The oxyfuel cutting method is still widely used nowadays, even though it is not a fully autonomous process. Thisthesis presents a computational model to study ion and electron transport and current-voltage characteristics inside a methane-oxygen flame. By finding the relationship between current-voltage characteristics and critical parameters,such as standoff, fuel oxygen ratio, and flow rate, a control algorithm could be implemented into the system and make it autonomous. Star CCM+ software is used to develop preheat phase computational models by splitting the simulations into the combustion and electrochemical transport parts. Both the laminar and turbulent flows are considered. Several laboratory experiments are used to compare test data with the numerical results generated using this model. The initial and boundary conditions used in the simulation were to the extent possible similar to the experimental conditions in the laboratory experiment. In the combustion part, the general GRI3.0 mechanism plus three additional ionization reactions are applied, and the combustion part results are then used as input into the electrochemical transport part. A particular inspection line inside the domain is created to analyze the results of the electrochemical transport part. Ions, electrons number density, and current density are studied in the interval from -40V to 40V electric potential. The ions are heavier and more challenging to move than electrons. The results show that at both the torch and work surfaces, charged sheaths are formed, which cause three different regions of current-voltage relations to form in a similar manner as observed in the tests. / Master of Science / Oxyfuel cutting is essential to numerous industries, such as shipbuilding, rail, earth moving equipment, commercial building construction, etc. Tuning the process parameters and diagnosing problems with the oxyfuel process still relies on experienced operators. The main obstacles to the automation of the oxyfuel process come from the limitations of the sensing suites currently in use. Since typical sensors are highly unreliable in the harsh environment near the high-temperature flame, an alternate method is proposed to find the co-dependence between the flame's electrical characteristics and critical parameters of the oxyfuel cutting system (standoff, flow rate, F/O ratio, etc.). The relevant electrical characteristics are the electrical potential and distribution of ions and electrons. Two-dimensional models are created to analyze the combustion of methane-oxygen flame and transport of ions and electrons. The models allow the derivation of the current-voltage characteristic between the torch and work surface. Also, the way sheath phenomena of ions and electrons on the surface affect the current-voltage relationship can be analyzed from ions and electrons distribution. The electric field is added to the model by applying a constant voltage to the torch tip surface. To validate the models, a laboratory experiment with a similar geometry arrangement is used as a comparison. The models' results reveal three different regimes in the current-voltage relationship.