Modeling, Simulation, and Optimization of Postcombustion CO2

Modeling, Simulation, and Optimization of Postcombustion CO2...

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Modeling, Simulation, and Optimization of Postcombustion CO2 Capture for Variable Feed Concentration and Flow Rate. 1. Chemical Absorption and Membrane Processes M. M. Faruque Hasan, Richard C. Baliban, Josephine A. Elia, and Christodoulos A. Floudas* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States ABSTRACT: Studies on leading technologies for industrial CO2 capture are performed. Each technology includes ﬂue gas dehydration, capture of at least 90% of CO2 from the feed, and compression to almost pure CO2 for sequestration at 150 bar. This paper presents the modeling, simulation, optimization, and energy integration of a monoethanolamine (MEA)-based chemical absorption process and a multistage membrane process over a range of feed compositions (1−70% CO2, 5.5−15% H2O, 5.5% O2, and the balance N2) and ﬂow rates (0.1, 1, 5, and 10 kmol/s). A superstructure of process alternatives is developed to select the optimum dehydration strategy for the feed to each process. A rigorous simulation-based optimization model is proposed to determine the minimum annualized cost of the MEA-absorption process. The MEA-absorption process is energy integrated through heat exchanger network optimization. A novel mathematical model is developed for the optimization of multistage and multicomponent separation of CO2 using membranes, which can be also used for a range of membrane-based gas separation applications. The results showing the optimum investment, operating, and total costs provide a quantitative approach toward technology comparison and scaling up the absorption- and membrane-based CO2 capture from various CO2 emitting industries. Explicit expressions for the investment and operating costs of each alternative postcombustion CO2 capture process as functions of feed ﬂow rate and CO2 composition are also developed for the ﬁrst time. This may assist the decisionmakers in selecting the cost-appropriate technology for comprehensive carbon management by taking the diverse emission scenarios into consideration.

1. INTRODUCTION Electricity and heat generation (41%) and industrial (20%) sectors including cement production, iron and steel, reﬁneries, petrochemicals, natural gas production, oil and gas processing, etc., are responsible for more than 60% of the total CO2 emissions worldwide.1 Industrial CO2 emissions have a signiﬁcant contribution to the increase in atmospheric CO2 leading to man-made climate change.2 Such emissions are primarily due to the use of fossil fuels. Scenarios assuming continued expansion of fossil-fuel-based infrastructure predict cumulative CO2 emissions of 2986−7402 Gtons during the remainder of this century.3 Even assuming CO2 emissions from existing infrastructures only, an increase of about 496 Gtons of atmospheric CO2 is projected in the next 50 years unless it is captured at the point of emission. Therefore, a signiﬁcant research eﬀort has been devoted to developing technologies for reducing CO2 emissions and mitigating their negative impact on climate change. CO2 capture and storage (CCS) is one such enabling technology.4−6 The Intergovernmental Panel on Climate Change (IPCC) has described CCS as a process consisting of the separation of CO2 from industrial and energyrelated sources, transport to a storage location, and long-term isolation from the atmosphere. CCS can play a role in reducing industrial and stationary CO2 emissions while continuing the use of fossil fuels such as coal, oil, natural gas, and their derivatives such as gas to liquid (GTL) and coal, biomass, and natural gas to liquid (CBGTL).7−15 CCS involves capture, compression, transportation, and sequestration of CO2 for geological storage. CO2 capture is the heart of a CCS chain and incurs the majority of the total © 2012 American Chemical Society

