ScienceDirect Optimal steady-state design of a post ...

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 63 (2014) 1608 – 1616

GHGT-12

Optimal steady-state design of a post-combustion CO2 capture plant under uncertainty Sami Saeed Bahakim, Luis A. Ricardez-Sandoval* Department of Chemical Engineering, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

Abstract This paper presents a study on the effect of process uncertainty on the optimal design of a CO2 capture plant. A recent method in the optimal design of large-scale chemical processes under uncertainty, which employs Power Series Expansion (PSE) models to approximate the process constraints, has been used in this work due to its computational benefits. Uncertainty in the CO2 content in the flue gas stream entering the plant is assumed; the problem under analysis aims to find the most economically feasible design, by sizing the plant’s process equipment, as well as obtaining its optimal operating conditions, in the presence of uncertainty. The results show that process uncertainty have a direct effect on the sizes of the absorber and stripper columns and operation of the reboiler duty, whereas the cross heat exchanger and condenser’s heat transfer areas are not significantly affected. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2013 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of GHGT. Peer-review under responsibility of the Organizing Committee of GHGT-12 Keywords: Type your keywords here, separated by semicolons ;

1. Introduction Among all the greenhouse gases, carbon dioxide is considered to have the most impact on global warming [1–4]. CO2 capture and storage is a strategy that has been adopted in chemical industries for controlling CO 2 emissions [5– 7] where post-combustion using chemical absorption [8–11] is a developed method for capturing CO2 from flue gas. An MEA-based post-combustion CO2 capture unit consists of an absorption tower where the amine solvent comes into contact with the entering flue gas (rich in CO2), a stripping column to regenerate the amine solvent using heat supplied by reboiler steam, along with other heat transfer equipment. There have been numerous studies to obtain the

* Corresponding author. Tel.: +1 519 888 4567 ext.38667; fax: +1 519 888 4347. E-mail address: laricard@uwaterloo.ca

1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of GHGT-12 doi:10.1016/j.egypro.2014.11.171

1609

Sami Saeed Bahakim and Luis A. Ricardez-Sandoval / Energy Procedia 63 (2014) 1608 – 1616

optimal design and operation of MEA-based post-combustion CO2 capture plants [12–19]. These studies were conducted at steady-state operation and assume that all the model parameters are completely known. However, uncertainty in the input variables or parameters is almost inherent in every process due to errors in measurements or lack of accurate process knowledge. Therefore, optimal designs of the CO 2 capture plant obtained using steady-state calculations may not be feasible while operating under process uncertainty. Studies of optimal design under uncertainty have been widely reported in the field of process systems [20–24]. With respect to CO2 capture plants, there have been several studies that have accounted for uncertainty in the prices of economic parameters (such as fuel, CO2, electricity) to obtain the optimal timing of investments or technology selection for power generation plants coupled with CO2 capture units [25–32]. Nevertheless, those studies have not analyzed the effect of processlevel uncertainties on the optimal design and operation of the CO2 capture plant flowsheet, which, to the authors’ knowledge has not yet been reported in the open literature. This article presents a study of the effect of process uncertainty on the optimal design of a CO 2 capture plant. A recent ranking-based approach for optimal design under uncertainty proposed by Bahakim et al [33] uses a Power Series Expansions (PSE)-based model to approximate large-scale nonlinear chemical processes has been used in this work to address the optimal design. The approach is efficient because it does not require simulating the plant model many times. Flue gas from power plants represents the main input to amine-based CO2 capture plants, and thus uncertainty in this stream will be considered while designing the main process equipment of the plant. The organization of this paper is as follows: Section 2 describes the PSE-based method in approximating actual nonlinear models, along with the optimal design under uncertainty formulation. An explanation of the CO 2 capture process along with the implementation and formulation of the problem is presented in Section 3. Results and discussions are presented in Section 4. Concluding remarks are presented in Section 5. 2. Optimal process design under uncertainty: PSE-based method A process model J of the system under analysis is assumed to be available for simulations and is represented as follows:

