In this study, stochastic uncertainty analysis is performed on a steady-state CO₂ capture model of a typical solvent-based full-scale absorption process (Figure 1). The case consists of removing CO₂ in the flue gas generated from a cement production plant using 30 wt% monoethanolamine (MEA) solvent. The process consists of five major pieces of equipment which are assessed in this study; an absorber column, a stripper column, a lean-rich heat exchanger, a cooler, and a reboiler. The flue gas received from the cement plant is first cooled in the direct contact cooler (DCC) to approximately 40°C and subsequently introduced to the absorber. The flue gas then flows upwards through the absorber countercurrent to the lean solvent flow (cold lean amine stream) where the CO₂ in the flue gas reacts with the solvent. The solvent heats as it gradually absorbs CO₂, with the temperature inside the absorber typically being between 40°C and 60°C and at 1 atm. The treated gas is then sent to a water wash column and vented to the atmosphere, while the condensed water is recovered and recycled back to the rich solvent (cold rich amine stream). The water wash unit is used to control the amount of water in the entire system as well as to reduce degradation products in the treated gas. The condensed water from this unit is recycled back to the rich solvent pump. The rich solvent from the bottom of the absorber is then transferred to the top of the stripper via a lean rich heat exchanger. In the stripper, CO₂ and MEA solutions were separated from the rich solvent mixture by heating between 110°C and 120°C and at a slightly higher atmospheric pressure of 1.8–2 atm. Typically, a slightly higher pressure than atmospheric pressure is selected for the stripper to gain advantage of reducing energy and sizing requirements. In this study, this pressure is chosen to match similar operating conditions implemented in the CO₂ capture from a cement plant process model for the CEMCAP project (Voldsund et al., 2019). The stripper is connected to the reboiler, providing heat requirements for solvent regeneration. The regenerated solvent (hot lean amine stream) is then pumped back to the absorber via the lean/rich heat exchanger that allows heat recovery from the hot lean solution to the cold rich solution to reduce the temperature. A trim cooler is used to further cool the lean solution before entering the absorber. The high-purity CO₂ from the top of the stripper is separated from the solvent in a flash separator (condenser unit) and is sent for additional conditioning to reach the transport specifications. The condensate stream (Condenser to Mix01 stream) from the separation is then recycled back to the top of the stripper column.

The steady-state rate-based CO₂ capture process model shown in Figure 1 was simulated using the flowsheet simulator CO2SIM version 7.1.0.5 (Einbu et al., 2022; Tobiesen et al., 2007). This is proprietary in-house software developed by SINTEF and NTNU which is specifically dedicated to model solvent-based CO₂ absorption post-combustion. The existing process setup was adapted as a basis for the MEA-based CO₂ capture simulation model (Tobiesen et al., 2017). While the adopted reference case in the existing simulation includes a DCC and a flue gas fan, these are here excluded as they are not impacted by uncertainties in solvent properties. This current model and the specific flowsheet tool have been selected for this study as it is an advanced platform specifically for modeling the CO₂ absorption process and for developing various solvent systems. It is a well-validated process modeling tool against pilot plant experimental data over a wide range of operating conditions and with various amine solvents. Performing uncertainty analysis for a complex model can be computationally demanding. The process was simulated using the inbuilt CO2SIM soft model thermodynamic fluid package expressed as temperature- and loading-dependent polynomial correlations to account for the vapor liquid equilibrium (VLE). The simulator also includes other important thermo-physical solvent property submodels to represent the heat and mass transfer, chemical reaction kinetics, and internal column hydraulics required to solve the complex reactive absorption process. More comprehensive knowledge about the underlying rate-based model implementation, including the soft model for VLE and property submodels, is described in detail in Einbu et al. (2022), Kvamsdal et al. (2011), Tobiesen et al. (2008), and Tobiesen et al. (2007).

In the present study, the case of CO₂ capture from a cement plant is considered based on the Horizon 2020 CEMCAP project (Gardarsdottir et al., 2019; Voldsund et al., 2019). The design of the CO₂ capture plant is thus based on Anantharaman et al. (2017) and Voldsund et al. (2018). The deterministic baseline case with the flue gas conditions from the stack during the second part of the year is used for the equipment sizing and economic evaluation in Gardarsdottir et al. (2019). Therefore, the flue gas composition and specification of this scenario will be considered for the process simulation. The composition is extracted directly from the inlet to the absorber (outlet stream DCC) stream data (Voldsund et al., 2019). Table 1 shows the specific input data of the flue gas stream provided in the CO2SIM simulator.

