The artificial pancreas is a closed-loop insulin delivery system that automatically regulates glucose levels in individuals with type 1 diabetes. In-silico testing using simulation environments accelerates the development of better artificial pancreas systems. Simulation environments need an accurate model that captures glucose dynamics during exercise to simulate real-life scenarios. We proposed six variations of the Bergman Minimal Model to capture the physiological effects of moderate exercise on glucose dynamics in individuals with type 1 diabetes. We estimated the parameters of each model with clinical data using a Bayesian approach and Markov chain Monte Carlo methods. The data consisted of measurements of plasma glucose, plasma insulin, and oxygen consumption collected from a study of 17 adults with type 1 diabetes undergoing aerobic exercise sessions. We compared the models based on the physiological plausibility of their parameters estimates and the deviance information criterion. The best model features (i) an increase in glucose effectiveness proportional to exercise intensity, and (ii) an increase in insulin action proportional to exercise intensity and duration. We validated the selected model by reproducing results from two previous clinical studies. The selected model accurately simulates the physiological effects of moderate exercise on glucose dynamics in individuals with type 1 diabetes. This work offers an important tool to develop strategies for exercise management with the artificial pancreas.