DOI: 10.3303/CET25120064 Paper Received: 15 May 2025; Revised: 17 July 2025 ; Accepted: 30 October 2025 Please cite this article as: Aviso K.B., Foo D.C.Y., Poplewski G., Tan R.R., 2025, Optimization Model for Progressive Industrial Decarbonization, Chemical Engineering Transactions, 120, 379-384 DOI:10.3303/CET25120064 CHEMICAL ENGINEERING TRANSACTIONS VOL. 120, 2025 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Bing Shen How, Viknesh Andiappan, Denny K.S. Ng, Hon Loong Lam, Petar S. Varbanov Copyright © 2025, AIDIC Servizi S.r.l. ISBN 979-12-81206-21-2; ISSN 2283-9216 Optimization Model for Progressive Industrial Decarbonization Kathleen B. Avisoa, Dominic C.Y. Foob, Grzegorz Poplewskic, Raymond R. Tana,* aDepartment of Chemical Engineering, De La Salle University, Philippines bDepartment of Chemical and Environmental Engineering/Centre of Excellence for Green Technologies, University of Nottingham Malaysia, Malaysia cDepartment of Chemical and Process Engineering, Rzeszow University of Technology, Poland raymond.tan@dlsu.edu.ph Many companies are setting corporate net zero emissions targets in response to the pressure of decarbonization trends. In industries that have hard-to-abate emissions, the options available for deep emissions cuts are limited to changing the fundamental process technologies, using carbon capture and storage (CCS), or purchasing carbon dioxide removal (CDR) credits. Investment decisions need to be carefully planned due to inherent techno-economic risks. In this work, a mixed-integer linear programming (MILP) model is developed for optimizing progressive industrial decarbonization plans. For a given system of multiple plants with specified baseline emissions, the model can be used to determine the cost-optimal timing of CCS retrofits to meet a series of interim emissions caps leading to an eventual net zero state; it is assumed that CDR credits can also be purchased at any time to offset any residual emissions from the system. The model is applied to two representative case studies to demonstrate how it can be used to support decision-making. 1. Introduction Deep decarbonization of industrial sectors will be necessary to achieve global net zero aspirations. There is intensive research on different enabling technologies, such as process heat electrification and CO2 capture, utilization and storage (CCUS), for making deep emissions cuts (Gailani et al., 2024). Sector-specific decarbonization roadmaps have been proposed for the carbon-intensive industries such as cement (Nehdi et al., 2024), chemicals (Thakker and Bakshi, 2024), iron and steel (Keramidas et al., 2024), and pulp and paper (Dai et al., 2024) production. However, the wide range of available options coupled with uncertainties inherent in new technologies complicates decision-making in practice. The development of tools to address current sustainability challenges is a priority area for researchers in the areas of process systems engineering (PSE) (Pistikopoulos et al., 2021) and process integration (PI) (Wang et al., 2022). Many optimization models have been proposed to support industrial decarbonization decisions (Tan et al., 2025). For example, Nair et al. (2023) developed an open-source software for optimizing industrial decarbonization using a suite of options including the purchase of externally sourced carbon dioxide removal (CDR) credits. Lee et al. (2025) developed a mixed-integer linear program (MILP) to optimize the electrification of industrial boilers. Migo-Sumagang et al. (2025) proposed a framework for optimizing the equitable allocation of CDR credits within an industrial sector, considering the financial capability of each company to pay for decarbonization. CCUS or CO2 capture, and storage (CCS) are essential technology options for making deep cuts in industries with hard-to-abate