The selected operating parameters for the main units as input to the CO2SIM simulator are summarized in Table 2. The approach here is to simulate the process model using the plant design specification as the CEMCAP simulation case using Aspen HYSYS V9 (Voldsund et al., 2019), except for some inputs that need to be adjusted to achieve a similar 90% CO₂ capture ratio scenario since the CO2SIM simulator is used in this study. In addition, the following specifications and assumptions are required to solve the developed close-loop flowsheet of the rate-based model uniquely in the CO2SIM simulator,

a) Sulzer Mellapak 250Y structured packing is adopted for both absorber and stripper columns in the CO2SIM simulator.

Solvent characteristics such as absorption capacity, kinetics, mass transfer, energy performance for solvent regeneration, and thermal and chemical stabilities are typically sources of uncertainty for the performances and design of the solvent-based CO₂ capture process, hence impacting its cost (Borhani and Wang, 2019). An accurate knowledge of solvent properties may thus be essential to assess CO₂ capture processes precisely. Solvent properties are typically represented using appropriate semi-empirical and empirical correlations which are then incorporated into the process model. While numerous correlations are reported in the literature, these correlations may differ in their accuracy and applicability depending on the specific solvent-based CO₂ capture system. The accuracy and applicability of these submodel correlations are induced by uncertainties that can arise from different sources such as measurement accuracy and regression uncertainties. By using the different options for solvent property models in rate-based capture models, significant prediction variations can be encountered, especially for the CO₂ absorption efficiency which defines overall capture performance (Kvamsdal and Hillestad, 2012; Luo and Wang, 2017; Mota-Martinez et al., 2017; Putta et al., 2017a; Putta et al., 2017b).

As we previously discussed (Kuncheekanna and Jakobsen, 2023; Kuncheekanna et al., 2020), the MEA solvent property submodels were quantified as the uncertain stochastic parameters of the planned uncertainty analysis. The corresponding submodels are based on the correlation models adopted in the CO2SIM tool. Therefore, this research focused on the characterization and quantification of the uncertainty in the MEA property submodels selected based on the solvent property packages applied in this simulator. The selected list of the stochastic parameters along with the uncertainty range adopted is shown in Table 3.

The uncertainties in the submodel prediction values are represented by a probability density function (PDF). Hence, the characterization of uncertainty may benefit from summarizing all the experimental dataset and fit distribution profiles for each of the solvent submodels considered to give a more credible distribution range. However, this is a challenging and time-consuming endeavor when multiple model correlations are available for the specific solvent property. In this study, the uncertainty range for the dedicated solvent property submodels are selected based on the literature and expert knowledge. The uncertainty range based on expert opinion implies that it is based on the degree of belief in the uncertainty distribution based on existing knowledge. For this study, this judgment pertains to the collected information from various experimental studies within the solvent absorption group in NTNU. Regarding the literature-based uncertainty range, the range is chosen either based on the maximum absolute percent deviation (MAD) or average absolute deviation (AAD) values found in the respective references shown in Table 3. The MAD and AAD values typically depict the difference between the experimental dataset and the outputs predicted by the correlation submodels. We have also previously explained this (Kuncheekanna and Jakobsen, 2023). The uncertainty in a submodel is assumed to vary from their nominal (i.e., deterministic) values estimated in the simulation where a wider range implies that the solvent property is more uncertain and a narrower range is less uncertain. It was furthermore assumed that each uncertain submodel has a normal type of uncertainty distribution.

As our aim is to understand the impact of solvent property uncertainties on the overall design and cost of the capture process, the impact of these uncertainties on the following four aspects will be computed.

• The heat duty of the reboiler, which impacts the required equipment size and thus the cost;

With the absorber and desorber characteristics being set, these fours parameters are those with the strongest impact on the plant design and cost (Gardarsdottir et al., 2019). Further details on how these parameters are subsequently linked to cost are presented in Section 2.3.

A Monte Carlo simulation (MCS) approach is employed here in order to perform the uncertainty analysis. This is done by using the UQLab software package V2.0 developed by ETH Zurich (Marelli and Sudret, 2014). This open-source MATLAB-based tool supports interfaces with existing third-party software in a nonintrusive approach also known as “black box-type”. As the CO₂ capture process flowsheet built in CO2SIM can be executed in MATLAB from the GUI functionality, the UQLab tool can be rather easily integrated with CO2SIM to evaluate the impact of the desired uncertainties. Based on the UQLab user manual, the model module (Lataniotis et al., 2015), the coupling of CO2SIM is achieved using a code wrapper—a plug-in that allows the execution of the external software as a simple function that possess a similar input–output format to UQLab algorithms.