J(d, κ, x, γ, u, δ) ? 0

(1)

where the model outputs and inputs of the process are denoted by γ and u, respectively, κ is the model parameters, x represents the state variables, and d is the vector of design variables. Uncertainty in the model inputs or parameters is denoted by δ and is assumed to follow a certain probability distribution function (PDF) with distribution parameters ψ , i.e.,

f c ~ PDF(ψc )

c ? 1,2,...C

(2)

where each of the c uncertain variables will be assigned a specific PDF with its own distribution parameters ψ c . The choice on the PDF usually comes from process heuristics or process experience or plant data analysis. Typically, normal or uniform distributions are considered reasonable assumptions as they fit well most of the engineering applications [34]. Once the PDF description of the uncertainties are set, N random Monte Carlo sampling from each PDF can be generated to obtain a set of N uncertain realizations for each uncertain parameter. To accommodate the input uncertainties, the optimal design need to satisfy the process constraints to become feasible. The process constraints are formulated as follows:

h(κ, x, γ, u, δ) 0

(3)

where h represent the set of process restrictions such as environmental, operational or safety constraints. In the present method, the actual process constraints h are approximated by PSE-based models ( h PSE ) as follows:

1610


h PSE (δ) ? h( δ ) - S (1) (δ / δ ) S (1) ? S ( 2) ?

•h •δ

1 (δ / δ )T S ( 2) (δ / δ ) - ... 2

δ?δ

(4)

• h 2

•δ 2

E[δ] ? δ ,

δ?δ

h Œ h,

h PSE Œ h PSE

where S (i ) refers to the ith sensitivity term of constraint function h, i.e., the first and second terms represent the Jacobian and Hessian matrices of the process constraint function h, respectively; δ are the steady-state values of the uncertain variables. hPSE is an approximation to the actual nonlinear process constraint h ; a thorough discussion on the approximation used by the present method is presented in [33]. In this method, a probabilistic ranking-based approach has been adopted, where each constraint will be assigned a user-defined probability of satisfaction ( Prh ) value which will act as the minimum probability that particular constraint is expected to remain feasible when operating under uncertainty. From the process constraint histogram obtained by evaluating the PSE-based model for all sampled uncertainty realizations, an extreme possible value yhPSE with respect to the input probability ( Prh ) can be calculated as shown in Figure 1.

Figure 1 Schematic representation of the process constraints’ distributional analysis.

The extreme possible value yhPSE refers to the highest possible value that the constraint will attain ( Prh %) of the time when operating under input uncertainties. Therefore, the probabilistic form of the process constraints can be expressed as follows: P*h(κ, x, γ, u, δ)

0+ Prh

yhPSE (Prh ) 0

(5)

The choice of the user-defined Prh values is an engineering decision that constitutes a tradeoff between reduced constraint violations and increased plant costs. Critical (safety) constraints are usually assigned very high values to ensure safe operation of the process. When the process constraint is assigned a probability limit close to unity ( Prh › 1 ), conservative designs are obtained and this is called the worst-case approach. Based on the above explanations, the optimal design of a process system under uncertainty can be formulated as follows [33]:

1611


min Φ ? CAP(d, δ) - OP(κ , x, γ , u, δ)

η?[d ,u ]

s.t.

J (d, κ , x, γ , u, δ) ? 0

y hPSE (Prh ) 0 dl

d

du

ul

u

uu

hPSE Œ h PSE

(6)

The above optimization formulation minimizes the objective cost function Φ , typically described in terms of the capital (CAP) and operating (OP) costs, by selecting feasible process designs d and operating conditions or model inputs u, which are aimed to satisfy the process constraints, at minimum cost, under process uncertainty. More details about the ranking-based method used in this work can be found in [33]. 3. Optimal design of a post-combustion CO2 capture plant Figure 2 presents a schematic diagram of a typical amine-based carbon capture unit. Flue gas rich in CO2 enters the absorber column where a solvent, typically monoethanolamine (MEA), absorbs the CO2. To regenerate the amine solvent (now rich in CO2), this is heated with steam from a reobiler inside a stripping column, resulting in a CO2 product at the top of the stripper column whereas the regenerated amine solvent at the bottom is recycled back to the absorber to continue removing CO2. In addition, the process includes a cross heat exchanger, which maintains the process temperatures within limits, and a condenser unit at the top of the stripper to ensure high CO2 product purity is achieved.

