复杂孔隙网络上反常输运过程的关键影响因素研究

The phenomenon of anomalous transport in geological formations has attracted much interest recently among researchers in the fields of petroleum engineering, soil science, hydrology, etc, mainly due to the growing number of both field and laboratory experiments that directly or indirectly verify such a common anomalous scenario. Moreover, different types of anomalous transport have been found to prevail in certain kinds of geological porous media, respectively. For example, typical transport in sandstones is quite different than that in carbonates. This fact has been noticed and ascribed to the different heterogeniety level of the rock pore structure. However, related study was quite limited, and only recently when the technique of visualizing pore structure becomes efficient and viable can one substantially begin to investigate how the microscopic structure affects the macroscopic transport behavior, and this is indeed the aim of this work. First, we will investigate from a general perspective and check in what manner the network properties such as degree distribution, area of throat cross section distribution, and throat length distribution will influence the breakthrough curve, the propagator shape, and transition time distribution of a transport process which is caused by imposing pressure difference at two boundaries of the pore network.Special focus will be put on the transition time distribution which typically displays a power law, with the exponent being pivotal to the nature of the transport process according to the continuous-time random walk theory. We can quantitatively measure how the exponent is varied as one or more network properties are changed. Then, we will run computational fluid dynamics simulations on pore images and random walk simulations on pore networks, both iamges and networks being obtained from real cores by micro-CT, to capture transport properties numerically; in the mean time, an experiment will be carried out to obtain the real breakthrough curves to compare with numerical results. Provided there results are in accord with one another, we can finally get reliable knowledge about the key structural factors that affect transport behaviors in complex pore networks.

石油工程和地下水研究领域大量的现场和实验室实验表明：地层中的输运过程往往会表现出反常输运行为，并且对于不同类型的岩石，发生在其上的反常输运类型也不同，而这与岩石的孔隙结构有关。本项目的目标即为考察岩石孔隙网络的结构如何影响发生在其上的输运过程行为。我们采用机理研究结合实验研究的方法。首先研究一般情况下孔隙网络的性质对输运过程特征的影响，包括考察网络的某单一统计性质的影响以及性质间存在关联的情况，并与连续时间随机行走理论对应；接着利用扫描获得的真实岩心孔隙图像及在其基础上得到的孔隙网络模型，分别进行流动模拟，并对岩心进行实验室实验，得到输运过程的有关特征，比较物理实验、基于孔隙图像的计算结果、基于孔隙网络的计算结果之间的一致性。最后综合机理和实验两方面研究的结果，得出结论。

我们对岩石进行了高精度CT扫描实验，获得了相应的孔隙空间数据，并基于这些数据得到了复杂孔隙网络。我们系统的统计了这些孔隙网络的结构特征，包括度分布、链长分布、截面积分布，以及子网络的空间分布和尺寸分布。接着利用格子玻尔兹曼方法和随机行走模拟，我们考察了不同Peclet数的情况下溶质在稳恒流场中的输运行为，我们发现在高Peclet数的情况下，总是会出现反常输运。我们也讨论了孔隙网络的结构是怎样影响了其上的动力学行为。在理论上我们还考察了一般网络的等效阻值问题，发现当网络稠密时，无论网络的结构细节是怎样的，两点电阻总是由局域性质决定，并且与两点的度的调和平均相关，这可以从拉普拉斯矩阵本征矢量的局域化解释。在基金的资助下我们还研究了有限尺寸热力学系统的有限时间热力学优化问题。我们分别在线性响应区和非线性响应区得到了获得最大输出功的最优协议，我们的结果扩展了之前Van den Broeck和Izumida等人在PRL上的结论。我们还发现了有限时间热力学与经典力学的相似性：熵产生率对应于拉格朗日量，我们据此还可以定义有限时间热力学过程的哈密顿量，并且定量给出非线性响应如何影响最大功率下的热机效率。