In this study, the analytical expression of field distribution of twisted elliptical Gaussian Schell-Model beams after they pass through a Gaussian absorption-type obstacle is derived based on the Collins formula, and a basic twisted-beam model is obtained that effectively enhances the beam's self-healing capability. The effects of the light source parameters on the beam's self-healing properties are analyzed. The laws of intensity, coherence, and orbital angular momentum flux density transmitted when partially blocked by obstacles and the intrinsic connection among the three quantities are revealed. The intrinsic self-healing properties of twisted beams are explained. It is shown that appropriately reducing the coherence length and twist factor can enhance the beam's self-healing capability while preserving the characteristics of the twisted beam. The findings can help optimize the overall performance of partially coherent light transmission in free space, thus enhancing potential applications in free space optical communication, LIDAR, remote sensing imaging, and other fields.