Operability-economics trade-offs in adsorption-based CO2 capture processes

Dispatchable low-carbon power underpins the transition to a sustainable energy system, providing balancing load for the integration of intermittent renewable power. In such load-following operation, the post-combustion carbon capture process must be capable of highly transient operation. Here we have developed a computational framework that integrates process design, operability and techno-economic assessment of a pressure-vacuum swing adsorption process for CO2 capture. We demonstrate that the cost-optimal design has limited process flexibility, challenging reactiveness to disturbances in the flue gas conditions. Flexibility can be introduced by relaxing the CO2 recovery constraint on the operation, albeit at the expense of the capture efficiency of the process. We discover that adsorption-based processes can be designed to enhance flexibility, while improving performance with respect to the operational constraints on CO2 recovery and purity. The results herein demonstrate a trade-off between process economics and process operability, which must be rationalised to integrate CO2 capture units in low-carbon energy systems.

Low-carbon energy system. A schematic representation of a flexible low-carbon energy system with intermittent renewables (non-dispatchable power) and low-carbon dispatchable power. Power generation by fossil fuels is expected to provide a variable power output to match supply and demand of energy at any given time. Downstream postcombustion capture (PCC) is subject to operation under variable flue gas feed flowrate and CO 2 composition.
losses owing to volatility [19]. As a result of these challenges, research efforts have been dedicated towards exploring alternative technologies for carrying out the separation.
Adsorption-based processes represent an attractive alternative to aminebased absorption for PCC, primarily owing to the comparatively low energy penalty associated with regeneration of the sorbent [20]. In an adsorptionbased process, a column is packed with pellets of a solid adsorbent material which is highly selective for concentrating CO 2 at its surface. An adsorption column is operated by cyclically varying the operating conditions to capture high purity CO 2 on the solid surface, and subsequently release it in a controlled manner [21]. The most widely studied adsorption cycle for PCC is pressurevacuum swing adsorption (PVSA) [22][23][24][25], where adsorption is carried out at high pressure and the CO 2 product is extracted from the bed using a vacuum.
The design of PVSA carbon capture processes is typically conducted to minimise the cost per tonne of CO 2 captured, while satisfying constraints on the effectiveness of the separation [26][27][28][29]. To be suitable for geological storage, the CO 2 product stream must have a purity of at least 95% [30,31]. It is generally an accepted standard, originally proposed by the United States Department of Energy (DoE), that post-combustion capture processes should attain a CO 2 recovery of at least 90% [32]. This approach for the design, according to minimisation of the capture cost, does not consider any aspects related to the flexibility of the process.
There is a clear need to move beyond the academic status-quo of designing for static, idealised scenarios, and incorporate flexibility into the design to ensure the long term viability of these processes throughout the energy transition. Firstly, there is currently very little available literature on the flexible operation of PVSA processes applied to PCC [33]. In addition, we do not currently understand well how these processes respond to transient operating scenarios. Third, with analogy to other chemical processes, we expect there to be a trade-off between flexibility and process economics [34][35][36]. Rationalising this trade-off is key to enabling industrial adoption of adsorption-based carbon capture processes.
In this work, we propose an approach for embedding flexibility assessment within the design of adsorption-based PCC systems to achieve low cost, while sufficiently prioritising operability from an early stage in the design. The approach utilises a high fidelity mathematical process model for the separation of CO 2 /N 2 by PVSA and an associated techno-economic assessment to quantify the performance of PCC from a typical coal-fired power plant [37].
We have coupled the mathematical model with a framework for identifying the design space for which the process can be operated while satisfying regulatory requirements on the CO 2 product stream [38]. For any chosen operating strategy, the flexibility of the process can be quantified with respect to the design space boundary. In the following, we calculate and compare the flexibility resulting from several proposed PVSA design approaches. We find that the proposed direct design space approach is effective, efficient and provides a rich set of information around the process flexibility which is not given through classical process design.

Results
Case Study: Coal Fired Power Plant With CO 2 Capture. In this work, we have analysed a four-step PVSA process, with feed pressurisation, applied for PCC from a typical coal fired power plant. The flue gas eluted from the power plant is considered to be a dry binary mixture of 15%CO 2 /85%N 2 at a pressure of 1 bar and a temperature of 298 K. We consider an adsorption process utilising a packed bed of zeolite 13X adsorbent, a commercially available and widely studied material for PCC. The considered power plant has a typical specification, with a gross electrical power output of 1,000 MW and producing approximately 9 Mtn/yr of CO 2 emissions to the atmosphere. Full details of the process modelling and economic assessment conducted for this case study can be found in the methods Section.