emissions (Bains et al., 2017), as evidenced by their inclusion in optimized decarbonization portfolios for the cement (Obrist et al., 2021), iron and steel (Li et al., 2023), and pulp and paper (Obrist et al., 2022) sectors. CCS/CCUS technologies can be used to drastically reduce emissions in power generation and industrial plants (Bains et al., 2017). The conventional benchmark is reduction of baseline emissions by 90 %, although “deep CCS” approaching 100 % reduction is possible in principle (Dods et al., 2021). Optimization models have been proposed to optimize planning of CCS/CCUS deployment. Tan et al. (2013) developed an early MILP model for planning CCS retrofit of power plants. More recent models cover a broader range of industrial CO2 point sources as well as utilization and sequestration options (Prousalis et al., 2024). However, there is still a need for generic, 379 computationally tractable models to plan the decarbonization of industrial facilities over extended time horizons; in addition, practical scenarios will often involve “check points” or interim emissions reduction targets. To address this research gap, a novel MILP model is developed for progressive decarbonization of multiple industrial sites towards an ultimate net zero goal. A discrete time formulation is employed with the option to use CCS and CDR to meet interim and final emissions targets. The model is computationally tractable and can be used to develop practical industrial decarbonization roadmaps. The rest of the paper is organized as follows. Section 2 defines the formal problem statement. Section 3 describes the MILP model formulation. Section 4 demonstrates the model on a tutorial case study, while Section 5 applies it to the case of decarbonizing Poland’s cement industry. Section 6 states the conclusions and future research directions. 2. Problem statement The formal problem is given as follows: • Given a set of industrial plants with known baseline annual emissions which need to be decarbonized within a specified time horizon; • Given that the planning horizon is divided into intervals with each interval having an interim decarbonization target; • Given that the industrial plants can be decarbonized primarily through retrofit with CCS technology with known capture rates and capture costs; • Given that the decision to retrofit should be made within a given period of time represented by the earliest time that the technology is available to the latest time of retrofit to ensure economic viability of the investment; • Given that each plant can also buy CDR credits or pay a penalty (carbon tax) if the emissions limit is exceeded. The problem then is to find the optimal decarbonization schedule which will minimize the over-all costs for the plants in the system. 3. Model formulation The overall objective is to minimize the total cost (Eq(1)) associated with reaching the CDR target. This consists of the costs incurred in each period k for capturing CO2 (CaptureCost𝑘), buying CDR credits (CDRCost𝑘), or paying penalties due to excess CO2 emissions (PenaltyCost𝑘). The capture cost is further defined in Eq(2) where BE𝑖 is the baseline emission of plant i, RR𝑖 is the removal rate with values ranging from 0 to 1, Z𝑖𝑘 is a binary parameter which indicates if plant i is still operational in period k (Z𝑖𝑘 = 1), C𝑖 is the unit cost for capturing CO2, and x𝑖𝑘 is a binary variable that indicates if the retrofit is implemented for plant i in period k (x𝑖𝑘 = 1) or not (x𝑖𝑘 = 0). Eq(3) defines the cost associated with the carbon credits where CDR𝑘 is the unit cost for carbon credits where y𝑖𝑘 indicates the amount of carbon credits needed by plant i in period k. TotalCost = ∑(CaptureCost𝑘 + CDRCost𝑘 + PenaltyCost𝑘) k (1) CaptureCost𝑘 = ∑ x𝑖𝑘C𝑖BE𝑖RR𝑖 i Z𝑖𝑘 ∀k (2) CDRCost𝑘 = ∑ y𝑖𝑘CDR𝑘 i ∀k (3) Any excess CO2 from