Low carbon and environmental protection are becoming increasingly important in the development and utilization of oil and gas resources, so it is crucial to effectively improve the efficiency of low-carbon management. Aiming at the operational requirements of the integrated energy system containing a large number of uncertain resources under the low-carbonization goal, this paper establishes a novel management method. Firstly, a low-carbonization synergistic operation model of carbon capture-P2G is constructed to promote the efficient interaction of the integrated energy system through the multimodal synergistic utilization of carbon cycle and hydrogen energy, and an optimal probabilistic energy flow model of the integrated energy system is established based on it. Then, to address the problem that it is difficult to balance the computational accuracy and solving efficiency of the existing solving methods, this paper proposes a new stochastic response surface (SRS) algorithm, which adopts Taylor series expansion to decouple and simplify the cross terms in the chaotic polynomials, so as to overcome the defects of the SRS that is difficult to deal with high-dimensional stochastic variables. Finally, the accuracy and adaptability of the proposed model and method are verified based on the test systems.