Process Behaviour in the Knowledge Space. The problem is formulated as follows. In the first step, the design decisions (DDs) for the system are identified. These are the design parameters and/or operational variables which will be varied to understand the flexibility of the process. Here, we consider a typical PVSA design problem, where we use the feed velocity (v F ), the high pressure (p H ), and the intermediate pressure (p I ) as DDs. In practice, implementation of PVSA processes on a large scale involves the operation of multiple columns in parallel. The columns are scheduled in such a way that the feed flue gas can be processed continuously. By-passing of flue gas and venting without capturing is not contemplated in this study. Therefore, in this setting, dynamically varying the cycling times (t ads -adsorption time, t bd -blowdown time, and t evac -evacuation time) of the adsorption process to address disturbances is not realistic as this would result in significant process scheduling complications. Therefore, in this work, the cycle times are fixed. Upon varying the DDs of the system, we monitor the purity, recovery, energy consumption, productivity, and capture cost as key performance indicators (KPIs). In the second step, the bounds on the DDs are identified and used to generate the knowledge space (KSp). The KSp defines the sub-space of the entire design decision space for which we perform quasi-random sampling to probe the behaviour of the process. We have used the Sobol sequence to sample the design decision space and generate the KSp by taking 4,096 quasi-random samples. Of these samples, 3,458 satisfied the feasibility constraint on the operating pressures (p H > p I ). For each of the sampled points, we record the DDs and respective KPIs of the process generated by running the process model and economic assessment.
Approximated Cost-Optimal Process Design. Before performing design space identification and assessing the flexibility of the process, the KSp data set is used to approximate Pareto optimal frontiers of the process performance, and to approximate the cost-optimal operating point given the process performance constraints. As a benchmark of optimality, we have deployed the widely used non-dominated sorting genetic algorithm II (NSGA-II) to conduct rigorous process optimization. Using the NSGA-II routine, we have calculated Pareto fronts of unconstrained purity/recovery and constrained productivity/energy usage, as well as the constrained cost-optimal point. For the constrained problems, we require that the process produces CO 2 with purity ≥ 95% and recovery ≥ 90%, in compliance with regulatory requirements. In Fig. 2, we provide a comparison between the optimal process behaviour identified using NSGA-II (solid lines), and that obtained by sampling the KSp using the quasi-random Sobol sequence (symbols). The labelled points in each panel show the position in each Pareto plane of the cost-optimal point obtained by each method (blue: Sobol sampling, red: NSGA-II). We can see that there is excellent agreement between the Pareto fronts generated by each approach, validating the use of quasi-random sampling for the purposes of initial identification of the optimal process performance. In Table 1, we present the values of the DDs and minimum capture cost associated with the cost-optimal point identified using each approach. Again, we can see that the solutions are very similar, with the Sobol sampling approach obtaining a solution with a minimum capture cost deviating from the optimum by only 1.1%. This is particularly impressive when considering the computational cost of each approach.
In total, 15,120 forward simulations are performed for solving all three optimization problems to obtain the Pareto fronts and cost-optimal design ( Fig.   2a, b) using NSGA-II. In comparison, only 3,458 forward simulations were required for Sobol sampling. We therefore contend that the Sobol sampling approach is an efficient and effective means to approximate the optimal performance of the adsorption process. Further to this, the outputs of Sobol sampling can further be used to generate a rich set of data around the flexibility of the process operation, as will be demonstrated below.
