CO_2煤层封存流动—力学理论及场地力学稳定性数值模拟方法
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摘要
二氧化碳是最主要温室气体,二氧化碳煤层封存(CO_2-ECBM)是一项有望同时实现CO_2大规模减排和增加煤层气资源产量的一举两得的技术。封存过程中多组分气体的渗流规律和场地的力学稳定性评价是该技术可行性研究的重要内容,然而我国这方面的研究目前还较少。在这样的背景下,本文利用岩土力学、渗流力学、有限元数值分析理论以及室内试验对深部非采煤层二氧化碳封存过程进行了较为系统的研究,内容涉及固气耦合理论、试验、程序开发及其初步应用四个方面,核心内容如下:
第一,分析了二氧化碳煤层封存流动和场地稳定性分析中的关键岩土力学问题,给出了CO_2-ECBM过程固气耦合分析的完整数学模型,并提出了一个新的考虑吸附膨胀效应的煤岩孔隙率、渗透率的动态演化方程。数值计算表明,这一演化方程能够正确体现煤岩吸附膨胀引起的孔隙率和渗透率降低的现象。(第三章)
第二,煤岩的试验研究。进行了煤岩的抗拉以及较低和较高围压下三轴抗压特性的试验研究,指出煤岩的抗拉强度可以忽略。较低围压下三轴试验,煤岩呈现明显的线性弹性变形特性,在深部围压较高条件下,煤岩很快呈现明显的塑性变形,应采用考虑塑性硬化的本构模型加以刻画。(第四章)
第三,煤岩塑性硬化特征描述。结合煤岩三轴试验数据,创新性地提出了岩土塑性理论中初始屈服的一个新的定义方法,并给出了应用三轴试验数据计算路径相关硬化参量的新方法。基于此,分析了煤岩塑性硬化过程中的内摩擦角、内聚力的变化趋势,基于试验数据用非线性函数拟合了后继屈服轨迹并比较了拟合效果,并发现q-p应力空间中的屈服轨迹的割线斜率不是定值而是随着塑性硬化而不断增加的。(第四章)
第四,提出了一个新的塑性硬化本构模型—基于伪强度参数的塑性硬化模型,该模型能够反映煤岩塑性硬化过程中q-p屈服轨迹斜率的非定值特性。将该模型嵌入作者开发的COALSEEP 1.0程序中,对三轴试验应力-应变曲线进行的数值模拟表明应力应变特性和试验结果吻合较好。(第四章和第五章)
第五,煤岩的吸附-弹性本构模型及参数估计。从理论上严格证明了缪协兴提出的湿度应力场理论并将其用作吸附膨胀介质一般的吸附-弹性本构模型。对该模型中线膨胀系数进行了研究,给出了煤岩吸附线膨胀系数的一个理论估计方法,这一方法不仅对估算煤岩线膨胀系数是有用的,而且还在作为煤岩力学参数的线膨胀系数和煤岩吸附特性参数之间架设了桥梁,对于全面而深入地理解煤岩的性质是有意义的。(第五章)
第六,塑性屈服破坏函数对应的耗散势及其热动力学限制。通过求解本文构造的耗散微分方程,给出了一族线性屈服破坏函数对应的耗散势函数,这不仅沟通了传统的屈服破坏函数与热动力学中耗散势函数之间定量的解析关系,也给屈服破坏函数的理性验证提供了一个新思路。(第五章)
第七,固相介质吸附-弹塑性本构框架和煤岩吸附-弹塑性本构模型。采用唯象的方法,将吸附量作为固相介质独立的热动力学状态变量引入到塑性屈服函数中,推导了吸附-弹塑性增量本构关系并给出了加卸载准则。当屈服函数与吸附量无关时,本构关系自动退化为只考虑吸附膨胀特性的增量弹塑性本构关系,如果还不考虑吸附量对固相介质膨胀效应,本构关系即退化为传统的增量弹塑性本构关系。将前文提出的基于伪强度参数的塑性硬化模型代入这一本构框架,得到了煤岩吸附-弹塑性本构模型。(第五章)
第八,耦合分析数学模型的求解算法和软件开发。给出了耦合微分方程组的整体求解方案及各个场方程有限元求解的弱解积分形式。特别是组分摩尔比场采用了特征线有限元算法,其中还用到了本文给出的一个判断点与多面体空间位置关系的一个新算法—向量判别法,该算法具有实现简单、计算量小的优点。基于上述一系列算法,编制了有限元固气耦合分析软件COALSEEP1.0。这些构成了本文的数值模拟方法的研究。(第六章)
第九,CO_2煤层封存流动及场地扰动的数值模拟研究。对非耦合、水平剖面上五点注采工况下CO_2-ECBM过程的流场分布规律以及流固耦合、地层纵剖面上双井抽注工况下CO_2-ECBM中渗流和场地变形进行了数值模拟研究。最后分析了煤层完全充满二氧化碳的极端条件下煤层膨胀对注采套管的影响。(第七章)
CO_2 is a main Green house gas that contributes the most to the Greenhouse effect of the Earth. CO_2-ECBM is an attractive technology that can store CO_2 massively underground and meanwhile enhance coalbed methane recovery. The flowing law of the multi-component fluids and the sequestration site stability in CO_2-ECBM are key contents of the feasibility study of this technology. However, there are few studies in this field in China as CO_2-ECBM still just starts here. In this thesis, the author took a systematic research in view of the geomechanics of coal and gases flow in CO_2 sequestration on the basis of existing related researches. The study results can be divided into four parts in the main, they are respectively the solid-gas coupling mathematical theory and models, lab tests, FE program developing and its preliminary application. They are as following.