Figure 2 Schematic diagram of the main units of a typical amine-based carbon capture unit.

The problem considered in this work aims to optimize the design of the main process equipment and the operation of the CO2 capture (CC) plant, i.e., the heights and diameters of both packed columns, the heat transfer areas of both the cross heat exchanger and the condenser, and the heat duty of the reboiler. Thus, the decision variables for this problem are as follows: d CC ? [ H abs, H strp , Dabs, Dstrp , AHX , Acond ] u CC ? [Qreb ]

ηCC ? [d CC , u CC ]

(7)

1612


Moreover, the following process constraints have been considered for the present analysis:

0.95 / l 0.95 / X

Treb / 383 393/ Treb

Tlean / 313 315 / Tlean

0

(8)

0

(9)

0

(10)

0

(11)

0

(12)

0

(13)

The first two constraints are performance constraints for minimum CO2 removal rate and CO2 product purity, respectively. The rest are operational constraints that are aimed to maintain the feasible operation of the process, e.g., the temperature constraint on the reboiler aims to prevent solvent degradation. All of the above constraints has been reformulated as in (5), i.e., in a probabilistic form. For example, constraint (8) has been formulated as follows:

yconstraint(8)

0

P*0.95 / l

0+

Prconstraint(8)

(14)

In addition to compliance with the constraints, the optimal design of a CO2 capture (CC) plant aims to minimize the economic costs consisting of the capital (CAP) and operating (OP) costs: ΦCC ? CAPCC - OPCC

CAPCC ? Cabs - C strp - C HX - Ccond OPCC ? Creb

(15)

where the capital costs include the costs of the main process equipment, i.e., absorber ( Cabs ), stripper ( C strp ), cross heat exchanger ( CHX ) and condenser ( Ccond ), whereas Creb denotes the operating costs associated with the reboiler heat duty ( Qreb ). The detailed expressions for these cost functions are presented [35]. In this study, the pilot plant presented by Dugas [36] on a CO2 capture plant using MEA has been used as the base plant, which design and operation is presented in Table 1. The cost of this plant is evaluated using the capital and operating cost functions shown in (14). Detailed equipment specification and operating conditions of the CO 2 plant can be found in [5,6,36]. The CO2 capture process has been modeled in Aspen HYSYS and validated with the base-case pilot plant of Dugas [36]. Since in this work the effect of uncertainty on the optimal design will be analyzed using this Aspen HYSYS model, a base design that has also been obtained from the same source model for comparison purposes. Therefore, the steady-state optimization (without uncertainty) of the CO2 plant has been performed and also presented in Table 1. 4. Effect of uncertainty on the optimal design of CO 2 capture plant In this work, the effect of uncertainty in the CO2 content in the flue gas stream (%CO2), on the design of the plant is studied. The uncertainty in this input variable is assumed to follow a normal distribution with the following distribution parameters: %CO2

~ N (17.5 mol %, 0.175 mol %)

(16)

1613

Sami Saeed Bahakim and Luis A. Ricardez-Sandoval / Energy Procedia 63 (2014) 1608 – 1616 Table 1 Base case plant design and the optimal steady-state plant design.

Decision variables

Dugas plant design [5,6,36]

Optimal steadystate (base-case)

153.6 6.1 0.43 6.1 0.43 22.47 14.40

172.12 6.1 0.3005 3.05 0.3011 19.80 11.10

4.66E+04 6.17E+03 5.27E+04

3.58E+04 7.42E+03 4.33E+04

Reboiler duty, Qreb (kW) Absorber height, Habs (m) Absorber diameter, Dabs (m) Stripper height, Hstrp (m) Stripper diameter, Dstrp (m) Heat trans. area, AHX (m2) Heat trans. area, Acond (m2) Annualized Costs CC ($/y) OC ($/y) Total Costs ($/y)

