Voluntary ignition of the exiting oil-gas mixture may be an acceptable response to a possible well blowout if the burning could be shown to be nearly 100% efficient. Oil-gas mixture burning is a very complex phenomenon. The efficiency of such burning depends on many parameters, which include the ratio of gas to oil, the size and velocity of oil droplets, thermo-physical properties of the oil and gas, the presence of water or other fire depressants, etc. Motivated by these considerations, in this work, the first part provides a review of the independent study based on the available literature to understand the key models/sub-models in determining the burning efficiency of well ignition. Then, instead of accurate modeling of this complex well ignition phenomenon, simplified models are used to systematically understand the extreme limits of key parameters and variables for capturing the worst case consequence. Lastly, we apply the proposed method to a well on artificial drilling islands in the Beaufort Sea, off the northern coast of Alaska.