(1) A solid–gas coupling mathematical model considering multi-component fluid and solid interactions was developed after the analysis to the key geomechanics and flow in CO_2-ECBM. In this model, pore and permeability are changing as a result of the deformation and adsorption induced swelling of the coal matrix . So new evolution equations of pore and permeability that can describe this affection were put forward. (Chapter 3.)
(2) Split tests and conventional triaxial loading-unloading tests of coal samples were conducted. The results show that the tensile strength is about 1% of the CTC strength thus can be neglected. For triaxial tests, when the confining pressure is relative low, the stress-strain curve is nice linear elasticity. When the confining pressure is relatively high, the stress-strain relation is nonlinear and obvious plasticity appears at quite early load stage. So the hardening constitutive models should be adopted at high confining pressures. (Chapter 4.)
(3) The description of the plastic characteristics of coal. Firstly a new method that defined the initial yield point on each stress–strain curve was put forward creatively. Then a new computational method for strain path dependent hardening parameters using the tiaxial test data was presented. On these two bases, the cohesion and the internal friction angle of coal during the hardening process were calculated and positively correlated to the plasticity. Hardening curves in q-p space were fitted using the CTC tests and the fitting effect of different functions were compared. The fitting results show that the slopes of the q-p curves are increasing with the plasticity hardening. (Chapter 4.)
(4) On the basis of the description of the hardening characteristics of coal, a new plastic hardening model called pseudo strength parameters-based plastic hardening model was presented. This model can properly discrib the increasing characteristic of the slopes of the q-p curves with the plasticity hardening. It was embedded into the FE program COALSEEP 1.0 developed by the author. Then it was used to simulate the CTC test of coal sample. The simulation result is quite consistent with the experiment. (Chapter 4.)
(5) Adsorptive-elasticity theory and its parameter estimation. Miao’s Humidity Stress Field Theory was proved strictly and then was used as the adsorptive-elastic constitutive model of adsorption induced swelling media. The swelling coefficient of this model is a key parameter. An estimate method for this parameter of coal was presented, which not only supplied a convenient parameter estimating method but also bridged this mechanical parameter with the adsorptive parameters. This is beneficial to getting a deeper and more comprehensive understanding of coal properties. (Chapter 5.)
(6) The thermodynamic restrictions of plastic yield and failure functions were studied. The dissipation potential functions corresponding to a class of yield /failure functions were got by solving the Dissipation Differential Equation constructed by the author. Thus the thermodynamic consistency of these yield /failure functions can be verified from this dissipation potential expediently. This bridges the dissipation and plasticity functions and supplies us with a new way for the rational verification of traditional plastic yield/failure functions. ( Chapter 5.)
(7) The adsorptive-elatoplastic constitutive frame of porous media was studied and a constitutive model of coal belonging to this frame was presented. Based on a phenomenological viewpoint, the adsorption was a independent state variable of coal was supposed.Then adsorption was introduced to the yield function if the fluid affect the yield function. The tensor form of the incremental adsorptive-elatoplastic constitutive relationship and the loading-unloading criterion were presented. Substitute the pseudo strength parameters based plastic hardening model to this constitutive relationship, an adsorption-elatoplastic constitutive model was got for coal. (Chapter 5.)
(8) The study of the solution algorithm of the coupling mathematical model and its FE program developing. In view of the process of CO_2-ECBM,a solving strategy for the coupling mathematical model and the weak form of each field equation were presented . Especially,the mole ratio field of CH4 was solved with the characteristic finite element method. A new algorithm of Vector Judging Method to judge the spatial relation between point and polyhedron was presented. This algorithm which was called by the program of characteristic finite element method. Then a coupling analysis program of COALSEEP1.0 was developed using FEPG.on the above bases.These constituted the study content of the simulating method in this thesis. (Chapter 6.)