As mentioned is Section 2, the PSE-based method gives the user an extra degree of freedom in selecting the minimum probability of satisfaction Prh for each constraint. In the current study, a value of 0.85 will be chosen for each of the constraints shown in (8)-(13), meaning that these constraints will be satisfied at least 85% of the time when operating under the uncertainty described in (16). PSE-based approximation models as shown in (4) were used to obtain the distributions of each constraint as a result of N randomly sampled uncertain realizations in %CO2. In order to select which expansion order (q) in the PSE approximation is most suitable for this problem and to demonstrate the convergence property of this method, the problem was solved several times using different expansion orders from q=1 to q=6. Figure 4 shows the PSE approximated fitting (in blue) to the actual distribution (histogram) of the CO2 capture rate constraint (8), which was obtained by random Monte Carlo simulations, and the optimal designs obtained using the different expansion orders are presented in Table 2. Table 2 Optimal steady-state plant designs under uncertainty. Decision variables

q=1

q=2

q=3

q=4

q=5

q=6

Reboiler duty, Qreb (kW)

184.5000

195.4961

194.2464

194.5281

197.2880

196.1544

Absorber height, Habs (m)

6.1

6.1

6.1

6.1

6.1

6.1

0.3950

0.3794

0.3401

0.3390

0.3345

0.3371

3.05

5.3375

5.3375

5.3375

5.3375

5.3375

0.3150

0.4322

0.6365

0.6377

0.6382

0.6379

Heat trans. area, AHX (m )

10.7991

10.8259

10.8553

10.8260

10.8259

10.8262

Heat trans. area, Acond (m2)

19.7984

19.7987

20.3930

20.3932

20.3935

20.3928

CC ($/y)

3.76E+04

4.12E+04

4.43E+04

4.44E+04

4.43E+04

4.44E+04

OC ($/y)

7.42E+03

7.86E+03

7.81E+03

7.82E+03

7.93E+03

7.88E+03

Total ($/y)

4.50E+04

4.91E+04

5.21E+04

5.22E+04

5.22E+04

5.22E+04

1.489

2.031

2.934

3.832

5.089

6.394

Absorber diameter, Dabs (m) Stripper height, Hstrp (m) Stripper diameter, Dstrp (m) 2

Cost

CPU Time (h)

Figure 3 show that, as the expansion order is increased, the more accurate the PSE approximation seems to fit the actual distribution. By inspecting the results shown in Table 2 it shows that the computational time increases rapidly as higher expansion order is used, thus discouraging the use of high-order PSE approximations if unnecessary. Table 2 also shows that the optimal designs converge at q=3, i.e., the maximum difference in the total costs with respect to the design obtained when q=6 is less than 1%. Therefore, a PSE expansion order q=3 is justified for this problem as it is 23% faster than q=4 and 54% faster than q=6 in obtaining the optimal designs.

1614


Figure 3 PSE fitting for the distribution of the CO2 capture rate constraint using different expansion orders.

From Table 2, it is clear that the effect of uncertainty in the flue gas stream’s CO 2 composition has a significant effect on the optimal design previously obtained without considering uncertainty (see Table 1). Larger absorber and stripper columns (both diameters and heights) as well as higher reboiler duty were obtained when compared to the optimal steady-state design without uncertainty (Table 1). With uncertainty in the flue gas stream’s CO 2 composition, there will be instances when the CO2 composition is higher than the nominal steady-state value. Therefore, to maintain the same plant performance, larger absorber is needed to maintain the CO 2 removal rate, and larger stripper and reboiler heat duty is required to maintain the CO 2 product purity on target, i.e., a minimum of 95% purity. Although this larger plant is 5% and 24% higher in operational and capital costs than that obtained at nominal conditions (base-case in Table 1), respectively, that plant design satisfies the constraints of this process (8)(13) according to the user-defined 85% probability of satisfaction (Figure 4a). On the other hand, the optimal steady-state design that did not consider uncertainty at the design stage was found infeasible when operating under uncertainty with more than 80% violations (Figure 4b). Note that the cross heat exchanger and condenser areas obtained from the present uncertainty analysis and shown in Table 2 remained relatively unchanged in the presence of uncertainty.

Figure 4 Frequency histograms for the CO2 capture rate constraint under single uncertainty for (a) Scenario B design, and (b) the base-case design.