the target set in period k (E𝑘 CAP) incurs a penalty cost (Eq(4)), where e𝑘 refers to the emissions in period k and P𝑘 is the unit penalty cost. The remaining emissions in period k (e𝑘) is defined by Eq(5) and will depend on whether the capture technology retrofit is activated for plant i in period k and if CDR credits are bought by the company. The total CDR credits used by companies in any given period k should not exceed what is available (CDR𝑘 cap ) as indicated in Eq(6). PenaltyCost𝑘 > (e𝑘 − E𝑘 CAP)P𝑘 ∀k (4) 380 e𝑘 = ∑[BE𝑖Z𝑖𝑘(1 − x𝑖𝑘) + BE𝑖Z𝑖𝑘(1 − RR𝑖)x𝑖𝑘 − y𝑖𝑘] i ∀k (5) ∑ y𝑖𝑘 i ≤ CDR𝑘 CAP ∀k (6) Once the retrofit is implemented, it remains operational until the end of the planning period (Eq(7)). The retrofit should be activated at a time (t𝑖 start) that will make the retrofit economical (Eq(8)), while Tmax is the end of the planning horizon. The retrofit should begin within defined earliest (TL𝑖) and latest (TU𝑖) times of activation (Eq(9) and Eq(10)) where b𝑖 is a binary variable that indicates if a retrofit was implemented for plant i (Eq(11)) and M is an arbitrary big number. Eq(12) and Eq(13) indicate the binary variables. x𝑖𝑘 ≤ x𝑖𝑘+1 ∀i, k (7) t𝑖 start = Tmax − ∑ x𝑖𝑘 k + 1 ∀i (8) t𝑖 start ≥ b𝑖TL𝑖 ∀i (9) t𝑖 start ≤ b𝑖TU𝑖 ∀i (10) ∑ x𝑖𝑘 k ≤ Mb𝑖 ∀i (11) x𝑖𝑘 ∈ {0,1} ∀i, k (12) b𝑖 ∈ {0,1} ∀i (13) This MILP model can be readily implemented and solved using branch-and-bound solvers embedded in spreadsheet applications such as Excel optimization software such as LINGO or GAMS. 4. Case Study 1 The first case study is a tutorial demonstration that considers four hypothetical industrial plants that intend to cut down their emissions. The detailed model files are available upon request. The planning horizon is for five periods, with each period consisting of 5 years. The relevant plant data is summarized in Table 1 while the temporal system–level data is shown in Table 2. Table 1: Plant data for case study 1 Units Plant 1 Plant 2 Plant 3 Plant 4 Baseline emissions, BE𝑖 kt/y 400 100 600 200 Earliest retrofit, TL𝑖 period 2 1 1 1 Latest retrofit, TU𝑖 period 4 4 3 2 Removal rate, RR𝑖 % 95 90 90 90 Capture cost, C𝑖 US$/t 40 40 30 35 Solving Eq(1) subject to the constraints in Eq(2) to Eq(13) results in a total system cost of US$ 994.50 M, majority of which will be spent capturing the CO2. The distribution of costs is shown in Figure 1. Emissions for periods 1 to 3 were below the emissions limit set for the respective periods while CDR credits were needed for periods 4 and 5. Plants 3 and 4 were retrofitted with carbon capture technology as early as period 1 while plant 1 was retrofitted in period 2 and plant 2 in period 4. 381 Table 2: Temporal system–level data for case study 1 Units Period 1 Period 2 Period 3 Period 4 Period 5 Emissions cap, E𝑘 CAP kt/period 3,000 1,500 750 250 0 CDR credit cost, CDR𝑘 US$/t 200 150 120 100 80 Penalty cost, P𝑘 US$/t 80 100 120 150 200 CDR supply cap, CDR𝑘 CAP kt/period 100 200 400 800 1,600 Figure 1. Cost distribution for optimal solution of case study 1 5. Case Study 2 The second case study considers industrial decarbonization in Poland. The detailed model files are also available upon request. As part of the European Union, Poland is committed to achieving carbon neutrality by 2050, with interim targets of 55 % emissions reduction by 2030 and 90 % by 2040. The country is facing challenges due to its high dependence on coal (Poplewski et al., 2025). Growth of non-fossil (renewables and nuclear) power generation and improved integration of the grid with neighbouring countries are expected to aid decarbonization efforts. This semi-hypothetical case study considers the decarbonization of 11 cement plants in Poland over a 25-year planning horizon (2025−2049) divided into 5-year intervals. The system data are shown in Tables 3 and 4. The annual CDR supply cap