ronghu, ZHANG Huiliang, MA Yujie, et al. Origin of extra low porosity and permeability high production reseroirs:A case from Bashijiqike Reservoir of Dabei 1 Oilfield, Kuqa Depression[J]. Natural Gas Geoscience, 2008, 19(1): 75-82. doi: 10.11764/j.issn.1672-1926.2008.01.75 [12] BREGE J J, PIETRANGELI G A, MCKELLAR A J, et al. Fluid formulations for cleaning oil-based or synthetic oil-based mud filter cakes: U. S. Patent Application 14/478, 510[P]. United States Patent and Trademark Office, 2014-9-5. [13] 张虎俊. 青西油田深层复杂岩性裂缝性油藏储层改造关键技术研究与应用[D]. 成都: 西南石油大学, 2009. ZHANG Hujun. Study and application of stimulatiing technology on deep fractured reservoir with complex lithology in Qingxi Oilfield[D]. Chengdu: Southwest Petroleum University, 2009. http://cdmd.cnki.com.cn/Article/CDMD-10615-2009255960.htm [14] 朱金智, 游利军, 李家学, 等. 油基钻井液对超深裂缝性致密砂岩气藏的保护能力评价[J]. 天然气工业, 2017, 37(2): 62-68. ZHU Jinzhi, YOU Lijun, LI Jiaxue, et al. Damage evaluation on oil-based drill-in fluids for ultra-deep fractured tight sandstone gas reservoirs[J]. Natural Gas Industry, 2017, 37(2): 62-68. doi: 10.3787/j.issn.1000-0976.-2017.02.008 [15] LAVROV A, TRONVOLL J. Mud loss into a single fracture during drilling of petroleum wells: Modeling approach[C]//Development and Application of Discontinuous Modelling for Rock Engineering: Proceedings of the 6th International Conference ICADD-6, Trondheim, Norway, 2003: 189-198. [16] LAVTOV A, TRONVOLL J. Modeling mud loss in fractured formations[C]. SPE 88700-MS, 2004. doi: 10.2118/-88700-MS https://www.researchgate.net/publication/314765187_Modeling_Mud_Loss_in_Fractured_Formations [17] LAVTOV A. Newtonian fluid flow from an arbitrarilyoriented fracture into a single sink[J]. Acta Mechanica, 2006, 186(1-4): 55-74. doi: 10.1007/s00707-006-0324-9 [18] SANFILIPPO F, BRIGNOLI M, SANTARELLI F J, et al. Characterization of conductive fractures while drilling[C]. SPE 38177-MS, 1997. doi: 10.2118/38177-MS http://dx.doi.org/10.2118/38177-MS [19] OZDEMIRTAS M, BABADAGLI T, KURU E. Effects of fractal fracture surface roughness on borehole ballooning[J]. Vadose Zone Journal, 2009, 8(1): 250-257. doi: 10.2136/vzj2007.0174 [20] OZDEMIRTAS M, KURU E, BABADAGLI T. Experimental investigation of borehole ballooning due to flow of non-Newtonian fluids into fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 2010, 47(7): 1200-1206. doi: 10.1016/j.ijrmms.2010.07.002 [21] OZDEMIRTAS M, BABADAGLI T, KURU E. Experimental and numerical investigations of borehole ballooning in rough fractures[J]. SPE Drilling & Completion, 2009, 24(2): 256-265. doi: 10.2118/110121-PA [22] BROWN S R. Fluid flow through rock joints:The effect of surface roughness[J]. Journal of Geophysical Research:Solid Earth and Planets, 1987, 92(B2): 1337-1347. doi: 10.1029/JB092iB02p01337 [23] BROWN S R, STOCKMAN H W, REEVES S J. Applicability of the Reynolds equation for modeling fluid flow between rough surfaces[J]. Geophysical Research Letters, 1995, 22(18): 2537-2540. doi: 10.1029/95GL02666 [24] BROWN S R, SCHOLZ S H. Broad bandwidth study of the topography of natural rock surfaces[J]. Journal of Geophysical Research:Solid Earth and Planets, 1985, 90(B14): 2575-2582. doi: 10.1029/JB090iB14p12575 [25] 范翔宇, 龚明, 夏宏泉, 等. 裂缝性致密砂岩储层钻井液侵入深度的定量计算方法[J]. 天然气工业, 2012, 32(6): 110-111. FAN Xiangyu, GONG Ming, XIA Hongquan, et al. A quantitative calculation method of the invasion depth of drilling fluids in fractured tight sandstone reservoir[J]. Nature Gas Industry, 2012, 32(6): 110-111. doi: 10.3787/j.-issn.1000-0976.2012.06.015 [26] 叶艳, 安文华, 滕学清, 等. 裂缝性碳酸盐岩储层的钻井液侵入预测模型[J]. 石油学报, 2011, 32(3): 504-508. YE Yan, AN Wenhua, TENG Xueqing, et al. The prediction model for the drilling fluid invasion in fractured carbonate reservoirs[J]. Acta Petrolei Sinica, 2011, 32(3): 504-508. doi: 10.7623/syxb201103021 [27] 鄢捷年. 钻井液工艺学[M]. 北京: 中国石油大学出版社, 2013: 89-90. YAN Jienian. Drilling fluid technology[M]. Beijing: China Petroleum University Publishing House, 2013: 89-90. [28] LIU Yuxuan, GUO Jianchun, CHEN Zhangxin. Leakoff characteristics and an equivalent leakoff coefficient in fractured tight gas reservoirs[J]. Journal of Natural Gas Science and Engineering, 2016, 31: 603-611. doi: 10.-1016/j.jngse.2016.03.054 [29] 练章华, 康毅力, 徐进, 等. 裂缝宽度的有限元数值模拟[J]. 天然气工业, 2001, 21(3): 47-50. LIAN Zhanghua, KANG Yili, XU Jin, et al. Predicting fracture width by finite element numerical simulation[J]. Natural Gas Industry, 2001, 21(3): 47-50. doi: 10.3321/j.-issn:1000-0976.2001.03.014 [30] 练章华, 康毅力, 唐波, 等. 井壁附近垂直裂缝宽度预测[J]. 天然气工业, 2003, 23(3): 44-46. LIAN Zhanghua, KANG Yili, TANG Bo, et al. Prediction of vertical fracture widths near borehole face of the wall[J]. Nature Gas Industry, 2003, 23(3): 44-46. doi: 10.3321/j.-issn:1000-0976.2003.03.013 [31] 童亨茂. 储层裂缝描述与预测研究进展[J]. 新疆石油学院学报, 2004, 16(2): 9-13. TONG Hengmao. Description and prediction of reservoir fractures networks[J]. Journal of Xinjiang Petroleum Institute, 2004, 16(2): 9-13. doi: 10.3969/j.issn.1673-2677.-2004.02.003