CCS cost. Diﬀerent physical and chemical processes such as absorption, adsorption, membrane, cryogenic, and microbial processes exist for CO2 capture.5,16−20 However, not all processes are equally economically attractive or even feasible. Factors that aﬀect the choice of a suitable capture process include feed gas characteristics (composition, ﬂow rate, pressure, and temperature), source type (power generation, gasiﬁcation, gas upgrading, etc.), source fuel type (solid or gas), capture type (precombustion, postcombustion, and oxycombustion), capture performance rating (CO2 purity, recovery, energy penalty, etc.), and cost.16,21−30 CO2 is generated from a diversity of stack emissions and intermediate chemical process streams. Flue gases from chemical and power industries in general show signiﬁcant variability in their compositions.27 [Flue gases are eﬄuents that contain CO2 with balance N2, O2, H2O, CO, H2, etc.] Table 1 shows the typical ﬂue gas compositions of major CO2 emitting plants in the world. These include coal and natural gas (NG) based power plants, gas turbines, cement production, reﬁneries, iron and steel, petrochemicals, oil, and gas processing, and the CBGTL process.8−14 It is remarkable that the CO2 content in industrial gases can be as low as 0.1% (by volune) and as high as 75% (by volume) or more. Natural gas supplied to a typical liqueﬁed natural gas (LNG) process31 contains, depending on the nature of the natural gas wells, 0.1−8% CO2. The coking Received: Revised: Accepted: Published: 15642

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Table 1. Volumetric Composition (in %) of Industrial CO2 Containing Streams plant

stream

CO2

N2

O2

H2O

CO

H2

others

gas turbines NG-ﬁred power plants fuel-oil-ﬁred power plant coal-ﬁred power plant coal-ﬁred power plant coal-ﬁred power plant LNG reﬁnery urea hydrogen cement steel steel steel CBGTL CBGTL CBGTL

postcombustion exhaust postcombustion ﬂue gas postcombustion ﬂue gas postcombustion ﬂue gas oxy-combustion ﬂue gas oxy-combustion ﬂue gasa feed natural gas ﬂue gas ﬂue gas syngas ﬂue gas blast furnace Corex CCF postcombustion ﬂue gas precombustion gas oxy-combustion ﬂue gas

3.4−3.8 8.6−9 11 12.6−14 58.1−59.6 74.2−76 0.1−8 7 8 12 19 20 24 44 11.96 21.89 62.21

74.4−75.7 70.9−71 73 71.4−74 17.6−16 22.5−20.4 0−5 77 68 − 61 56 12 9 71.91 0.12 15.9

12.6−13.8 2.4−13 3 3−4.3 4−4.1 − 0−0.2 3 1 − 8 − 0 − 12.88 − 15.33

6.9−8.3 7.8−17.3 13 8−10.8 17.4 − − 14 22 29 13 − 1 − 1 0.01 6.47

− − − − − − − − − 1 − 21 44 24 − 24.38 −

− − − − − − − − − 50 − 3 17 20 − 48.51 −

0−0.9 0−0.9 − 0.9−1 2.9 3.3−3.6 87−99 − 1 8 − − 2 − 2.25 5.09 0.09

a

Dehydrated and O2 scrubbed.

ranges of CCS costs for several industries.23 This study reported the abatement cost ranges of each ton of CO2 avoided for ﬁve major industrial sectors, namely, high-purity CO2 sources ($30−70), biomass conversion ($35−80), reﬁneries ($45−120), cement ($55−150), and iron and steel ($60−80). Two widely used economic criteria to evaluate the feasibility of a capture process are, among others, (i) the cost of 1 ton of CO2 captured, and (ii) the cost of 1 ton of CO2 avoided. The main diﬀerence between these two criteria is that the former does not take into account the overall reduction of CO2 emission from the reference plant, but the latter does. Although they provide useful information for technology comparison, neither of them says anything about the plant capacity and economy of scale. Most capture technologies are at their preliminary growth stages at this time, and the demonstration plants are not always built to the industrial scale. This imposes a challenge in estimating the investment cost of an industrial scale capture plant. Since each chemical industry generates diﬀerent amounts of CO2-containing ﬂue gases (ranging from tens of metric tons to thousands of metric tons of CO2 per day), we need to understand how cost varies with the capture plant CO2 feed ﬂow rate. It is usual that the cost factor for scale-up is not the same for all processes, which in turn would aﬀect the selection of a capture technology. The selection process becomes even more challenging when changes in both the ﬂow rate and composition are taken into consideration simultaneously. Since the CO2 composition and amount of ﬂue gas vary from plant to plant, it is important to investigate whether the approach of “one technology suits all” is always the best strategy. Most existing research selects a capture technology a priori and then optimizes its performance. Many contributions are introduced on absorption-based processes since it is a popular separation technology in many industries. Oyenekan and Rochelle36 developed a framework for evaluating the energy performance of diﬀerent stripper conﬁgurations for CO2 capture using aqueous amines. Pellegrini et al.37 simulated a monoethanolamine (MEA)-based absorption process and proposed several column conﬁgurations for saving energy. ́ Rodriguez et al.30 studied the optimization of postcombustion CO2 capture with an absorption process that uses a