1615

5. Conclusions This study evaluates the effect of process uncertainty on the optimal design of a post-combustion CO2 capture plant using a novel ranking-based method has been presented. The search for the optimal plant’s design is carried out by searching for the sizes of the key process units included in the CO 2 capture plant (e.g., packed column’s height and diameters, heat exchanger and condenser areas) that minimizes the process economics in the presence of uncertainty in the flue gas stream conditions. The optimal designs obtained under uncertainty yielded a larger sized plant and needed more utility (i.e., reboiler duty). As a result, these designs were more expensive than the actual plant’s design and the design obtained from optimization (without considering uncertainty) with higher operational and capital costs. However, while the present method yielded larger and thus more expensive designs, it ensures that the environmental and operational constraints are satisfied according to the user-defined probability of satisfaction, whereas the base-case design did not meet the CO2 removal rate target most of the time when operating under uncertainty. Therefore, the designs presented in this study will potentially lead to savings since the plant’s CO 2 removal rate may not need to be reduced, or the plant itself may not need to be shut down, when changes in the flue gas stream’s conditions may occur. Instead, the proposed designs will ensure that the plant can continuously operate at its design specifications since it can accommodate the potential changes that may occur in the fossil-fired power plant’s operation due to varying changes in the electricity demands. Acknowledgements The authors would like to acknowledge the financial support provided by the United Mining Investments Co. (UMIC) to carry out the research work presented in this article. References [1] Nuchitprasittichai A, Cremaschi S. Sensitivity of amine-based CO2 capture cost: The influences of CO2 concentration in flue gas and utility cost fluctuations. Int J Greenh Gas Control 2013;13:34–43. [2] Zhang X, Duncan IJ, Huang G, Li G. Identification of management strategies for CO2 capture and sequestration under uncertainty through inexact modeling. Appl Energy 2014;113:310–7. [3] Zhang X, Huang G. Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program. J Hazard Mater 2013;246-247:257–66. [4] Zhang Y, Chen H, Chen C, Plaza JM, Dugas R, Rochelle GT. Rate-Based Process Modeling Study of CO2 Capture with Aqueous Monoethanolamine Solution 2009:9233–46. [5] Harun N, Nittaya T, Douglas PL, Croiset E, Ricardez-Sandoval L a. Dynamic simulation of MEA absorption process for CO2 capture from power plants. Int J Greenh Gas Control 2012;10:295–309. [6] Nittaya T, Douglas PL, Croiset E, Ricardez-Sandoval L a. Dynamic modelling and control of MEA absorption processes for CO2 capture from power plants. Fuel 2014;116:672–91. [7] Metz B, Davidson O, de Coninck H, Loos M, Meyer L, editors. Special report on carbon dioxide capture and storage, Intergovernmental Panel on Climate Change. Cambridge University Press; 2005. [8] Hedin N, Andersson L, Bergström L, Yan J. Adsorbents for the post-combustion capture of CO2 using rapid temperature swing or vacuum swing adsorption. Appl Energy 2013;104:418–33. [9] Plaza MG, González a. S, Pevida C, Pis JJ, Rubiera F. Valorisation of spent coffee grounds as CO2 adsorbents for postcombustion capture applications. Appl Energy 2012;99:272–9. [10] Wang M, Lawal A, Stephenson P, Sidders J, Ramshaw C. Post-combustion CO2 Capture with Chemical Absorption : A State-of-the-art Review. Chem Eng Res Des 2011;89:1609–24. [11] Nittaya T, Douglas PL, Croiset E, Ricardez-Sandoval LA. Dynamic Modelling and Evaluation of an Industrial-Scale CO2 Capture Plant Using MEA Absorption Processes 2014. [12] Rodríguez N, Mussati S, Scenna N. Optimization of post-combustion CO2 process using DEA–MDEA mixtures. Chem Eng Res Des 2011;89:1763–73. [13] Nuchitprasittichai A, Cremaschi S. Optimization of CO2 Capture Process with Aqueous Amines − A Comparison of Two Simulation − Optimization Approaches. Ind Eng Chem Res 2013;52:10236-243. [14] Khakdaman HR, Zoghi AT, Abedinzadegan M, Ghadirian HA. Revamping of gas refineries using amine blends. Int J Eng Sci 2008;19:27– 32. [15] Chang H, Shih C. Simulation and Optimization for Power Plant Flue Gas CO2 Absorption Stripping Systems. Sep Sci Technol 2005;40:877–909. [16] Alie C, Backham L, Croiset E, Douglas PL. Simulation of CO2 capture using MEA scrubbing: a flowsheet decomposition method. Energy Convers Manag 2005;46:475–87. [17] Mofarahi M, Khojasteh Y, Khaledi H, Farahnak A. Design of CO2 absorption plant for recovery of CO2 from flue gases of gas turbine.

