Carbon capture and storage (CCS) technology and pricing policies are two mitigation strategies that attempt to tackle the carbon emission problem. Nonetheless, the uncertainty of public reaction to CCS infrastructure installation has been noted as a significant issue that may lead to either cancelations, delays, or influence the deployment cost of CCS infrastructure. Although these strategies are solutions to reduce carbon emissions, the entire supply chain itself needs to align with sustainability policy. While some previous studies have addressed mitigation strategies or the combination of social objective and CCS technology, the impact of social objectives on reservoir openness has not been explored. This article contributes to the literature by illustrating the effect of social objectives on reservoir openness and the total cost of the CCS supply chain. Through the development of a two-stage mixed-integer linear programming model, we optimize the supply chain network design. In the first stage, a single-objective model minimizes capture, transportation, and sequestration costs along with CO2 emission costs to the atmosphere, considering various carbon tax prices. In the second stage, a bi-objective model maximizes social acceptance towards CO2 injection wells (reservoirs) to analyze the impact of cultural dimensions. Our findings reveal that maximizing the social objective leads to increased costs compared to the economic optimum, and it significantly influences the openness of reservoirs based on cultural dimensions. Furthermore, we demonstrate that an increase in the CO2 tax enhances the amount of captured carbon and the complexity of the pipeline network in the supply chain. This insight has implications for governments and decision-makers who can encourage industries to adopt CCS technology by setting appropriate carbon tax prices. To validate the model, we apply it to a case study in the European Union cement industry, one of the major carbon emitters among all industries. Our results not only confirm the model's effectiveness but also show its potential for practical application. Overall, our study presents a comprehensive framework for designing a twostage sustainable supply chain network for CCS technology that optimizes economic and social objectives while considering CO2 pricing.