油藏渗流–应力耦合分析的FEM-FVM混合方法的改进

doi:10.13722/j.cnki.jrme.2019.0714

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摘要在油藏开采过程中，岩石应力场变化的波及范围远大于发生渗流的储层区域，因而现有渗流–应力全耦合方法数值模拟的计算量往往十分巨大。为了提高数值模拟的计算效率，考虑渗流计算区域和应力计算区域的差异，对FEM-FVM(有限元–有限体积)混合方法进行了改进。对储层渗流区域采用细密的网格进行计算，以获得地下流体较为准确的分布情况；对应力计算区域则采用粗网格进行计算，从而降低计算耗时。全耦合理论中的力学平衡方程采用有限元法在粗网格上进行离散；质量守恒方程则在细网格上采用有限体积法进行离散。对Terzaghi一维固结问题和Mandel二维固结问题的数值模拟表明，该方法的计算结果与解析解吻合较好。通过对一个二维单相流单井开采问题和一个三维两相流五点井网开采问题的数值计算，分析了油藏数值模拟中渗流–应力耦合效应的影响。

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	邸元1
	吴大卫1
	WU Yushu2

关键词 ：岩石力学, 油藏数值模拟, 渗流–应力耦合, 有限体积法, 有限元法, 耦合问题

Abstract：For the practical procedure of oil production，stress field affects a much larger area than the reservoir domain，which requires a large amount of computation to simulate using recent approaches for fully coupled fluid flow-mechanics reservoir simulation. In order to increase numerical simulation efficiency，a hybrid method mixing finite element method(FEM) and finite volume method(FVM) is improved to consider the differences of computational domain between fluid flow and mechanics. A fine mesh is used for the computation of seepage in the reservoir domain to catch the detail distribute of fluids，whereas a coarse mesh for stress computation to reduce computational cost. The equilibrium equation of fully coupled approaches is discretized on the coarse grid by finite element method，and the mass balance equation is discretized on the fine grid by finite volume method. Numerical results of both Terzaghi′s and Mendal′s consolidation problems show great consistency with their analytical solutions，which verifies the proposed method. In order to analyze the fluid flow-mechanics coupling effect to reservoir simulation，the numerical results of a two dimensional single-phase flow problem with constant pressure pumping and a three dimensional two-phase flow case in five-spot scheme are carried out.

Key words： rock mechanics reservoir simulation flow-mechanics coupling finite volume method finite element method coupled problem

引用本文:

邸元1，吴大卫1，WU Yushu2. 油藏渗流–应力耦合分析的FEM-FVM混合方法的改进[J]. 岩石力学与工程学报, 2020, 39(S1): 2645-2654.
DI Yuan1，WU Dawei1，WU Yushu2. Improvement of a mixed FEM-FVM method for reservoir simulation coupling fluid flow and mechanics. , 2020, 39(S1): 2645-2654.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2019.0714 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/IS1/2645