1616


Energy 2008;33:1311–9. [18] Abu-Zahra MRM, Niederer JPM, Feron PHM, Versteeg GF. CO2 capture from power plants. Int J Greenh Gas Control 2007;1:135–42. [19] Abu-Zahra MRM, Schneiders LHJ, Niederer JPM, Feron PHM, Versteeg GF. CO2 capture from power plants. Int J Greenh Gas Control 2007;1:37–46. [20] Halemane KP, Grossmann IE. Optimal process design under uncertainty. AIChE J 1983;29:425–33. [21] Grossmann IE, Sargent RWH. Optimum design of chemical plants with uncertain parameters. AIChE J 1978;24:1021–8. [22] Ierapetritou MG, Acevedo J, Pistikopoulos EN. An optimization approach for process engineering problems under uncertainty. Comput Chem Eng 1996;20:703–9. [23] Bahakim SS, Ricardez-Sandoval LA. Simultaneous design and MPC-based control for dynamic systems under uncertainty: A stochastic approach. Comput Chem Eng 2014;63:66–81. [24] Sánchez-Sánchez K, Ricardez-Sandoval LA. Simultaneous process synthesis and control design under uncertainty: A worst-case performance approach. AIChE J 2013;59:2497–514. [25] Fuss S, Johansson DJA, Szolgayova J, Obersteiner M. Impact of climate policy uncertainty on the adoption of electricity generating technologies. Energy Policy 2009;37:733–43. [26] Yang M, Blyth W, Bradley R, Bunn D, Clarke C, Wilson T. Evaluating the power investment options with uncertainty in climate policy. Energy Econ 2008;30:1933 – 1950. [27] Fuss S, Szolgayova J, Obersteiner M, Gusti M. Investment under market and climate policy uncertainty. Appl Energy 2008;85:708 – 721. [28] Szolgayova J, Fuss S, Obersteiner M. Assessing the effects of CO2 price caps on electricity investments—A real options analysis. Energy Policy 2008;36:3974 – 3981. [29] Li MW, Li YP, Huang GH. An interval-fuzzy two-stage stochastic programming model for planning carbon dioxide trading under uncertainty. Energy 2011;36:5677 – 5689. [30] Han J-H. A multi-objective optimization model for sustainable electricity generation and CO2 mitigation (EGCM) infrastructure design considering economic profit and financial risk. Appl Energy 2012;95:186 – 195. [31] Cristóbal J, Guillén-Gosálbez G, Kraslawski A, Irabien A. Stochastic MILP model for optimal timing of investments in CO2 capture technologies under uncertainty in prices. Energy 2013;54:343–51. [32] Kim S, Koo J, Lee CJ, Yoon ES. Optimization of Korean energy planning for sustainability considering uncertainties in learning rates and external factors. Energy 2012;44:126–34. [33] Bahakim SS, Rasoulian S, Ricardez-Sandoval LA. Optimal design of large-scale chemical processes under uncertainty: A ranking-based approach. AIChE J 2014: doi 10.1002/aic. [34] Ricardez-Sandoval LA. Optimal design and control of dynamic systems under uncertainty: A probabilistic approach. Comput Chem Eng 2012;43:91–107. [35] Bahakim S. Efficient Ranking-Based Methodologies in the Optimal Design of Large-Scale Chemical Processes under Uncertainty. M.A.Sc. Thesis, University of Waterloo; 2014. [36] Dugas ER. Pilot Plant Study of Carbon Dioxide Capture by Aqueous Monoethanolamine. M.S.E. Thesis, University of Texas at Austin; 2006.