By exploiting the different software interfaces, the overall stochastic modeling framework setup shown in Figure 2 is employed in this work. The computational setup of the UQLab tool consists of creating three required modules with specific configurations: (1) an input module, (2) a model module, and (3) an analysis module. The first step to create an input module in UQLab is to define the uncertain variables by assigning a statistical description using probabilistic distribution. A probability distribution is expressed in terms of a probability density function (PDF) that requires the specification of distribution moments or parameters, such as mean and standard deviation. The marginal distribution for the selected uncertain stochastic parameters from Table 3 are estimated based on the 95% confidence interval of the uncertainty range. The nominal value (i.e., mean) is determined by the model correlation output, and the standard deviation value is estimated based on the 95% confidence interval following a standard normal distribution.

The second step, the computational model created as a MATLAB m-file, is used as a model module in the UQLab platform. In the final step, the uncertainty analysis module can be deployed where the Monte Carlo method is applied. The basic framework of the Monte Carlo simulation technique consists of generating sample points (i.e., stochastic values) from the selected solvent property submodels. In this case, the samples were drawn from the assumed probability density function (PDF) for each of the uncertain submodels. The joint probability distribution for all eight uncertain submodels was constructed with the assumption that all eight were independent. This implies that the resulting samples are a product of the marginal distribution of each of the submodels. For the purpose of the analysis, a 1,500 sample size was used, and a series of repeated simulation evaluations were then performed to propagate the uncertainties simultaneously across the full CO₂ capture process model. The choice of sampling strategies is necessary, and as the UQLab tool includes a variety of sampling strategies, the Sobol sequence strategy was implemented. According to our previous study (Kuncheekanna and Jakobsen, 2023), the Sobol sequence strategy was computationally more efficient to achieve the targeted accuracy for the KPI. This was measured through convergence analysis based on the sensitivity of the rate of convergence with sample size. Therefore, a sample size of 1,500 equivalent to the number of simulation runs was chosen for this study. To make inferences about the uncertainty in the model predictions, the resulting model outputs with respect to statistical outputs (i.e., minimum, maximum, percentiles, and mean) were then used to construct the distribution profiles using PDF plot. Subsequently, the lower and upper uncertainty bounds were then plotted from the deterministic output values generated from the simulated baseline capture case.

Additional computational details and functionalities of the UQLab required to complete the present uncertainty analysis study are described in Kuncheekanna and Jakobsen (2023).

The uncertainties in the eight solvent property submodels were propagated simultaneously through the CO₂ capture process model built in the CO2SIM flowsheet simulator. The stochastic nature of the influenced submodel property values was quantified based on a 95% confidence interval for the standard normal distribution. As a result, the distribution profiles for all the KPIs are statistically visualized in the PDF plot shown in Figure 4. On the generated PDF, the mean, 2.5^th, and 97.5th percentile lines which are the two extremities for a 95% confidence interval are also shown in the figure to describe the performance characteristics of the distribution. The figures also display the different key percentile, the deterministic baseline described in Section 3.1, and the kernel fit ¹ represented by the fitted red line. In addition, Table 5 shows the resulting statistical indicator values (i.e., mean, minimum, maximum, range width, and percentiles) which can be inferred from the PDF output. The minimum and maximum values signify the lower and upper bounds of the derived PDF plot with a range width value computed as the difference between the maximum and minimum value.

Overall, significant uncertainty exists in predicting all performance parameters based on the ranges obtained. This denotes that the larger the density distribution spread, the larger the impact of uncertainties on the model predictions. However, there was a varying extent of uncertainty found in the different targeted outputs. In general, based on the minimum to maximum range values examined, the lowest impact of solvent property uncertainty is shown for a reboiler duty parameter with a range of 94.4–100.2 MW (i.e., 3.28% lower and 2.72% higher than the deterministic value of 97.5 MW), while the highest impact was shown for a lean loading parameter with a range of 0.165–0.223 mol CO₂/mol MEA (i.e. 14% lower and 16% higher than the deterministic value of 0.19 mol CO₂/mol MEA). Beyond these two ends of the spectrum, the tested output going from the lowest to the highest impact in uncertainties are the condenser duty (between −4.5 and +1.8% compared to the deterministic value of 32.5 MW), the specific reboiler duty (between −4.3% and +5.6% compared to the deterministic value of 3.83 MJ/kgCO₂), the rich loading (between −5.5% and +3.7% compared to the deterministic value of 0.482 mol CO₂/mol MEA), the CO₂ capture ratio (between −5.2% and +3.7% compared to the deterministic value of 90%), and the lean rich heat exchanger duty (between −7.3% and +3.4% compared to the deterministic value of 92.1 MW). These results indicate that given the prescribed uncertainty in the solvent property submodels, it is possible that the process model is not able to precisely predict all the KPIs, and the actual model predictions falls between the bounds for some targeted values.