process in an iron industry produces a large amount of cokeoven (CO) gas which contains only 1% CO2.32 CO2 contents are about 7% in typical reﬁnery ﬂue gases, 8−11% in urea, natural gas processing, upstream LNG, and fuel oil plants, 19% in cement plants, 20−24% in conventional blast furnace and Corex steel plants, and 44% in CCF steel plants. The CO2 content from an iron and steel plant is even greater than usual if CO is converted into CO2 using a shift reaction. Similar conversion takes place in a hybrid feedstock (coal, biomass, natural gas) CBGTL plant to increase the CO2 content of the gas coming from the Fischer−Tropsch (FT) converters.8 The CBGTL plant is a special case where at least three CO2 streams with diﬀerent compositions (11.96, 21.89, and 62.21% CO2) are present. Even the power plants, depending on their types, produce ﬂue gases with signiﬁcantly diﬀerent CO2 contents. While ﬂue gases from natural gas combined-cycle (NGCC) power plants contain only 3−4% CO2, coal-ﬁred power plants produce postcombustion ﬂue gases containing 12−14% CO2. The composition of the ﬂue gas from an oxy-combustion-based coal-ﬁred power plant is much diﬀerent. The ﬂue gas coming from the oxy-combustion boiler has a high CO2 content of 58− 60%, which after dehydration and O2 scrubbing increases to 74.2−76%.33 Mahasenan and Brown27 pointed out that industrial emissions with higher CO2 content in ﬂue gas may provide early opportunities for CCS implementation. However, most literature related to postcombustion CO2 capture focused on ﬂue gases with ﬁxed CO2 composition, usually that correspond to a typical coal or natural gas based power plant. The CCS costs for U.S. national gas-ﬁred power plants have been assessed by several recent cost studies. As summarized by Rubin and Zhai,22 the cost of CO2 avoided ($/ton CO2) ranges from $72 to $114 ($92 by DOE/NETL, 2007;34 $106 by DOE/NETL, 2010;24 $74 and $95 by EPRI, 2009; $114 by International Task Force, 201035). While IPCC in a 2005 report2 assessed and summarized wide ranges of CCS costs within and across industries, there have been very limited studies on CO2 capture costs for industrial processes compared to the number of studies for power plants. Only recently, the International Energy Agency (IEA) and United Nations Industrial Development Organization (UNIDO) assessed the 15643

