考虑流固耦合效应的整体压裂数值模拟研究
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摘要
水力压裂技术作为油气水井增产增注的进攻性措施已广泛应用于低渗透油气田的开发。90年代已明确提出必须将水力压裂与油藏工程有机结合起来才能最有效地满足低渗透油气藏开发要求。
油田测试和实验研究表明，很多储层—尤其是低渗透或超低渗储层，其渗透率对压力变化是敏感的，地下流体渗流问题实际上是一个油气水渗流与储集层岩石多孔介质弹塑性变形的动态耦合作用极强的过程。但长期以来，无论是单井水力压裂还是整体压裂，都是将岩石和流体作为两个独立系统进行研究，并没有考虑流固耦合作用。本文率先将流固耦合理论引入压裂技术领域，研究流固耦合渗流下的整体压裂生产动态模拟，为整体压裂设计提供依据。主要工作是
1 在三轴实验仪上测试了沙三段储层的岩石力学性质，获得了弹性模量与泊松比，为流固耦合的整体压裂奠定了基础；
2 从孔隙度和渗透率的定义出发，考虑岩石骨架变形对孔隙度和渗透率的影响，建立了应变孔隙度和应变渗透率模型，用以模拟储层应力和流体压力对孔隙度和渗透率的影响。
3 根据物质平衡原理和达西定律，考虑基质和人工裂缝作用下三维三相渗流模型，并考虑了重力作用影响，结合应变孔隙度模型、应变渗透率模型，建立了流固耦合整体压裂数学模型。
4 根据有限元基本思想，研究了流固耦合整体压裂的统一有限元求解方法，并编制了相应的数值模拟器。改进了以前用有限差分方法求解油藏渗流、用有限元方法求解岩石变形的计算模式
5 通过示例计算，证明了本文理论方法和程序的正确性和有效性，表明了流固耦合效应对压裂开采有较大影响，尤其对于应力敏感性油藏。
6 该模拟器为预测油藏整体压裂开发动态提供了一套可行的方法。既可用于预测均质、非均质油藏的单井压裂动态两相和三相流动下的整体压裂的油水井动态，还可以模拟不同裂缝长和导流能力下井组或区块开发效果，为编制整体压裂方案提供了工具。
Hydraulic fracturing as a positive stimulation treatment in reservoirs has been widely used in low permeability reservoirs. In 1990's, it has been put forward that hydraulic fracturing must be combined with reservoir engineering to meet the development requirement of low permeability reservoirs.The reservoir survey and experimental study show that many reservoirs, especially low permeability reservoirs or ultra low permeability reservoirs are sensitive to the variation of formation pressure. As a matter of fact, the fluid flowing though porous medium is intensively influenced by the coupling of formation fluid and rock elastic-plastic deformation. However, rock and fluid are considered as two independent systems, and the coupling effect has not considered in individual well's fracturing or integral fracturing. In this thesis, coupling theory was introduced into the hydraulic fracturing field, and numerical simulation of integral fracturing with coupling was researched.(1) The characters of rock mechanics in SHA-3 payzone have been tested by tri-axial instrument; the elastic modulus and Poisson's ratio were obtained. This work laid a foundation for the integral fracturing with coupling.(2) According to definition of porosity and permeability, effect of rock deformation on porosity and permeability were considered. And the model of strain porosity and strain permeability were established, the effect of formation pressure on porosity and permeability could be simulated.(3) Based on Darcy's law and material balance principle, mathematical model of three-dimensional three-phase was derived in porous medium with artificial fractures, and the gravity was considered in the model. Then, model of the strain porosity and strain permeability was combined, and the mathematical model of integral fracturing with coupling was established.(4) According to the finite element theory, numerical formula of finite element analysis of the integral fracturing model with coupling was given, and a simulator was developed. This work improved the previous calculation, which used finite difference in fluid flow and finite element in rock deformation.(5) The case studying the thesis proven the correction and validation of the theoretical modeling and simulator. The coupling between rock and fluid on production are strong, especially in the stress sensitive reservoirs.(6) The simulator can be used to predict the productivity performance in homogeneous and non-homogeneous reservoir, single fracturing and/or integral fracturing, two-phase or three-phase flow. Moreover, it can simulate the production performance in well group and block with different fracture lengths and different fracture conductivities. The simulator is an effective tool for integral fracturing project.