[19]	PREVOST J H. Consolidation of an elastic porous media[J]. ASCE Journal of Engineering Mechanics，1981，107(1)：169–186.
[39]	DAVIES J P，DAVIES D K. Stress-dependent permeability：characterization and modeling[J]. SPE Journal，2001，6(2)：224–235.
[37]	VERRUIJT A. Elastic storage of aquifers[J]. Flow Through Porous Media，1969，1：331–376.
[11]	BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics，1941，12(2)：155–164.
[21]	ZIENKIEWICZ O C，CHAN A H C. Coupled problems and their numerical solution[J]. Advances in Computational Nonlinear Mechanics，2014，300：139–176.
[3]	赵政璋，杜金虎. 致密油气[M]. 北京：石油工业出版社，2012.(ZHAO Zhengzhang，DU Jinhu. Tight oil and gas[M]. Beijing：Petroleum Industry Press，2012.(in Chinese))
[5]	康玉柱. 中国非常规致密岩油气藏特征[J]. 天然气工业，2012，32(5)：1–4.(KANG Yuzhu. Characteristics of tight hydrocarbon reservoirs in China[J]. Natural Gas Industry，2012，32(5)：1–4.(in Chinese))
[8]	ALPAK F O. Robust fully-implicit coupled multiphase-flow and geomechanics simulation[J]. SPE Journal，2015，20(6)：1 366–1 383.
[1]	贾承造，郑民，张永峰. 中国非常规油气资源与勘探开发前景[J]. 石油勘探与开发，2012，39(2)：129–136.(JIA Chengzao，ZHENG Min，ZHANG Yongfeng. Unconventional hydrocarbon resources in China and the prospect of exploration and development[J]. Petroleum Exploration and Development，2012，39(2)：129–136.(in Chinese))
[2]	李阳. 中国石化致密油藏开发面临的机遇与挑战[J]. 石油钻探技术，2015，43(5)：1–6.(LI Yang. Opportunities and challenges for Sinopec to develop tight oil reservoirs[J]. Petroleum Drilling Techniques，2015，43(5)：1–6.(in Chinese))
[7]	邹才能，朱如凯，吴松涛，等. 常规与非常规油气聚集类型?特征?机理及展望——以中国致密油和致密气为例[J]. 石油学报，2012，33(2)：173–187.(ZOU Caineng，ZHU Rukai，WU Songtao，et al. Types，characteristics，genesis and prospects of conventional and unconventional hydrocarbon accumulations：taking tight oil and tight gas in China as an instance[J]. Acta Petrolei Sinica，2012，33(2)：173–187.(in Chinese))
[9]	WU Y S，RUTQVIST J，KARASAKI K，et al. A mathematical model for rock deformation′s effect on flow in porous and fractured reservoirs[J]. Social Service Review，2008，6(3)：490–492.
[12]	BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. low-frequency range[J]. The Journal of the Acoustical Society of America，1956，28(2)：168–178.
[15]	SMALL J C，BOOKER J R，DAVIS E H. Elasto-plastic consolidation of soil[J]. International Journal of Solids and Structures，1976，12(6)：431–448.
[4]	秦伟军，付兆辉. 中国石化特低渗砂岩油和致密砂岩气资源勘探潜力[J]. 当代石油石化，2012，20(2)：13–16.(QIN Weijun，FU Zhaohui. Sinopec′s resources exploration potential of extremely low permeability sandstone oil and tight sand gas[J]. Petroleum and Petrochemical Today，2012，20(2)：13–16.(in Chinese))
[14]	BOOKER J R，SMALL J C. An investigation of the stability of Biot′s equations of consolidation[J]. International Journal of Solids and Structures，1975，11(7/8)：907–917.
[17]	CARTER J P，BOOKER J R，DAVIS E H. Finite deformation of an elasto-plastic soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1977，1(1)：25–43.
[22]	ZIENKIEWICZ O C，SHIOMI T. Dynamic behaviour of saturated porous media：the generalized Biot formulation and its numerical solution[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1984，8(1)：71–96.
[24]	WU Y S，PRUESS K. A multiple-porosity method for simulation of naturally fractured petroleum reservoirs[J]. SPE Reservoir Engineering，1988，3(1)：327–336.
[25]	WU Y S，DI Y，KANG Z J，et al. A multiple-continuum model for simulating single-phase and multiphase flow in naturally fractured vuggy reservoirs[J]. Journal of Petroleum Science and Engineering，2011，78(1)：13–22.