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CO2 capture. For instance, some27,43 concluded that the membrane process can be the technology of choice when the pressure and the CO2 content of the feed gas are high. Others42 mentioned that the use of multistage operation at elevated pressure would make the membrane process energy eﬃcient and competitive with other capture processes. Some of the literature points out that chemical absorption (e.g., using MEA) is less costly option than others,32 especially when the partial pressure of CO2 in the ﬂue gas is low. However, the critical CO2 composition(s) for which a changeover of technology option would happen is not known. We investigate how the cost of CO2 capture changes with changing CO2 feed composition and ﬂow rate of the gas mixtures coming from the source plant, for four leading CO2 capture technologies, namely, (1) absorption, (2) membrane, (3) pressure swing adsorption (PSA), and (4) vacuum swing adsorption (VSA). We also investigate how we can select the most cost-eﬀective capture technology for diﬀerent chemical and power industries. Part 1 focuses on the absorption- and membrane-based processes. Studies on the adsorption-based processes, namely, PSA and VSA are presented in part 2.50 In this article, we report rigorous mathematical modeling, simulation, and optimization of (a) MEA-based chemical absorption and (b) multistage membrane processes for CO2 capture and sequestration from industrial gas mixtures. Our approach is applicable to diﬀerent ﬂue gas conditions and pressures. We illustrate our approach for the postcombustion capture of CO2 from industrial ﬂue gases at atmospheric conditions, including those from heat generation and power plants. Each process is modeled, optimized, and energy integrated over a wide range of feed gas compositions and ﬂow rates. The novel features of this work include the following: (i) feed dehydration using a superstructure of process alternatives (ii) CO2 capture coupled with compression (iii) rigorous rate-based modeling of the MEA absorption based CO2 capture coupled with heat integration (iv) multistage superstructure model for CO2 capture using membranes (v) variation in feed CO2 composition and total feed ﬂow rate (vi) cost-based comparison of the absorption- and membrane-based CO2 capture processes (vii) explicit expressions for the investment and operating costs The article is organized as follows. First, the process and economic parameters considered in this work are presented in sections 2 and 3. The feed dehydration which may be required prior to CO2 capture is discussed in section 4. Then, in section 5 the process conﬁguration and the mathematical modeling of the absorption-based process for CO2 capture are described, and the implementation of the simulation-based optimization framework for the absorption process is outlined. The framework for the heat exchanger network optimization is also described in detail. Next, the detailed mathematical model for the optimization of the membrane-based multistage CO2 capture process is presented, and the model implementation is discussed. In section 6, the results on the optimized annual investment and operating costs are presented for the absorption- and membrane-based technology alternatives over a range of feed CO2 compositions and feed ﬂow rates. Also, in

diethanolamine (DEA)−methyldiethanolamine (MDEA) mixture as the solvent. They proposed a set of operating conditions for the process based on minimum total annual costs of the plant. Oexmann et al.38 used the Aspen Plus based simulation tool to optimize the CO2 loading in the piperazine-promoted potassium carbonate solvent. This study focused on coal-ﬁred power plants only. Harkin et al.39 applied pinch analysis for reducing the overall energy penalty of a coal-ﬁred power plant integrated with a MEA-based capture plant. Signiﬁcant modeling contributions have been introduced toward the optimal stripper design for CO2 capture. Mores et al.28 developed an equilibrium stage-based operational model to optimize a conventional MEA-based chemical absorption process for the postcombustion CO2 capture. On the other hand, a rate-based CO2 stripper model was developed by Oyenekan and Rochelle.40 For a comprehensive list of recent contributions on absorption-based CO2 capture, the reader is referred to Wang et al.18 and Mores et al.28 While the membrane technology has yet to be commercially used to concentrate CO2 from industrial ﬂue gas, recent developments in polymeric materials for gas separation41 along with inherently simple plant conﬁguration and operation, compactness, lightweightness, mobility, etc. make the membrane technology a promising and viable option for CO2 capture. Kaldis et al.42 studied and estimated the energy usage and capital cost parameters for CO2 removal in a typical coal integrated gasiﬁcation combined-cycle (IGCC) process with the use of a shift reactor and a membrane separator. Their study included low and high temperature operations, feed gas at relatively higher pressures, and two types of membranes, namely, polymeric and ceramic membranes. Hägg and Lindbråthen43 simulated two alternative membrane systems for CO2 removal from an exhaust gas stream in a NG-ﬁred power plant. Ho et al.44 reported an economic evaluation for the cost of CO2 recovery that includes feed gas desulfurization, CO2 capture using gas-separation membranes under vacuum, and compression. The feed gas characteristics were chosen from an existing coal-ﬁred power plant. Most of these membrane studies reported high costs of CO2 capture, mainly because of the high capital costs associated with feed gas compression to increase the driving force for separating CO2 with low partial pressure.44,45 However, it is noteworthy that these studies considered CO2 capture from power plants only for which the CO2 content in the feed gas is 15% or lower. To summarize, most studies on CO2 capture are based on ﬁxed feed gas compositions, ﬂow rates, and process conﬁgurations. Although many contributions16,21−26,34,35,44,46−48 exist that evaluate and compare the economic performances of absorption, adsorption, and/or membrane processes, most of them considered ﬁxed characteristics of the feed gas. Fewer works considered process synthesis (plant conﬁguration, equipment sizing, heat integration,49 etc.) to propose novel and energy integrated processes for CO2 capture even for a constant feed gas composition and ﬂow rate. A comprehensive and benchmarking study that provides a means for comparing various capture processes over a wide range of feed gas compositions and ﬂow rates is clearly missing from the literature. In order to address the important problem of carbon management, we must consider plant to plant ﬂue gas characteristics and apply a rigorous approach to select the optimal capture process. Often, qualitative arguments are placed while advocating for a particular technology to adopt for 15644