Furthermore, while the lean rich heat exchanger duty showed a significant variability range (Figure 4e), it also exhibits a substantial negatively skewed distribution profile. The skewness for a probability distribution describes the degree of asymmetry observed for the given dataset. A median value corresponding to a 50th percentile output of 92.9 MW establishes that the distribution is indeed negatively skewed (also known as “left skewed” for statistical notation) as the mean value for the duty of 92.5 MW is lesser than the median value. In a symmetrically distributed profile, the mean and median should hold an equivalent value. Therefore, in practice, the uncertainties are unlikely to result in a significantly larger duty than the deterministic value but could result in a significantly smaller duty.

On the other hand, the distribution profiles for all the other KPIs present almost non-skewed profiles, where the distribution curves are not distorted more toward the right or left, such as for the lean rich heat exchanger duty profile. While the specific reboiler duty, lean, and rich loading shown in Figures 4c, f,g exhibit symmetrically distributed profiles which are demonstrated through their similar mean and median value (i.e., at 50th percentile), the rest of the parameters (CCR in Figure 4a, reboiler duty in Figure 4c, and condenser duty in Figure 4d) present a marginal difference between mean and median value of 0.18%, 0.03%, and 0.07% respectively, which are statistically insignificant. Therefore, these distributions can be concluded to be as symmetrically distributed as the rest. Although all the uncertain inputs are characterized with a normal distribution profile, it can be concluded from this observation that it does not lead to the expectations that a similar distribution type should be matched for the process model responses as shown for the lean rich heat exchanger duty profile.

It is also worth noting that, overall, the distributions’ mean is in good accordance with the deterministic value, as the maximum discrepancy is 2.1% (obtained for lean loading). The inclusion of uncertainties in the process model can result in predictions that are higher or lower than the deterministic value: CO₂ capture ratio 0.74% lower, SRD 0.78% higher, reboiler duty 0.6% lower, condenser duty 0.1% lower, lean loading 2.1% lower, and rich loading 0.62% higher. A point of interest compared to our previous research (Kuncheekanna and Jakobsen, 2023) is that the difference between deterministic and mean CCR are more pronounced, while there were virtually identical previously. This can be linked to both the difference in underlying models and/or uncertainty interaction between different parts of the process.

To understand the full impact of these uncertainties, it is important to understand how these will impact the design of key equipment and the overall cost of the process. The obtained distribution of the heat exchanger’s direct cost and CCR are shown in Figures 5a–d with comparison to the deterministic and CEMCAP values. On the other hand, Figure 6 describes the obtained distribution in CO₂ avoidance cost, also in comparison with the deterministic and CEMCAP value. Table 6 summarizes the distribution characteristics (min, max, key percentiles, etc.), the deterministic, and CEMCAP values corresponding to these two sets of figures.

In terms of equipment design, the results show that oversizing the heat exchangers with 4% (i.e., to supply the maximum value of the duty distribution) would be sufficient to guarantee that the required duty could be supplied independently of the uncertainties. It is worth noting that this is within the typical 10% overdesign factor considered in engineering practice. However, to not reduce this design margin, which may provide operational flexibility during operations, it is here assumed that heat exchange areas and cost will also be updated based on the uncertainties. In any case, as the heat exchanger costs are typically linear to the duty, the uncertainty in equipment cost is similar to the uncertainties in duties and is thus limited in extent as shown in Figures 5a–c. To specify here, the mean value for the condenser direct cost is similar to the deterministic value; hence, the mean line is not observed in Figure 5b.

Ultimately, it is important to look at the CO₂ avoidance cost, which is the most important parameter to consider when seeking to understand the impact of uncertainties on the cost of the process. The results show that the calculated CO₂ avoidance cost ranges from 83.8 to 78.7 €/ton CO₂. The deterministic CO₂ avoidance cost (79.6 €/ton CO₂) is rather close to the lower end of the range, while the mean value (81.3 €/ton CO₂) is closer to the middle of the uncertainty range. Considering that these uncertainties are only linked to solvent properties, the resulting 5.3% uncertainty range is significant. Interestingly, most of this uncertainty seems to be linked to the uncertainty in CCR, which impacts the amount of CO₂ avoided in the CAC calculation. A possibility to reduce the CCR (and thus cost) uncertainty could be to increase the absorber height. However, as we indicated earlier (Kuncheekanna et al., 2020), ensuring that a 90% capture rate is met with high confidence may require drastically increasing the absorber height. Hence, confirming the optimal height to achieve a 90% CCR via pilot testing might be the best way to reduce the impact of solvent property uncertainties on the CCR and, ultimately, the CO₂ avoidance cost.