煤层气运移LBM模型与井间干扰模拟研究
摘要
储层模拟是煤层气开发工程中的一个必要环节，通过储层模拟可以获得煤层气井的生产特征，对煤层气的采收做出预测。在储层模拟中，描述煤层气运移的控制方程通常采用数值方法进行求解，如有限差分法，求解的关键步骤是连续方程的离散化和求解网格的划分，不同的离散方法和网格划分方法，解算时的计算量和求解精度不同。本文对煤层气运移控制方程求解方法进行了探索，引入计算流体力学中的格子Boltzmann方法（LatticeBoltzmann Method，LBM）来求解煤层气运移问题。有别于传统数值方法离散（物理现象抽象概括）——连续（建立宏观控制方程）——再离散（形成差分方程等）的求解思路，LBM方法的求解思路是用离散的控制方程模拟离散的物理现象，将离散到宏观的抽象及宏观到再离散的过程仅使用在理论建立阶段，而并不参与到流体运移的解算过程当中，相比数值方法省去了最困难的一步——连续的偏微分方程组离散化的步骤，从而可以降低求解难度、简化程序设计。
与数值方法类似的是，LBM也需要建立解算网格。借鉴常规油藏数值模拟中的对储层使用PEBI网格划分的方法，采用分块控制单元影响因子的方法建立适用于煤储层的PEBI网格，该网格能够根据垂直井、水平井、断层、边界等控制单元对储层的影响程度和控制范围调整网格的疏密，近井区域易于进行网格加密形成小而密的单元，远离控制单元的区域则可形成大且稀疏的单元。在垂直井近井区域，PEBI网格形状类似于结构化网格中的径向网格，能够突出煤储层垂直井近井区域网格在储层模拟中的重要性，也能够对水平井近井区域的重要性予以凸显，并且消除了径向网格或笛卡尔网格等结构化网格方法难以对水平井、断层、边界等线性单元进行精确网格划分、非结构化网格生成网格数量过大的问题，同时包含结构化网格和非结构化网格的优点，在保证近井区域网格数量的同时，更少的储层网格数量意味着更少的计算量。结合煤储层PEBI网格非结构化及LBM的特点，对非规则网格运用LBM时，方程形式不需改变，仅需根据网格进行插值变换，提出了使用改进的LBM模型——有限体积LBM（Finite Volume LBM，FVLBM）模型进行煤层气运移模拟的方法。
在深入探讨LBM求解物质运移问题的方法原理之后，基于二维LBGK模型和煤层气扩散所遵循的Fick第二定律，建立了微观尺度下煤层气扩散作用的二维非稳态LBM模型；结合Darcy定律，建立了宏观尺度下的煤层气单组分单相渗流的二维LBM模型，并分别通过计算机程序予以实现。
随后，假设煤储层网格单元的边界是宏观裂隙，每个储层网格单元视为一个扩散单元，扩散单元之间只发生渗流作用，不发生扩散作用。采用四参数生长法（Quartet StructureGeneration Set，QSGS）根据煤基质单元的孔隙度生成扩散单元的二维随机多孔介质模型，运用建立的LBM模型对煤层气的扩散作用进行了模拟。模拟实例结果显示，所建立的模型能够反映煤储层压力、吸附气量在煤层气扩散过程中的实时动态变化，并且能够反映解吸气量、储层压力、吸附气量三者的动态关系。
根据研究区的储层参数，运用建立的渗流LBM模型对煤层气垂直井井组开发中的井间干扰现象进行了模拟。模拟过程能够反映井间干扰对降低储层压力的促进作用，在设计的三种井间距中，布井方式和井间距对井间干扰产生的时间、对储层压降的贡献能够清晰展现，结合常规数值模拟软件Computer Modeling Group（CMG）的产能模拟结果，可以确定研究区的最佳井间距，以期在保证各单井的排采面积的同时充分利用井间干扰的积极作用促进煤层气采收。
Reservoir simulation is a vital link in coalbed methane (CBM) development project, and itskey technology and difficulty are the solutions to the governing equations of the CBM migration.The discretization of the equations and meshing of the reservoir determine the computationalcomplexity and the solution precision. Conventionally, numerical approaches like finitedifferential method (PDM) or finite element method (FEM) are the extensively employedmethods, and their solving ideas are "discretization"(the abstract of physical phenomena)--"continuum"(the macro governing equations)--"discretization"(the discrete differentialequations). In this dissertation, the authors involve the Lattice Boltzmann Method (LBM), aparticle method which has been extensively employed in the computational fluid dynamics, intothe solutions of the governing equations of the CBM migration.
According to the coal reservoir characteristics, borrowing the idea of a reservoir meshingmethod from the conventional reservoir simulation, we involved an unstructured grid namelyperpendicular bisection (PEBI) grid in the CBM reservoir meshing to establish the solving lattice.Then, combined with the features of LBM, the finite volume LBM (FVLBM) method wasproposed based on PEBI grid. Considering the CBM migration laws and the LBM features,2Dunsteady-state diffusion model and single component single-phase seepage model for CBMdiffusion and flow are established and programmed respectively. Consequencely, the diffusionprocess was simulated in a2D stochastic porous medium model which generated by a porositycontrolled stochastic growth method--Quartet Structure Generation Set (QSGS). And wellinterference of the vertical well-group drainage was simulated as well. Under the premise ofmaximizing the drainage area of each single well while making full use of well interference'sacceleration for promote the CBM recovery, the optimal well spacing in the study area was fixedvia the simulations and in combination with the CBM productions resulted from the conventionalnumerical simulation software CMG.