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the minimum recovery and purity to be 90% for the capture plant. While any CO2 purity from the capture unit is feasible as long as the output gas is compressed to 150 bar, low CO2 purity would mean that the compression system must compress a large volume of gas, resulting in an excessively high compression cost. Note that it is not possible to increase the CO2 purity during compression, unless we use refrigeration for the interstage coolers.51 Therefore, achieving 90% purity during the capture is important. Although the absorption-based process is usually able to capture CO2 with high purity, the capture and compression costs show trade-oﬀs. This is also true for the membrane-based process. Therefore, we allow the cost trade-oﬀs between the capture and compression units as long as the minimum recovery and purity speciﬁcations are met.

section 6, a cost-based input−output model for the CO2 capture processes is proposed and explicit cost expressions as the function of feed ﬂow rate and CO2 composition for the absorption- and membrane-based processes are developed.

2. PROCESS PARAMETERS A potential source of industrial CO2 for CCS may contain CO2, N2, O2, H2O, CO, H2, and trace amounts of NOx and SOx. In this work, we consider the feed as a gaseous mixture of CO2, N2, O2, and H2O. H2 is usually not present in the postcombustion and oxy-combustion ﬂue gases, and CO can be converted to CO2 using a shift reaction. Furthermore, we assume that NOx and SOx are already removed using a feed desulfurization unit. The gas coming from the desulfurization unit would be usually saturated with water vapor. Therefore, the H2O content in the feed gas cannot be neglected. Most ﬂue gases from power plants are highly humid with 5.5−15% H2O or more (see Table 1). In this work, the feed compositions are chosen to be the following: CO2, 1−70%; H2O, 5.5−15%; O2, 5.5%; balance N2. Let x (1 ≤ x ≤ 70) and y (5.5 ≤ y ≤ 15) be the percent volumetric compositions of CO2 and H2O in the feed, respectively. Therefore, the volumetric composition of N2 in the feed is given by (100 − x − y − 5.5). The variation in O2 content does not seem to have much eﬀect on the process performance. That is why we ﬁx the composition of O2 at 5.5%. The conceptual CCS structure considered in this work is illustrated in Figure 1. We have considered feed preprocessing

3. ECONOMIC PARAMETERS Our goal is to optimize the processes for minimum total annualized cost (TAC), which is deﬁned as (1) TAC = AIC + AOC where AIC and AOC are the annualized investment and operating costs, respectively. While AOC depends on the utilities, AIC is computed as follows: AIC = ϕTPC + AMC (2) where TPC and AMC represent the total plant cost and annual maintenance cost, respectively, and ϕ is the capital recovery factor. The evaluation of these economic parameters is tabulated in Table 2. A value of 0.154 is used for ϕ throughout Table 2. Assumed Economic Parameters for the Investment Cost parameter equipment (mover) installation cost (EIC) equipment (column, exchanger, etc.) installation cost (EIC) total installed cost (TIC) indirect cost (IDC) balance of plant cost (BPC) total plant cost (TPC) annual maintenance cost (AMC) capital recovery cost

Figure 1. Conceptual CCS structure (transportation is excluded) and the basis for the feed and product.