is also indicated in Table 4. Any retrofits must be in place at least 10 y before plant decommissioning or the end of the planning horizon. Table 3: Plant data for case study 2 Plant Units 1 2 3 4 5 6 7 8 9 10 11 Baseline emissions, BE𝑖 Mt/y 5.11 2.40 2.00 2.20 0.80 1.60 2.50 0.60 0.45 0.06 5.00 Year of decommissioning 2047 2047 2034 2042 2026 2046 2044 2068 2030 2040 2046 Earliest retrofit, TL𝑖 kth year 1 1 1 1 1 1 1 1 1 1 1 Latest retrofit, TU𝑖 kth year 13 13 1 8 1 12 10 17 1 6 12 Removal rate, RR𝑖 % 90 90 95 90 95 90 95 95 95 90 95 Capture cost, C𝑖 US$/t 35 35 30 40 35 30 30 35 35 40 35 Table 4: Temporal system-level data for case Units Period 1 Period 2 Period 3 Period 4 Period 5 Emissions cap, E𝑘 CAP Mt/period 75 50 25 15 0 CDR credit cost, CDR𝑘 US$/t 200 150 120 100 80 Penalty cost, P𝑘 US$/t 80 100 120 150 200 CDR supply cap, CDR𝑘 CAP kt/y 1,000 2,000 4,000 8,000 16,000 Solving Eq(1) yields a total cost of US$ 6.092 M. The cost distribution is illustrated in Figure 2. A penalty is paid from 2025–2029 while CDR credits are purchased in 2040 and 2041 as well as in 2045 to 2049. Only 5 plants were retrofitted for CCS, as shown in Table 5. 382 Table 5: Temporal system-level data for case Earliest Latest 𝑡𝑖 𝑠𝑡𝑎𝑟𝑡 Decommissioning Plant 1 2025 2037 2030 2047 Plant 2 2025 2037 2035 2047 Plant 3 2025 2025 No retrofit 2034 Plant 4 2025 2032 No retrofit 2042 Plant 5 2025 2025 No retrofit 2026 Plant 6 2025 2036 2035 2046 Plant 7 2025 2034 2025 2044 Plant 8 2025 2041 2040 2068 Plant 9 2025 2025 No retrofit 2030 Plant 10 2025 2030 No retrofit 2040 Plant 11 2025 2036 No retrofit 2046 Figure 2. Cost distribution for optimal solution of case study 2 6. Conclusions A MILP model was developed for optimal planning of the progressive fleet decarbonization towards net zero targets. The model uses a discrete-time formulation to time carbon capture retrofits to meet periodic emissions reduction check points; it also allows the purchase of CDR credits from an external supplier to deal with residual emissions. The model was first applied to a tutorial example, and then demonstrated on an industrial case study based on cement plants in Poland. Results show that carbon neutrality can be achieved optimally by retrofitting 5 out of 11 plants, and then using CDR credits to offset the remaining emissions. The model itself is generic and can be applied to any fleet of GHG emissions point sources, whether stationary (e.g., power plants, steel mills) or mobile (e.g., aircraft, ships). Future work can extend this model by introducing multiple internal decarbonization and CDR options. It can also be scaled up for planning the decarbonization of entire geographic regions. More sophisticated variants can be developed to model government-industry interactions, parametric uncertainties, and endogenous technology learning curves. Nomenclature i – index for plant k – index for period Decision variables b𝑖 – binary variable that indicates a retrofit in i CaptureCost𝑘– costs incurred for CO2 capture CDRCost𝑘– cost incurred due to CDR e𝑘 – emissions in period k PenaltyCost𝑘– costs due to penalty t𝑖 start – time when retrofit is activated initially x𝑖𝑘– binary variable that indicates activation of retrofit in plant i in period k y𝑖𝑘 – carbon credits in plant i in period k Parameters BE𝑖 – baseline emissions of plant i C𝑖– unit cost for CO2 capture, CDR𝑘 – unit cost for carbon credits in period k CDR𝑘 CAP – CDR cap in period k E𝑘 CAP – emissions cap in period k 383 RR𝑖– removal rate in plant i TL𝑖 , TU𝑖 – earliest and latest times of retrofit activation Z𝑖𝑘 – binary parameter that indicates if plant i is operational in period k References Bains P., Psarras P., Wilcox J., 2017, CO2 capture from the industry sector. Progress in Energy and Combustion Science, 63, 146 – 172. 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