基于粗糙岩体裂隙表面反应的格子Boltzmann渗流–溶解耦合模型

为了研究粗糙岩体裂隙渗流–溶解耦合作用机制,根据分段线性法构建粗糙裂隙面,并采用分形维数对其粗糙程度进行表征。基于格子Boltzmann方法,采用双分布函数分别模拟速度场和浓度场的演化过程,假定裂隙表面处的溶解作用满足一阶动力学反应模型,建立基于岩体裂隙表面反应的格子Boltzmann渗流–溶解耦合模型,并结合2个经典算例验证其有效性。最后,讨论分形维数、Pe数和Da数等因素对粗糙裂隙渗流–溶解耦合作用机制的影响。研究表明:裂隙壁面的分形维数越大,溶质的运移速度越缓,导致壁面处的溶解速率越慢。在裂隙壁面凸起位置优先发生溶解,使得壁面逐渐趋于光滑。当Pe数较大时,裂隙渗流流速相对较大,从而加速了溶质的运移以及壁面处的溶解反应,导致壁面几何形貌扁平化,提高了裂隙的渗透特性。裂隙的Da数越大,其在入口处的溶解速率越快,从而导致孔隙率相同时裂隙末端聚集的未溶解部分越多,进而影响裂隙的渗透性。

A coupled seepage and dissolution model of rough rock fractures considering surface reaction based on lattice Boltzmann method

To study the seepage and dissolution coupling mechanisms of rough rock fractures,the pricewise linear method is adopted to generate the fracture surface and the fractal dimension is utilized to characterize the roughness. A lattice Boltzmann model,applying the double distribution function to respectively simulate the evolutions of velocity field and concentration field and assuming that the dissolution at the fracture surface satisfies the first-order dynamic reaction model,is proposed to simulate the coupling mechanism considering the effect of surface reaction. The validity of the proposed model is verified by two classical examples,and the effects of the fractal dimension,Pe number and Da number on the seepage and dissolution coupling mechanism of rough fractures are discussed. The results show that the larger the fractal dimension is,the slower the solute transport is,which results in a slower dissolution rate at the fracture surface. The dissolution occurs preferentially at the raised position of fractures,which makes the surface smooth gradually. When the Pe number is larger,the seepage velocity is relatively higher,which promotes the solute transport and the dissolution reaction,causes the surface geometry flattening and increases the permeability. The larger the Da number is,the faster the dissolution rate at the entrance is,which leads to more undissolved parts accumulated at the end of the fracture when the porosity is the same and affects the permeability of the fracture.