(mainly, dehydration), CO 2 capture, and compression components of a CCS chain, since dehydration and compression are directly linked to and often depend on the selected technology for CO2 capture. We also consider the feed to be available at 1 bar and 55 °C with variable feed compositions and ﬂow rates. The goal is to capture and compress no less than 90% of the CO2 from feed to sequester at 150 bar. The absorption- and membrane-based processes are modeled, simulated, energy integrated, and optimized over this stipulated range of feed compositions for four total feed ﬂow rates, namely, 0.1, 1, 5, and 10 kmol/s. For each process, we select several feed compositions and the four feed ﬂow rates and obtain the optimal investment, operating, and total costs of capture and compression. These represent the most realistic feed compositions and conditions, particularly suitable for CCS with the “end of the pipeline” or the postcombustion capture and compression of CO2 from most power plants and heat generation, chemical, petrochemical, and other processes worldwide. If required, a preprocessing/pretreatment of feed is done before the gas enters the capture process. Once CO2 is captured using absorption- or membrane-based process, it is compressed to 150 bar using a six-stage compression system with intercoolers. The purity of the captured CO2 stream is also important. Note that a capture process may or may not achieve high purity and high recovery at the same time. However, to realize a separation, we specify

value 80% of EPC 4% of EPC all EPCs and EICs 32% of TIC 20% of TIC TIC + IDC + BPC 5% of TPC 15.4% of TPC

the work. TPC is the total equipment installed costs (TIC) plus the indirect cost plus the balance of the plant cost. We consider the indirect cost and the balance of plant cost to be 32 and 20% of TIC, respectively. AMC is taken to be 5% of TPC. Lastly, the installed cost (TIC) of an equipment includes the equipment purchase cost (EPC) and the equipment installation cost (EIC). We considered the installation costs to be 4 and 80% of the purchase costs46 for general equipment (columns, heat exchangers) and movers (compressors and vacuum pumps), respectively. The following base conditions and costs are used for all cases: 1. Cooling water is available as the cold utility. The price of cooling water is $0.001/ton. 2. Saturated steam at 5 bar is available as the hot utility, with cost at $6/ton. 3. Electricity is available at $0.07/kWh. 4. The cost of membrane44 is $50/m2. 5. Equipment costs are based on 2009 values. 15645

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Figure 2. Superstructure for feed dehydration.

Figure 3. TEG absorption process for feed dehydration.

6. All mover costs are taken from Uppaluri et al.52 and converted to 2009 values. 7. Each plant operates 8000 h in a year.

process. Therefore, depending on the moisture content of the feed gas, we must remove H2O and dry the gas before sending it to the CO2 capture process. While the absorption-based process can handle such saturated feed, other processes including membrane and adsorption may require a moisture content of 0.1% or less. To this end, we propose a superstructure that allows multiple options for feed dehydration. The superstructure is shown in Figure 2. First, the feed which contains 5.5−15% H2O at 55 °C is cooled to 35 °C by a direct contact cooler. The advantage is that this reduces the moisture content to 5.5%, which is the

4. FEED DEHYDRATION Not every process for CO2 capture can tolerate a feed saturated with H2O or that has high moisture content. H2O can condense during desorption in an adsorption-based capture process, and reduce the capacity of a sorbent, create corrosion problems, and reduce the CO2 purity and recovery of a membrane-based 15646

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composition of H2O in a saturated ﬂue gas at 35 °C, irrespective of the initial moisture content (5.5−15%) at 55 °C. Now, we can either bypass any further dehydration and send the gas directly to the capture process, or dehydrate the gas to 0.1% H2O. The feed dehydration can be achieved using the following processes: refrigeration, compression and cooling, membrane separation, and TEG (triethylene glycol) absorption. If we only want to use cooling to reduce the moisture content below its saturation composition at 35 °C, we have to use refrigeration which can be prohibitive for cryogenic limitations. A compression and cooling can be used if we want to avoid refrigeration. However, it may not be costeﬀective to compress a large amount of feed gas to high pressure and then cool it to 35 °C. Another option could be to use polymeric membranes such as PEBAX or sulfonated poly(ether ether ketone) (SPEEK).53 This option includes a feed compressor, a membrane unit, and a vacuum pump on the permeate side. The feed compressor and the vacuum pump would create the necessary driving force (partial pressure diﬀerences) to selectively pass H2O through the membrane on the permeate side. The dry gas (CO2, N2, O2) has little permeance through the membrane and will be collected on the retentate side. Among the gas dehydration processes, absorption is the most common, where H2O in the feed gas is absorbed in liquid solvent ﬂowing countercurrently in an absorption column. In the TEG absorption process54,55 (Figure 3), the wet feed gas ﬂows through the bottom of the absorption column and lean triethylene glycol (TEG) ﬂows through the top and absorbs H2O from the gas. The dry gas leaves the column from the top. The H2O-rich solvent from the bottom of the column is pumped and then heated in a heater to about 73 °C. The heated solvent is then ﬂashed under vacuum (about 0.04 bar) for regeneration. The regenerated TEG solvent is pumped back to the absorption column after being cooled to 65 °C. Table 3 lists the cost correlations, references, and factors used to compute the purchase cost of the equipment present in