(9) Numerical simulation study of the flow of multicomponent fluids and the injecting induced deformation of reservoir and ground surface. Three simulating cases were carried. The first was the seepage law of multicomponents fluids at the working condition of five-point method. The second was the injecting induced deformation of reservoir and ground surface at the working condition of one well injecting and the other pumping. The third was influence of CO_2-induced swelling on casing stability in CO_2-ECBM. (Chapter 7.)
第一,分析了二氧化碳煤层封存流动和场地稳定性分析中的关键岩土力学问题,给出了CO_2-ECBM过程固气耦合分析的完整数学模型,并提出了一个新的考虑吸附膨胀效应的煤岩孔隙率、渗透率的动态演化方程。数值计算表明,这一演化方程能够正确体现煤岩吸附膨胀引起的孔隙率和渗透率降低的现象。(第三章)
第二,煤岩的试验研究。进行了煤岩的抗拉以及较低和较高围压下三轴抗压特性的试验研究,指出煤岩的抗拉强度可以忽略。较低围压下三轴试验,煤岩呈现明显的线性弹性变形特性,在深部围压较高条件下,煤岩很快呈现明显的塑性变形,应采用考虑塑性硬化的本构模型加以刻画。(第四章)
第三,煤岩塑性硬化特征描述。结合煤岩三轴试验数据,创新性地提出了岩土塑性理论中初始屈服的一个新的定义方法,并给出了应用三轴试验数据计算路径相关硬化参量的新方法。基于此,分析了煤岩塑性硬化过程中的内摩擦角、内聚力的变化趋势,基于试验数据用非线性函数拟合了后继屈服轨迹并比较了拟合效果,并发现q-p应力空间中的屈服轨迹的割线斜率不是定值而是随着塑性硬化而不断增加的。(第四章)
第四,提出了一个新的塑性硬化本构模型—基于伪强度参数的塑性硬化模型,该模型能够反映煤岩塑性硬化过程中q-p屈服轨迹斜率的非定值特性。将该模型嵌入作者开发的COALSEEP 1.0程序中,对三轴试验应力-应变曲线进行的数值模拟表明应力应变特性和试验结果吻合较好。(第四章和第五章)
第五,煤岩的吸附-弹性本构模型及参数估计。从理论上严格证明了缪协兴提出的湿度应力场理论并将其用作吸附膨胀介质一般的吸附-弹性本构模型。对该模型中线膨胀系数进行了研究,给出了煤岩吸附线膨胀系数的一个理论估计方法,这一方法不仅对估算煤岩线膨胀系数是有用的,而且还在作为煤岩力学参数的线膨胀系数和煤岩吸附特性参数之间架设了桥梁,对于全面而深入地理解煤岩的性质是有意义的。(第五章)
第六,塑性屈服破坏函数对应的耗散势及其热动力学限制。通过求解本文构造的耗散微分方程,给出了一族线性屈服破坏函数对应的耗散势函数,这不仅沟通了传统的屈服破坏函数与热动力学中耗散势函数之间定量的解析关系,也给屈服破坏函数的理性验证提供了一个新思路。(第五章)
第七,固相介质吸附-弹塑性本构框架和煤岩吸附-弹塑性本构模型。采用唯象的方法,将吸附量作为固相介质独立的热动力学状态变量引入到塑性屈服函数中,推导了吸附-弹塑性增量本构关系并给出了加卸载准则。当屈服函数与吸附量无关时,本构关系自动退化为只考虑吸附膨胀特性的增量弹塑性本构关系,如果还不考虑吸附量对固相介质膨胀效应,本构关系即退化为传统的增量弹塑性本构关系。将前文提出的基于伪强度参数的塑性硬化模型代入这一本构框架,得到了煤岩吸附-弹塑性本构模型。(第五章)
第八,耦合分析数学模型的求解算法和软件开发。给出了耦合微分方程组的整体求解方案及各个场方程有限元求解的弱解积分形式。特别是组分摩尔比场采用了特征线有限元算法,其中还用到了本文给出的一个判断点与多面体空间位置关系的一个新算法—向量判别法,该算法具有实现简单、计算量小的优点。基于上述一系列算法,编制了有限元固气耦合分析软件COALSEEP1.0。这些构成了本文的数值模拟方法的研究。(第六章)
第九,CO_2煤层封存流动及场地扰动的数值模拟研究。对非耦合、水平剖面上五点注采工况下CO_2-ECBM过程的流场分布规律以及流固耦合、地层纵剖面上双井抽注工况下CO_2-ECBM中渗流和场地变形进行了数值模拟研究。最后分析了煤层完全充满二氧化碳的极端条件下煤层膨胀对注采套管的影响。(第七章)
CO_2 is a main Green house gas that contributes the most to the Greenhouse effect of the Earth. CO_2-ECBM is an attractive technology that can store CO_2 massively underground and meanwhile enhance coalbed methane recovery. The flowing law of the multi-component fluids and the sequestration site stability in CO_2-ECBM are key contents of the feasibility study of this technology. However, there are few studies in this field in China as CO_2-ECBM still just starts here. In this thesis, the author took a systematic research in view of the geomechanics of coal and gases flow in CO_2 sequestration on the basis of existing related researches. The study results can be divided into four parts in the main, they are respectively the solid-gas coupling mathematical theory and models, lab tests, FE program developing and its preliminary application. They are as following.
