The In-Situ Upgrading (ISU) of heavy oil and oil shale is investigated. We develop a mathematical model for the process and identify the full set of dimensionless numbers describing the model. We demonstrate that for a model with nf fluid components (gas and oil), ns solid components and k chemical reactions, the model was represented by 9 + k x (3 + nf + ns - 2) + 8nf + 2ns dimensionless numbers. We calculated a range of values for each dimensionless numbers from a literature study. Then, we perform a sensitivity analysis using Design of Experiments (DOE) and Response Surface Methodology (RSM) to identify the primary parameters controlling the production time and energy efficiency of the process. The Damköhler numbers, quantifying the ratio of chemical reaction rate to heat conduction rate for each reaction, are found to be the most important parameters of the study. They depend mostly on the activation energy of the reactions and of the heaters temperature. The reduced reaction enthalpies are also important parameters and should be evaluated accurately. We show that for the two test cases considered in this paper, the Damköhler numbers needed to be at least 10 for the process to be efficient. We demonstrate the existence of an optimal heater temperature for the process and obtain a correlation that can be used to estimate it using the minimum of the Damköhler numbers of all reactions.