复杂介质煤层气运移模型及数值模拟研究
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摘要
我国煤层气资源十分丰富,开发煤层气对改善我国能源结构,具有重要的战略意义。本文在含甲烷原煤煤样的气体渗流物理特性、低煤阶煤层气开采数值模拟以及考虑井筒压降影响的煤层气羽状水平井开采数值模拟方面开展了实验分析、数学建模、数值求解和计算机模拟等研究,取得了一定的研究进展。
本文首先在实验室条件下研究了含甲烷块状原煤煤样的渗流物理特性,着重探讨了有效应力和煤中水分含量对煤中甲烷渗流速度的影响规律,并考虑煤体变形和甲烷渗流之间的相互作用,提出了描述煤层甲烷非线性渗流物理特性的运动方程。在此基础上,根据低煤阶煤储层区别于中高阶煤储层的显著特征,即低煤阶煤层裂隙基本不发育、基质孔隙度相对较大,认为低煤阶煤层是由基质微孔隙系统、基质孔隙系统和裂隙系统组成的多孔介质,建立了能准确描述低煤阶煤储层气—水两相运移规律的数学模型,该模型考虑气—水两相在基质孔隙和裂隙中的运移以及煤体变形对裂隙渗透率的影响。
其次,采用全隐式有限差分方法得到了低煤阶煤储层气—水两相运移数学模型的线性差分方程组,进而利用块系数不完全LU分解预处理的正交极小化方法对其进行了求解。编制相应的计算程序对模型的影响参数进行了分析,并通过对阜新刘家区块内的3口煤层气试验井的生产历史拟合和动态产能预测研究检验了模型的合理性。结果表明:煤基质孔隙的绝对渗透率、孔隙度以及含水饱和度通过影响低煤阶煤层的排水降压效果,进而对气井的产气量产生较大影响;与非平衡吸附模型相比,该模型预测的排水降压初期和稳产期的产气量较低,而相应的产水量较高。
再次,根据煤体的岩石力学性质和弹性本构关系,建立了考虑煤体应力敏感特性以及煤基质收缩效应的煤储层孔隙度、渗透率理论模型,并在孔渗理论模型的基础上,建立了煤储层气—水两相流动模型;另一方面,基于煤层气羽状水平井井身结构的特殊性以及井筒流体的流动特点,考虑井筒变质量流动的摩擦压降、加速度压降以及分支流体和主支流体汇合的混合压降影响,建立了羽状水平井的井筒变质量流压降模型。将上述井筒变质量流压降模型与煤储层气—水两相流动模型相耦合,建立了考虑水平井筒压降影响的煤层气羽状水平井开采数学模型及数值模型。利用模型分析了影响煤层气羽状水平井开采的各种因素,为多分支水平井的分支参数优化设计提供了科学的理论依据。影响因素分析表明:煤基质收缩效应对裂隙渗透率的改善不能忽略,当按主水平井眼与煤层最大渗透性方向垂直的方式钻井开发时,煤层气羽状水平井可以获得更高的采收率。
最后,针对煤层气羽状水平井井身结构特点,采用相应的经济净现值预测模型研究分析了羽状水平井井身几何参数对其净现值影响规律,并进行了相应的优化设计。
Coalbed methane resource is very abundant in China,so the exploitation of coalbed methane has very important strategic significance for improving China’s energy structure. In this paper, the gas-water flow characteristics in low rank coalbed methane reservoirs, as well as that coupling the flow in coalbed methane reservoir and variable mass flow in pinnate horizontal wellbore, are investigated by experimental study, theoretical analysis and numerical simulation, and the research has made some progress.
Firstly, this paper investigated the gas seepage characteristics in block raw coal samples, and emphatically discussed the effects of effective stress and moisture content on the seepage flow velocity. Considering the interaction between coal deformation and methane seepage flow, a motion equation was presented to describe the nonlinear seepage characteristics of coalbed methane in coal. According to the above experimental research and the different characteristics of low rank coal seams, that is fractures are hardly developed and matrix porosity is relatively larger than high rank coal, the low rank coal seams were considered as a porous media composed of matrix micropore system, matrix macropore system and fracture system and a new mathematical model for the gas-water seepage flow in low rank coalbed methane reservoirs was established. Furthermore, not only gas-water two phases flow in matrix macropores and fractures but also coal deformation effects on the fracture permeability was taken into consideration in this model.
