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Application the GALO system for basin modeling gives an opportunity to analyze changes in thermal, maturation and generation histories of probable source rocks related to transition from the shallow to deep shelf of the eastern passive margin of India. The Lower Cretaceous rocks in modern sedimentary section of the deep shelf are overmature (Ro > 1.30%), whereas the same rocks in shallow shelf occur within the “oil window”. The modeling shows that intensive deposition of sediments carried by the river Ganges in the Miocene-Pliocene led to considerable subsiding of «oil window» in both basins, but its influence is more pronounced in the Mahanadi basin. In present-day sedimentary section of the deep shelf, depth of roof of the “oil window” (Ro = 0.50%) is nearly by 1 km deeper than the one in the shallow shelf, whereas depth of base of the “window” (Ro = 1.30%) is by 1 – 3.5 km deeper than in the shallow shelf. As whole, the rocks within the “oil window” are younger in the deep shelf areas. In the deep shelf and in the GS-41 and GS-5-1 areas of the shallow shelf, the rocks at the base of the Cretaceous according to modeling are gas prone. Liquid hydrocarbons, generated by organic matter at these areas, were totally destroyed even in Upper Cretaceous – Eocene due to secondary cracking. In deep shelf, organic matter of the rocks in top of the Upper Cretaceous is oil prone except the areas near the mouth of the Ganges River. In the shallow shelf, the Upper Cretaceous formation is oil prone in the deepest wells of the area (wells 1 (GS-41-1), 3 (GS-5-1) and 9 (NEC-1)) and immature in other wells. The source rocks of Upper Eocene and Oligocene are early mature and generate negligible volume of hydrocarbons.