Heterogeneity across a broad range of scales in geologic porous media often manifests in observations of non-Fickian or anomalous transport. While traditional anomalous transport models can successfully make predictions in certain geological systems, increasing evidence suggests that assumptions relating to independent and identically distributed increments constrain where and when they can be reliably applied. A relatively novel model, the Spatial Markov model (SMM), relaxes the assumption of independence. The SMM belongs to the family of correlated continuous time random walks and has shown promise across a wide range of transport problems relevant to natural porous media. It has been successfully used to model conservative as well as more recently reactive transport in highly complex flows ranging from pore scales to much larger scales of interest in geology and subsurface hydrology. In this review paper we summarize its original development and provide a comprehensive review of its advances and applications as well as lay out a vision for its future development.

地质多孔介质中各种尺度的非均质性通常表现在非菲克或异常输送的观测中。尽管传统的异常运输模型可以在某些地质系统中成功进行预测，但越来越多的证据表明，与独立且分布均匀的增量有关的假设限制了可以可靠地应用它们的时间和地点。一个相对新颖的模型，即空间马尔可夫模型（SMM），放宽了独立性的假设。SMM属于相关的连续时间随机游走族，并且已显示出与天然多孔介质有关的各种运输问题的希望。它已被成功地用于模拟从地质尺度和地下水文学中的孔尺度到更大尺度的高度复杂的流动中的保守以及最近的反应性输运。在这篇综述文件中，我们总结了它的原始发展，并对它的进步和应用进行了全面的回顾，并提出了其未来发展的愿景。