Our previous work [1] has shown that carbon capture technologies are generally preferred over electrification-based options in the short to medium term, unless there is a substantial drop in electricity prices. Moreover, while CO₂ taxes do promote earlier adoption of carbon capture, they do not necessarily speed up the shift to electrification. Our results have also shown that accounting for hourly variations in electricity pricing, allowing for hybrid operation and use of storage for leveraging these variations can favor earlier adoption of e-based technologies.
In this work, we extend our modeling framework by employing stochastic programming to address key uncertainties, including long-term and short-term exogenous uncertainties in natural gas and electricity prices [2], as well as type 2 endogenous uncertainties [3] in capital expenditures (CAPEX) and efficiency of electrification and capture technologies. A multistage stochastic programming model is formulated that is solved using a using a sequence of 2-stage stochastic programming within a shrinking horizon approach [4]. In order to improve computational efficiency, decomposition techniques are developed to handle the long-term and short-term uncertainties, and the large number of non-anticipativity constraints arising from the endogenous and exogenous uncertainties [3].
We finally evaluate the effectiveness of the stochastic solution by calculating the Value of the Stochastic Solution (VSS) to compare it with the deterministic solution across all scenarios. Our results demonstrate that incorporating uncertainty into decision-making significantly improves cost efficiency over the deterministic solution when evaluated across several scenarios of price and technology improvements.
References
[1] Chattopadhyay, S., Karthikeyan K, Gandhi R, Grossmann I. E., and Torres. A. I "Optimal Retrofit of Carbon Capture and Electrification Technologies in Oil Refineries for Reducing Direct CO₂ Emissions." Industrial Engineering and Chemistry Research. (Submitted).
[2] Zhang, H., Grossmann, I. E., & Tomasgard, A. (2024). Decomposition methods for multi-horizon stochastic programming. Computational Management Science, 21, 32
[3] Apap, R. M., & Grossmann, I. E. (2017). Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties. Computers & Chemical Engineering, 103, 233–274
[4] Balasubramanian, J., & Grossmann, I. E. (2004). Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Industrial & Engineering Chemistry Research, 43(14), 3695–3713.