与数值方法类似的是，LBM也需要建立解算网格。借鉴常规油藏数值模拟中的对储层使用PEBI网格划分的方法，采用分块控制单元影响因子的方法建立适用于煤储层的PEBI网格，该网格能够根据垂直井、水平井、断层、边界等控制单元对储层的影响程度和控制范围调整网格的疏密，近井区域易于进行网格加密形成小而密的单元，远离控制单元的区域则可形成大且稀疏的单元。在垂直井近井区域，PEBI网格形状类似于结构化网格中的径向网格，能够突出煤储层垂直井近井区域网格在储层模拟中的重要性，也能够对水平井近井区域的重要性予以凸显，并且消除了径向网格或笛卡尔网格等结构化网格方法难以对水平井、断层、边界等线性单元进行精确网格划分、非结构化网格生成网格数量过大的问题，同时包含结构化网格和非结构化网格的优点，在保证近井区域网格数量的同时，更少的储层网格数量意味着更少的计算量。结合煤储层PEBI网格非结构化及LBM的特点，对非规则网格运用LBM时，方程形式不需改变，仅需根据网格进行插值变换，提出了使用改进的LBM模型——有限体积LBM（Finite Volume LBM，FVLBM）模型进行煤层气运移模拟的方法。
在深入探讨LBM求解物质运移问题的方法原理之后，基于二维LBGK模型和煤层气扩散所遵循的Fick第二定律，建立了微观尺度下煤层气扩散作用的二维非稳态LBM模型；结合Darcy定律，建立了宏观尺度下的煤层气单组分单相渗流的二维LBM模型，并分别通过计算机程序予以实现。
随后，假设煤储层网格单元的边界是宏观裂隙，每个储层网格单元视为一个扩散单元，扩散单元之间只发生渗流作用，不发生扩散作用。采用四参数生长法（Quartet StructureGeneration Set，QSGS）根据煤基质单元的孔隙度生成扩散单元的二维随机多孔介质模型，运用建立的LBM模型对煤层气的扩散作用进行了模拟。模拟实例结果显示，所建立的模型能够反映煤储层压力、吸附气量在煤层气扩散过程中的实时动态变化，并且能够反映解吸气量、储层压力、吸附气量三者的动态关系。
根据研究区的储层参数，运用建立的渗流LBM模型对煤层气垂直井井组开发中的井间干扰现象进行了模拟。模拟过程能够反映井间干扰对降低储层压力的促进作用，在设计的三种井间距中，布井方式和井间距对井间干扰产生的时间、对储层压降的贡献能够清晰展现，结合常规数值模拟软件Computer Modeling Group（CMG）的产能模拟结果，可以确定研究区的最佳井间距，以期在保证各单井的排采面积的同时充分利用井间干扰的积极作用促进煤层气采收。
Reservoir simulation is a vital link in coalbed methane (CBM) development project, and itskey technology and difficulty are the solutions to the governing equations of the CBM migration.The discretization of the equations and meshing of the reservoir determine the computationalcomplexity and the solution precision. Conventionally, numerical approaches like finitedifferential method (PDM) or finite element method (FEM) are the extensively employedmethods, and their solving ideas are "discretization"(the abstract of physical phenomena)--"continuum"(the macro governing equations)--"discretization"(the discrete differentialequations). In this dissertation, the authors involve the Lattice Boltzmann Method (LBM), aparticle method which has been extensively employed in the computational fluid dynamics, intothe solutions of the governing equations of the CBM migration.
According to the coal reservoir characteristics, borrowing the idea of a reservoir meshingmethod from the conventional reservoir simulation, we involved an unstructured grid namelyperpendicular bisection (PEBI) grid in the CBM reservoir meshing to establish the solving lattice.Then, combined with the features of LBM, the finite volume LBM (FVLBM) method wasproposed based on PEBI grid. Considering the CBM migration laws and the LBM features,2Dunsteady-state diffusion model and single component single-phase seepage model for CBMdiffusion and flow are established and programmed respectively. Consequencely, the diffusionprocess was simulated in a2D stochastic porous medium model which generated by a porositycontrolled stochastic growth method--Quartet Structure Generation Set (QSGS). And wellinterference of the vertical well-group drainage was simulated as well. Under the premise ofmaximizing the drainage area of each single well while making full use of well interference'sacceleration for promote the CBM recovery, the optimal well spacing in the study area was fixedvia the simulations and in combination with the CBM productions resulted from the conventionalnumerical simulation software CMG.
引文
①http://exa.com/powerflow.html
②http://www.xflowcfd.com/
③http://www.ingrainrocks.com/
④http://www.opencimulation.org/
⑤http://www.futureenergy.ox.ac.uk/research/oil-gas
⑥粘性指进是油田开发中普遍存在的一种现象，指在两相不混溶流体驱替工程中，由于两相粘度的差异造成前沿驱替相呈分散液束形式（即像“手指”一样向前推进），是一种粘度小的流体驱替粘度较大的流体时产生的一种不稳定界面现象，是多相渗流的一个重要特性。
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②http://www.xflowcfd.com/
③http://www.ingrainrocks.com/
④http://www.opencimulation.org/
⑤http://www.futureenergy.ox.ac.uk/research/oil-gas
⑥粘性指进是油田开发中普遍存在的一种现象，指在两相不混溶流体驱替工程中，由于两相粘度的差异造成前沿驱替相呈分散液束形式（即像“手指”一样向前推进），是一种粘度小的流体驱替粘度较大的流体时产生的一种不稳定界面现象，是多相渗流的一个重要特性。
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