Quantification of Acceptable Operating Ranges. Following the design space identification framework established in [38], an artificial neural Sobol sampling. a Unconstrained purity-recovery Pareto front. b Constrained energyproductivity Pareto front. In both a and b, the solid lines correspond to the NSGA-II Pareto fronts, while the scattered points correspond to Sobol sampling. The cost-optimal design of optimization using NSGA-II is highlighted as a red square in each Pareto plane, and that of the Sobol sampling is a blue circle. The corresponding design decisions and KPI values are summarised in Table 1. network (ANN) is trained and used as an interpolator to increase the resolution of the KSp data set (see methods Section). Based on this high-resolution data set, we identify the design space via alpha shapes -as illustrated in for which operation is guaranteed to be within the design space. Here, we investigate the cost-optimal design obtained above as the NOP of interest and identify its AOR, as shown in Fig. 3. We can see that the cost-optimal design has very low flexibility, as the AOR is not visible with reasonable axis scaling in Fig. 3. As it can be anticipated from the position of the cost-optimal design in the purity/recovery plane (Fig. 2 (a) Through application of the design space identification framework, we are able to quantitatively ascertain that the status-quo design approach for PVSA processes yields an inflexible design with low operability in practice. At this stage, we seek to understand if there is scope in the design workflow to accommodate flexibility. More specifically, we aim at understanding how much flexibility can be allowed for in the design, and what impacts the accommodation of flexibility has on the other design outcomes -such as process efficiency and economics. To analyse this in detail, we will study two further design cases using the design space identification framework and the existing KSp data set. First, we will consider the "relaxed cost-optimal design" -a case which maintains the original cost-optimal point, but allows for some relaxation of the recovery constraint to handle disturbances. Second, we will consider the "maximum flexibility design" -a case which maximises flexibility within the original design space. In the following, we analyse each of these cases in further detail, and subsequently compare their performance. This showcases the usefulness of the design space identification framework for efficiently exploring different design options to attain process flexibility. Fig. 4 shows the design spaces identified with different recovery targets, ranging from 85-90%. As we can see, the design space expands predominately in the direction of increasing p H as the recovery constraint is relaxed. When relaxing the recovery constraint to 89% (1% decrease from nominal target), the size of the AOR formed increased by 4 orders of magnitude ( Fig. 4 (a) and (b)).
The relaxation of the recovery constraint from 89% to 88% yields a further increase of the AOR (Fig. 4 (b) and (c)), while the latter does not change upon relaxing the constraint down to 85% (Fig. 4 (c) and (d)). This behaviour can be explained by the change of the active constraint from recovery to purity.
Recall, from Figure 2 (a), that the obtained cost-optimal point from the Sobol sequence lies relatively further away from the purity constraint compared to the recovery constraint. This indicates that the recovery constraint is active, and is further proven by the increase in AOR size when the recovery constraint is relaxed. When the active constraint switches from recovery to purity, the region cannot expand further without violating the purity constraint because the identified AOR is centered around the cost-optimal design. It is noteworthy that if the cost-optimal solution from the NSGA-II were to be investigated as the NOP, both the recovery and purity constraints would need to be relaxed to see an increase in flexibility, as both constraints are active at that particular solution. In Fig. 5, the three relaxed cost-optimal designs are compared quantitatively. As anticipated above, the AOR size increases substantially (×4. 5) when the recovery constraint is relaxed from 89% to 88%, whereas the relative increase is quite modest (7%) with a further relaxation of the constraint down to 85% (Fig. 5 (a)). The corresponding multivariate proven acceptable ranges of the different cases are summarised in Fig. 5 (b). Generally, all three cases have relatively low flexibility, whereby a maximum disturbance of ≤ 4.5% on the three operating variables (v F , p H and p I ) can be accommodated by the design. In Fig. 5 (c), we show the corresponding distributions of the process KPIs within the AOR. We find that the KPI distributions for the 88% and 85% cases are essentially overlapping, in accordance with these two cases having virtually identical AORs. Not surprisingly, the mean of the distribution of recovery is reduced with increasing relaxation of the recovery constraint, and the distribution becomes more skewed towards lower recovery values. On the contrary, the distribution of purity expands more symmetrically and its mean remains the same for each design (including the original cost-optimal design).
This observation supports our previous hypothesis that purity becomes the active constraint in the relaxed designs. The behaviour of the mean of the distribution of the energy usage and capture cost (both increasing with relaxation) appears less intuitive, as one would expect the relaxed scenarios to consume less energy. However, these scenarios carry higher specific energy demand and cost, because less CO 2 is captured. Yet, the 88% recovery case has a mean capture cost of 62.47 $/tonne which is only 2% higher than the cost-optimal solution, while offering an AOR that is 63% larger than that of the 89% recovery case. Hence, this could represent an effective method for increasing process flexibility.
The framework has successfully quantified the impact of performance constraint relaxation on the process flexibility. In this case, a relaxation of the recovery constraint to 85% is not considered to be a worthy trade-off in the design, given the diminishing return on process flexibility. It is also worth noting that while this strategy does allow for a moderate increase in the process flexibility, it also demands that there is some decrease in the amount of CO 2 emissions captured from the power plant flue gas. Ultimately, at the industrialscale, such violation may not be desirable from an environmental perspective, as small changes in the recovery can lead to significant increases in the absolute plant emissions.