Secondly, linear difference equations of the gas-water flow model in low rank coal seams were obtained by the fully implicit finite difference method and solved by the OrthoMin iterative method with block incomplete LU factorization preconditioner. Moreover, a calculation program was developed to analyze influence parameters of the model and the model reliability was validated by production history matching and dynamic forecasting of three coalbed methane test wells in Liujia prospecting district. The results showed that the permeability, porosity and water saturation of matrix macropore have large influence on the water drainage performance, and then on the gas production. Comparing with the non-equilibrium adsorption model, the forecasting gas production of this model in initial and stable production periods is relatively low, while the forecasting water production is high.
Thirdly, based on rock mechanics properties and elastic constitutive relation, new theoretical formulations for stress-dependent permeability and porosity were presented, which include both stress effects and matrix shrinkage. On the basis of the theoretical formulations, a mathematical model of gas-water seepage flow in coalbed methane reservoirs was given. Besides that, a pressure drop model of variable mass flow in pinnate horizontal wellbore was established in consideration of the mixing loss resulted from the multilateral aggregate flow as well as friction loss and acceleration loss. The mathematical and numerical models of pinnate horizontal wells for coalbed methane recovery were obtained by coupling the gas-water seepage flow model in coalbed methane reservoirs with the pressure drop model of variable mass flow in pinnate horizontal wellbore. And then various factors influencing the pinnate horizontal well productivity were analyzed, which provided a scientific theoretical basis for the optimal design of lateral parameters. The analysis of influencing factors indicates that the contribution of matrix shrinkage to the fracture permeability can’t be neglected and higher gas recovery factor could be obtained when the main horizontal wellbore is drilled perpendicular to the maximum permeability orientation.
Finally, the influence of wellbore structural parameters on the corresponding forecast model of economic net present value(NPV) was analyzed to achieve optimize design in view of the wellbore structural features of pinnate horizontal wells.
本文首先在实验室条件下研究了含甲烷块状原煤煤样的渗流物理特性,着重探讨了有效应力和煤中水分含量对煤中甲烷渗流速度的影响规律,并考虑煤体变形和甲烷渗流之间的相互作用,提出了描述煤层甲烷非线性渗流物理特性的运动方程。在此基础上,根据低煤阶煤储层区别于中高阶煤储层的显著特征,即低煤阶煤层裂隙基本不发育、基质孔隙度相对较大,认为低煤阶煤层是由基质微孔隙系统、基质孔隙系统和裂隙系统组成的多孔介质,建立了能准确描述低煤阶煤储层气—水两相运移规律的数学模型,该模型考虑气—水两相在基质孔隙和裂隙中的运移以及煤体变形对裂隙渗透率的影响。
其次,采用全隐式有限差分方法得到了低煤阶煤储层气—水两相运移数学模型的线性差分方程组,进而利用块系数不完全LU分解预处理的正交极小化方法对其进行了求解。编制相应的计算程序对模型的影响参数进行了分析,并通过对阜新刘家区块内的3口煤层气试验井的生产历史拟合和动态产能预测研究检验了模型的合理性。结果表明:煤基质孔隙的绝对渗透率、孔隙度以及含水饱和度通过影响低煤阶煤层的排水降压效果,进而对气井的产气量产生较大影响;与非平衡吸附模型相比,该模型预测的排水降压初期和稳产期的产气量较低,而相应的产水量较高。
再次,根据煤体的岩石力学性质和弹性本构关系,建立了考虑煤体应力敏感特性以及煤基质收缩效应的煤储层孔隙度、渗透率理论模型,并在孔渗理论模型的基础上,建立了煤储层气—水两相流动模型;另一方面,基于煤层气羽状水平井井身结构的特殊性以及井筒流体的流动特点,考虑井筒变质量流动的摩擦压降、加速度压降以及分支流体和主支流体汇合的混合压降影响,建立了羽状水平井的井筒变质量流压降模型。将上述井筒变质量流压降模型与煤储层气—水两相流动模型相耦合,建立了考虑水平井筒压降影响的煤层气羽状水平井开采数学模型及数值模型。利用模型分析了影响煤层气羽状水平井开采的各种因素,为多分支水平井的分支参数优化设计提供了科学的理论依据。影响因素分析表明:煤基质收缩效应对裂隙渗透率的改善不能忽略,当按主水平井眼与煤层最大渗透性方向垂直的方式钻井开发时,煤层气羽状水平井可以获得更高的采收率。
最后,针对煤层气羽状水平井井身结构特点,采用相应的经济净现值预测模型研究分析了羽状水平井井身几何参数对其净现值影响规律,并进行了相应的优化设计。
Coalbed methane resource is very abundant in China,so the exploitation of coalbed methane has very important strategic significance for improving China’s energy structure. In this paper, the gas-water flow characteristics in low rank coalbed methane reservoirs, as well as that coupling the flow in coalbed methane reservoir and variable mass flow in pinnate horizontal wellbore, are investigated by experimental study, theoretical analysis and numerical simulation, and the research has made some progress.
