The marine subsurface is characterized by a wide range of processes involving diagenesis of organic and inorganic substrates and fluid-rock interactions, which significantly alter composition of the pore fluids. Organic diagenesis is intimately linked with a wide variety of microbial processes that lead, under some cases, to the production and consumption of gases. Minerals delivered to the ocean from rivers and volcanoes also contain reactive silicates that are subject to alteration under a variety of temperature and pH conditions. Temperatures in the deep sediment can be as high as 160oC, and warmer temperatures occur within the underlying oceanic crust. These high temperatures result in dehydration reactions that liberate water previously found within mineral structures. The generation of gases and excess water create overpressures that then drive advection of both aqueous and gaseous fluids. Collectively these processes have important implications ranging from global budgets of mass and energy, economic resources and earthquake generation. Quantifying these integrated processes requires complex computational approaches. Although models used to date are improving, there is a growing need for easily accessed computational models that incorporate thermodynamic constraints, variable state conditions and transport mechanisms to a wide range of processes occurring in the marine subseafloor. I will summarize these challenges and present an illustration of a collaborative project between geoscience and mathematics where the use of computational models was developed to explain the evolution of gas hydrates, a large and dynamic carbon reservoir in marine sediments.