[27]	AKAI K，TAMURA T. Study of two-dimensional consolidation accompanied by an elasto-plastic constitutive equation[J]. Proceedings of Japan Society of Civil Engineers，1978，269：98–104.
[29]	DI Y，SATO T. Liquefaction analysis of saturated soils taking into account variation in porosity and permeability with large deformation[J]. Computers and Geotechnics，2003，30(7)：623–635.
[34]	SETTARI A. Reservoir compaction[J]. Journal of Petroleum Technology，2002，54(8)：62–69.
[10]	TERZAGHI B K. Theoretical soil mechanics[M]. Chapman，1959：11–14.
[20]	PREVOST J H. Nonlinear transient phenomena in saturated porous media[J]. Computer Methods in Applied Mechanics and Engineering，1982，30(1)：3–18.
[30]	DI Y，SATO T. A practical numerical method for large strain liquefaction analysis of saturated soils[J]. Soil Dynamics and Earthquake Engineering，2004，24(3)：251–260.
[32]	邸元，唐小微. 饱和多孔介质大变形分析的一种有限元–有限体积混合方法[J]. 计算力学学报，2008，25(4)：483–487.(DI Yuan，TANG Xiaowei. An finite element-finite volume hybrid method for large deformation analysis of porous media[J]. Chinese Journal of Computational Mechanics，2008，25(4)：483–487.(in Chinese))
[35]	WANG X S，CHEN C X，JIAO J J. Modified theis equation by considering the bending effect of the confining unit[J]. Advances in Water Resources，2004，27(10)：981–990.
[40]	FERRONATO M，CASTELLETTO N，GAMBOLATI G. A fully coupled 3-D mixed finite element model of Biot consolidation[J]. Journal of Computational Physics，2010，229(12)：4 813–4 830.
[18]	VOYIADJIS G Z，ABU-FARSAKH M Y. Coupled theory of mixtures for clayey soils[J]. Computers and Geotechnics，1997，20(3/4)：195–222.
[28]	OKA F，YASHIMA A，SHIBATA T，et al. FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model[J]. Applied Scientific Research，1994，52(3)：209–245.
[38]	RUTQVIST J，WU Y S，TSANG C F，et al. A modeling approach for analysis of coupled multiphase fluid flow，heat transfer，and deformation in fractured porous rock[J]. International Journal of Rock Mechanics and Mining Sciences，2002，39(4)：429–442.
[6]	魏海峰，凡哲元，袁向春. 致密油藏开发技术研究进展[J]. 油气地质与采收率，2013，20(2)：62–66.(WEI Haifeng，FAN Zheyuan，YUAN Xiangchun. Review on new advances in foreign tight oil development technology and their enlightment[J]. Petroleum Geology and Recovery Efficiency，2013，20(2)：62–66.(in Chinese))
[13]	BOOKER J R. A numerical method for the solution of Biot′s consolidation theory[J]. Quarterly Journal of Mechanics and Applied Mathematics，1973，26(4)：445–470.
[16]	CARTER J P，BOOKER J R，SMALL J C. Analysis of finite elasto-plastic consolidation[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1979，3(2)：107–129.
[23]	PRUESS K，NARASIMHAN T N. A practical method for modeling fluid and heat flow in fractured porous media[J]. SPE Journal，1985，25(1)：14–26.
[26]	邸元，彭浪，WU Yushu，等. 缝洞型多孔介质中多相流的有限体积法数值模拟[J]. 计算力学学报，2013，30(增1)：144–149.(DI Yuan，PENG Lang，WU Yushu，et al. Numerical simulation of multiphase flow in fractured vuggy porous medium using finite volume method[J]. Chinese Journal of Computational Mechanics，2013，30(Supp.1)：144–149.(in Chinese))
[33]	MINKOFF S E，STONE C M，BRYANT S，et al. Coupled fluid flow and geomechanical deformation modeling[J]. Journal of Petroleum Science and Engineering，2003，38(1/2)：37–56.
[36]	YIN S，DUSSEAULT M B，ROTHENBURG L. Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered[J]. Advances in Water Resources，2007，30(5)：1 160–1 167.
[31]	张锋. 计算土力学[M]. 北京：人民交通出版社，2007：144–161.(ZHANG Feng. Computational soil mechanics[M]. Beijing：China Communications Press，2007：144–161.(in Chinese))