Flexibility by Design. We have used an iterative quasi-random grid search approach to find the design which gives the largest possible AOR, while meeting the original purity/recovery constraints. As shown in Fig. 3, we can see that this design that maximises flexibility lies at the center of the design space. The capture cost of the flexible design is 70.16 $/tonne, which represents an increase of 12.5% relative to the cost-optimal design. Therefore, we can infer that there is an inherent trade-off in the design between capture cost and flexibility. This trade-off will need to be effectively rationalised in the design workflow to yield carbon capture processes which are both economical and operable. Notably, different from the relaxed design case, it will be shown in the following that the higher cost of this new design case is associated with an improved performance of the separation.
We compare in Fig. 6 the most flexible design and the relaxed cost optimal design (recovery ≥ 88%). The most flexible design offers an AOR that is 13fold larger than that of the relaxed cost-optimal design ( Fig. 6 (a)). The larger AOR translates directly onto the width of the MPARs for p H , p I and v F , as shown in Fig. 6 (b). The most flexible design can now accommodate larger variations in the design decisions, namely of up to 10% (p H and v F ) and 20% (p I ). The cost-operability trade-off is visible also in the relative location of each design decision. For example, relative to the relaxed cost optimum design, the flexible design has a higher high pressure (p H ), and a lower intermediate pressure (p I ). The lower value of p I generates higher purity for the process by rejecting more nitrogen from the bed during blowdown. The higher value of p H increases the recovery of CO 2 by increasing the CO 2 affinity during the adsorption step. However, increasing the value of p H is achieved by operating the feed compressor at a higher pressure, increasing the electricity usage of the process. We thus expect the capture cost of the flexible design to be larger than the relaxed cost optimal design. The distribution of the KPIs for these two design cases offers additional insight into the cost-operability trade-off (Fig. 6 (c)). Across all KPIs, the flexible design is shown to have larger distribution ranges. This is expected as a larger AOR encompasses more combinations of the design decisions. For example, the nominal productivity of the two designs is similar (approx. 2 mol/m 3 /s), but the most flexible design shows a standard deviation of 0.15 mol/m 3 /s, which is 2.5x larger than the value observed for the cost-optimal designs. Notably, the purity and recovery distributions for the relaxed costoptimal design push against the respective constraints, whereas the most flexible design displays purity and recovery distributions shifted towards enhanced separation performance. To generate additional flexibility for the most flexible process design, the grid search algorithm needs to move the NOP away from the boundary of the design space. This means that the purity and recovery achieved by the process need to exceed the strict requirements to give space around the NOP. This is a key co-benefit of the most flexible design, wherein the flexibility of the process comes with a higher specific capture cost (13% higher) and specific energy consumption (20% greater) -but the performance of the separation is also increased. The most flexible design prevents a greater amount of CO 2 emissions from the power plant from reaching the atmosphere and the outlet CO 2 stream is purer and could therefore be suitable for use in a wider variety of downstream utilisation processes.

Conclusion
We have analysed the operational flexibility of an adsorption-based postcombustion CO 2 capture process through a design space identification framework. We discover that the design approach of minimising capture cost yields a process that is inherently inflexible. In practical scenarios of transient flue gas production, such design would fail to meet the commonly adopted purity-recovery (95%-90%) constraints on the produced CO 2 . We propose and compare two alternative design approaches aimed at introducing operational flexibility. First, we consider relaxation of the recovery constraint (down to 85%), while retaining the cost-optimal design as the nominal operating point.
This approach yields moderate flexibility (variation in the operating variables of up to 4.5%), but also demands that the capture rate of the plant decreases during disturbed operation (up to 7%). Second, we identify the operating point with maximum flexibility in the design space and observe that the process can accommodate for variations in the operating variables of up to 10-20%. However, the capture cost increases by 12.5% relative to the cost-optimal design, because this added flexibility is achieved by exceeding the purity-recovery constraints.
The transition to a sustainable and reliable energy system will encompass a growing proportion of baseline generation provided by intermittent renewables with load-balancing handled by low-carbon fossil fuel-fired power generation.
As such, the latter must be associated with a CO 2 capture process that can accommodate for disturbances in flue gas conditions resulting from the load balancing requirements. The results herein demonstrate a trade-off between process economics and process operability, which must be effectively rationalised to integrate CO 2 capture units in low-carbon energy systems. In this context, future work must consider the integration of constraints related to the process operability within the design framework to arrive at capture processes which both have an acceptable capture cost, and are sufficiently flexible to handle highly transient flue gas production. Such information should be obtained by detailed model-based control studies using realistic process disturbance data as an input to understand the required level of flexibility to arrive at a controllable process design and operational scheme.