Liquefied Natural Gas (LNG) has been carried since 1959 in methane carriers, which are the essential link in the movement of LNG between the locations of production and consumption. This thesis presents modeling to: (i) the fluid mechanics of spills/scattering at sea of a cryogenic fluid, due to puncture the hull of these vessels, and (ii) the subsequent burning of the pool by turbulent diffusion fire. The literature review contemplated six decades, and no evidence was found that the themes such as scattering of cryogenic pool followed by turbulent diffusion fires were treated in a single work. This gap was identified, and the subjects were connected in an unprecedented manner and implemented in two computer codes. The spill/scattering is modeled with conservative integral formulation, having as parameters the area of maximum pool poured on the sea and unloading and vaporization times of cryogenic. The flow was modeled with tears between 10 and 100 m(2), consistent with the LNG industry, forming semicircular pools. The modeling of the fire thermal plumes considers circular pools with diameters varying between 10 and 500 m, and combustion and intermittency zones of the thermal plume. Provides a consistent and robust scheme for the development of dimensionless scale parameters, allowing to correlate and extrapolate the length of the visible plume, with the its tilt and drag, its surface emissive power and with cryogenic fuel vaporization mass flow rate in the pool. It also evaluates: (i) the axial variation of emissive power with height of the visible plume, (ii) the burning of fuel along the luminous zone (the base of the fire), and (iii) the transport of thermal radiation emitted by gray gases and soot particles within the combustion zone, considering the emission and absorption in optically thin and thick regions of the thermal plume.