(1) A solid–gas coupling mathematical model considering multi-component fluid and solid interactions was developed after the analysis to the key geomechanics and flow in CO_2-ECBM. In this model, pore and permeability are changing as a result of the deformation and adsorption induced swelling of the coal matrix . So new evolution equations of pore and permeability that can describe this affection were put forward. (Chapter 3.)
(2) Split tests and conventional triaxial loading-unloading tests of coal samples were conducted. The results show that the tensile strength is about 1% of the CTC strength thus can be neglected. For triaxial tests, when the confining pressure is relative low, the stress-strain curve is nice linear elasticity. When the confining pressure is relatively high, the stress-strain relation is nonlinear and obvious plasticity appears at quite early load stage. So the hardening constitutive models should be adopted at high confining pressures. (Chapter 4.)
(3) The description of the plastic characteristics of coal. Firstly a new method that defined the initial yield point on each stress–strain curve was put forward creatively. Then a new computational method for strain path dependent hardening parameters using the tiaxial test data was presented. On these two bases, the cohesion and the internal friction angle of coal during the hardening process were calculated and positively correlated to the plasticity. Hardening curves in q-p space were fitted using the CTC tests and the fitting effect of different functions were compared. The fitting results show that the slopes of the q-p curves are increasing with the plasticity hardening. (Chapter 4.)
(4) On the basis of the description of the hardening characteristics of coal, a new plastic hardening model called pseudo strength parameters-based plastic hardening model was presented. This model can properly discrib the increasing characteristic of the slopes of the q-p curves with the plasticity hardening. It was embedded into the FE program COALSEEP 1.0 developed by the author. Then it was used to simulate the CTC test of coal sample. The simulation result is quite consistent with the experiment. (Chapter 4.)
(5) Adsorptive-elasticity theory and its parameter estimation. Miao’s Humidity Stress Field Theory was proved strictly and then was used as the adsorptive-elastic constitutive model of adsorption induced swelling media. The swelling coefficient of this model is a key parameter. An estimate method for this parameter of coal was presented, which not only supplied a convenient parameter estimating method but also bridged this mechanical parameter with the adsorptive parameters. This is beneficial to getting a deeper and more comprehensive understanding of coal properties. (Chapter 5.)
(6) The thermodynamic restrictions of plastic yield and failure functions were studied. The dissipation potential functions corresponding to a class of yield /failure functions were got by solving the Dissipation Differential Equation constructed by the author. Thus the thermodynamic consistency of these yield /failure functions can be verified from this dissipation potential expediently. This bridges the dissipation and plasticity functions and supplies us with a new way for the rational verification of traditional plastic yield/failure functions. ( Chapter 5.)
(7) The adsorptive-elatoplastic constitutive frame of porous media was studied and a constitutive model of coal belonging to this frame was presented. Based on a phenomenological viewpoint, the adsorption was a independent state variable of coal was supposed.Then adsorption was introduced to the yield function if the fluid affect the yield function. The tensor form of the incremental adsorptive-elatoplastic constitutive relationship and the loading-unloading criterion were presented. Substitute the pseudo strength parameters based plastic hardening model to this constitutive relationship, an adsorption-elatoplastic constitutive model was got for coal. (Chapter 5.)
(8) The study of the solution algorithm of the coupling mathematical model and its FE program developing. In view of the process of CO_2-ECBM,a solving strategy for the coupling mathematical model and the weak form of each field equation were presented . Especially,the mole ratio field of CH4 was solved with the characteristic finite element method. A new algorithm of Vector Judging Method to judge the spatial relation between point and polyhedron was presented. This algorithm which was called by the program of characteristic finite element method. Then a coupling analysis program of COALSEEP1.0 was developed using FEPG.on the above bases.These constituted the study content of the simulating method in this thesis. (Chapter 6.)
(9) Numerical simulation study of the flow of multicomponent fluids and the injecting induced deformation of reservoir and ground surface. Three simulating cases were carried. The first was the seepage law of multicomponents fluids at the working condition of five-point method. The second was the injecting induced deformation of reservoir and ground surface at the working condition of one well injecting and the other pumping. The third was influence of CO_2-induced swelling on casing stability in CO_2-ECBM. (Chapter 7.)
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