油田测试和实验研究表明，很多储层—尤其是低渗透或超低渗储层，其渗透率对压力变化是敏感的，地下流体渗流问题实际上是一个油气水渗流与储集层岩石多孔介质弹塑性变形的动态耦合作用极强的过程。但长期以来，无论是单井水力压裂还是整体压裂，都是将岩石和流体作为两个独立系统进行研究，并没有考虑流固耦合作用。本文率先将流固耦合理论引入压裂技术领域，研究流固耦合渗流下的整体压裂生产动态模拟，为整体压裂设计提供依据。主要工作是
1 在三轴实验仪上测试了沙三段储层的岩石力学性质，获得了弹性模量与泊松比，为流固耦合的整体压裂奠定了基础；
2 从孔隙度和渗透率的定义出发，考虑岩石骨架变形对孔隙度和渗透率的影响，建立了应变孔隙度和应变渗透率模型，用以模拟储层应力和流体压力对孔隙度和渗透率的影响。
3 根据物质平衡原理和达西定律，考虑基质和人工裂缝作用下三维三相渗流模型，并考虑了重力作用影响，结合应变孔隙度模型、应变渗透率模型，建立了流固耦合整体压裂数学模型。
4 根据有限元基本思想，研究了流固耦合整体压裂的统一有限元求解方法，并编制了相应的数值模拟器。改进了以前用有限差分方法求解油藏渗流、用有限元方法求解岩石变形的计算模式
5 通过示例计算，证明了本文理论方法和程序的正确性和有效性，表明了流固耦合效应对压裂开采有较大影响，尤其对于应力敏感性油藏。
6 该模拟器为预测油藏整体压裂开发动态提供了一套可行的方法。既可用于预测均质、非均质油藏的单井压裂动态两相和三相流动下的整体压裂的油水井动态，还可以模拟不同裂缝长和导流能力下井组或区块开发效果，为编制整体压裂方案提供了工具。
Hydraulic fracturing as a positive stimulation treatment in reservoirs has been widely used in low permeability reservoirs. In 1990's, it has been put forward that hydraulic fracturing must be combined with reservoir engineering to meet the development requirement of low permeability reservoirs.The reservoir survey and experimental study show that many reservoirs, especially low permeability reservoirs or ultra low permeability reservoirs are sensitive to the variation of formation pressure. As a matter of fact, the fluid flowing though porous medium is intensively influenced by the coupling of formation fluid and rock elastic-plastic deformation. However, rock and fluid are considered as two independent systems, and the coupling effect has not considered in individual well's fracturing or integral fracturing. In this thesis, coupling theory was introduced into the hydraulic fracturing field, and numerical simulation of integral fracturing with coupling was researched.(1) The characters of rock mechanics in SHA-3 payzone have been tested by tri-axial instrument; the elastic modulus and Poisson's ratio were obtained. This work laid a foundation for the integral fracturing with coupling.(2) According to definition of porosity and permeability, effect of rock deformation on porosity and permeability were considered. And the model of strain porosity and strain permeability were established, the effect of formation pressure on porosity and permeability could be simulated.(3) Based on Darcy's law and material balance principle, mathematical model of three-dimensional three-phase was derived in porous medium with artificial fractures, and the gravity was considered in the model. Then, model of the strain porosity and strain permeability was combined, and the mathematical model of integral fracturing with coupling was established.(4) According to the finite element theory, numerical formula of finite element analysis of the integral fracturing model with coupling was given, and a simulator was developed. This work improved the previous calculation, which used finite difference in fluid flow and finite element in rock deformation.(5) The case studying the thesis proven the correction and validation of the theoretical modeling and simulator. The coupling between rock and fluid on production are strong, especially in the stress sensitive reservoirs.(6) The simulator can be used to predict the productivity performance in homogeneous and non-homogeneous reservoir, single fracturing and/or integral fracturing, two-phase or three-phase flow. Moreover, it can simulate the production performance in well group and block with different fracture lengths and different fracture conductivities. The simulator is an effective tool for integral fracturing project.
引文
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[4] Remond L R & Binder G G. Productivity of wells in vertically fractured damaged formations. JPT, Jan. 1967
[5] J Van Dum. Planning of optimum production for a Matural Gas Reservoir. J. of the Institute of Petroleum 54, March, 1968:531:55-67
[6] Hoditch S A et al. The optimization of well spacing and fracturing length in low-permeability gas reservoirs. SPE 7496
[7] P F Lemen and H J Patel. Effects of fracture and reservoir parameters on recovery from low-permeability gas reservoir. SPE 5111
[8] J K Tison et al. A method for selecting potential infill location in the East Texas Cotton Valley gas play. SPE 11022
[9] D N Meehan & B F Pennijgton. Numerical simulation results in the Carthage Cotton Valley Field. JPT, 34 9838, Jan.1982
[10] Soliman M Y. modification to production increase calculation for a hydraulic fractured well. OGJ, Oct. 1986
[11] Tinsley J M et al. Vertical fracture height—Its effect on steady-state production increase. JPT, May 1969:633-6381
[12] Soliman M Y. Numerical model estimates fracture production increase. OGJ, Feb, 1986
[13] 何艳青，王鸿勋．用数值模拟方法预测压裂井的生产动态．石油大学学报，1990，Vol 14，No4
[14] Agarwal R G et al. Evaluation and performance prediction of low-permeability gas well stimulated by massive hydraulic fracturing. JPT, March 1979: 262-372
[15] 张士诚．水力压裂参数对采收率影响的研究．低渗透油藏开发技术，1994年
[16] 杨兆中．西南石油学院博士论文，1996
[17]Geertsma J. The effect of fluid pressures decline on volumetric changes of porous rocks. Pet.Trans. AIME, 1957, 210: 331-340
[18]Duncan JM, Chang CY. Non-linear analysis of stress and strain in solids, Journal of the soil mechanics and foundation division. ASCE, 1970, 96, SMS: 1629-1651
[19]Van W, Knaap D. Nonlinear behavior Of elastic porous media. Petroleum Transcatios, AIME, 1959, 216: 179-187
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