Firstly, this paper investigated the gas seepage characteristics in block raw coal samples, and emphatically discussed the effects of effective stress and moisture content on the seepage flow velocity. Considering the interaction between coal deformation and methane seepage flow, a motion equation was presented to describe the nonlinear seepage characteristics of coalbed methane in coal. According to the above experimental research and the different characteristics of low rank coal seams, that is fractures are hardly developed and matrix porosity is relatively larger than high rank coal, the low rank coal seams were considered as a porous media composed of matrix micropore system, matrix macropore system and fracture system and a new mathematical model for the gas-water seepage flow in low rank coalbed methane reservoirs was established. Furthermore, not only gas-water two phases flow in matrix macropores and fractures but also coal deformation effects on the fracture permeability was taken into consideration in this model.
Secondly, linear difference equations of the gas-water flow model in low rank coal seams were obtained by the fully implicit finite difference method and solved by the OrthoMin iterative method with block incomplete LU factorization preconditioner. Moreover, a calculation program was developed to analyze influence parameters of the model and the model reliability was validated by production history matching and dynamic forecasting of three coalbed methane test wells in Liujia prospecting district. The results showed that the permeability, porosity and water saturation of matrix macropore have large influence on the water drainage performance, and then on the gas production. Comparing with the non-equilibrium adsorption model, the forecasting gas production of this model in initial and stable production periods is relatively low, while the forecasting water production is high.
Thirdly, based on rock mechanics properties and elastic constitutive relation, new theoretical formulations for stress-dependent permeability and porosity were presented, which include both stress effects and matrix shrinkage. On the basis of the theoretical formulations, a mathematical model of gas-water seepage flow in coalbed methane reservoirs was given. Besides that, a pressure drop model of variable mass flow in pinnate horizontal wellbore was established in consideration of the mixing loss resulted from the multilateral aggregate flow as well as friction loss and acceleration loss. The mathematical and numerical models of pinnate horizontal wells for coalbed methane recovery were obtained by coupling the gas-water seepage flow model in coalbed methane reservoirs with the pressure drop model of variable mass flow in pinnate horizontal wellbore. And then various factors influencing the pinnate horizontal well productivity were analyzed, which provided a scientific theoretical basis for the optimal design of lateral parameters. The analysis of influencing factors indicates that the contribution of matrix shrinkage to the fracture permeability can’t be neglected and higher gas recovery factor could be obtained when the main horizontal wellbore is drilled perpendicular to the maximum permeability orientation.
Finally, the influence of wellbore structural parameters on the corresponding forecast model of economic net present value(NPV) was analyzed to achieve optimize design in view of the wellbore structural features of pinnate horizontal wells.
引文
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