Publisher Summary In addition to the generation and migration of petroleum, there must be a reservoir rock available, and it must have adequate values of permeability and porosity. The processes that lead to these characteristics, such as winnowing away of fine-grained materials, generally lead to low organic contents. As reservoirs contain insufficient organic matter to generate the oil and gas now contained in them, it is widely assumed that the petroleum is generated elsewhere in organic rich source rocks and subsequently migrates into the reservoir over distances that may range from a few meters to hundreds of kilometers. This is the so-called “Source Rock Concept”. For compaction to occur water must flow out; and modeling then requires information about the permeability distribution in adjacent, and more distant rocks. Again, 1-D models are not adequate for describing the complete system. A variety of 2-D and 3-D models is being developed to cope with the additional complexities. As well as describing petroleum generation status, they deal with water flow, lateral heat transfer, two-phase migration of fluids, and the development of abnormal pressures. This requires considerable additional physical and chemical information as input, and, in particular, it is important to be able to describe the distribution of permeability in some detail. The extended models that are being developed to include these parameters are described in this chapter.