溶解气驱过程中的分形生长模型

/ A MODEL FOR FRACTAL GROWTH OF BUBBLES IN DISPLACEMENT PROCESS

临界气体饱和度是溶解气驱过程的重要参数，在不同的领域内它的定义不同，因此，不加说明易产生混淆。应用气体气泡的生长过程确定了临界气体饱和度，从宏观和微观的结合上来理解溶解气驱的机理。建立了分形生长过程的偏微分方程模型（ＰＤＥ），并给出相应的定解条件，将分形生长过程问题归结为具有移动边界的自由边界值问题。在一定的条件下，这个方程的自由边界值问题可应用拟静态近似分解为一系列稳定问题来求解。在渗滤网络上应用拟静态近似对气泡的生长进行了模拟计算，分析了单集团生长和多集团生长过程中生长构型的分形特征，研究了过饱和度和核化分数等对气驱过程中气泡生长的影响。

Solution gas drive is an important displacement process. Critical gas saturation is an operating parameter which has different definition in different fields. The critical gas saturation is defined by using growth process of gas bubbles in order to understand the mechanism of solution gas drive process. A partial differential equation model (PDE) and the conditions of fractal growth of bubbles are established, which can be cast as a problem of free boundary value with a moving boundary. A theoretical model is developed, based on which the percolation network simulation is constructed. The fractal properties of growth configuration and growth rate for single cluster and multiply clusters growth are discussed by using statistical models, such as percolation and DLA. It shows that gas evolution in porous medium is different from that in bulk fluid. Critical gas saturation was studied in terms of nucleation fraction and pressure decline rate.