CO2 capture and compression. Although any of the alternatives, except the bypass, shown in Figure 2 can be used to dehydrate the feed, it would cause some CO2 loss with drained H2O. This CO2 loss would vary depending on the alternative chosen for dehydration. For the refrigeration and compression and cooling based dehydration alternatives, the loss could be signiﬁcant. Since our goal is to capture and compress at least 90% of the CO2 in the feed, the tolerable limit of CO2 loss during feed dehydration is 10%.

5. PROCESS MODELING In this section, we describe the process models for the absorption- and membrane-based technologies. Each model includes both capture and compression components of CCS. These models will be used to simulate and optimize for minimum annualized cost over a range of feed CO 2 compositions and feed ﬂow rates. 5.1. Absorption-Based CO2 Capture and Compression. Absorption of CO2 can be physical or chemical. Selexol and Rectisol are two of the most popular physical absorption processes for CO2. For chemical absorption, several amine (MEA, MDEA, DEA, MDEA-PZ, etc.) and caustic solutions are used as solvents. In this work, we have selected chemical absorption of CO2 in an aqueous solution of 30 wt % MEA (monoethanolamine). MEA is reported to be one of the most suitable solvents for CO2 capture.37,56,57 We ﬁrst discuss our proposed conﬁguration of the absorption process. 5.1.1. Process Conﬁguration. Figure 4 shows the process ﬂow diagram of the MEA-based absorption process. Feed ﬂue gas (a mixture of CO2, N2, O2, and H2O at 55 °C and 1 bar) ﬁrst enters a feed compressor. It then enters the feed dehydration section, which is the superstructure conﬁguration shown in Figure 2. In this section, the gas is ﬁrst cooled to 35 °C using a direct contact cooler. It is then split into substreams, either to bypass the dehydration process or to use a dehydration process (refrigeration, compression and cooling, membrane, and TEG absorption). If the bypass is chosen, then the moisture content remains to be 5.5% H2O. Otherwise, the moisture content is reduced to 0.1% using dehydration. The gas after the dehydration section is fed to the packed absorber column, where it countercurrently ﬂows with the lean MEA solution. The absorber has 10 nonequilibrium stages. As the ﬂue gas ﬂows through the absorber, most of the CO2 is chemically reacted with the solvent and transferred to the liquid phase. The CO2-free clean gas comes out of the column and is vented to the atmosphere. A water wash is staged before the gas comes out of the column. The solvent exiting the column, on the other hand, is loaded with chemically reacted CO2, and it is deﬁned as the rich solvent. Before the rich solvent is sent to the stripper, it is heated using a heater and ﬂashed in a ﬂash drum to recover some CO2 from the liquid phase just by using simple phase separation.58 This phase separation can be advantageous, especially at high CO2 concentrations, since it reduces the reboiler heat load of the stripper. The pump is used to deliver the rich solvent at the stripper column pressure. The stripper is a packed column with 10 nonequilibrium stages and has a kettle type partial reboiler. CO2 is transferred to the gas phase from the rich solvent, while the heated solvent is regenerated as it ﬂows through the stripper. The regenerated solvent is then cooled to 35 °C and recycled back to the absorber as the lean solvent. Some MEA and water are lost with the gaseous streams from the columns. Therefore, make-up MEA and water are added with the lean solvent.

Table 3. Cost Correlations Used for Feed Dehydration item compressor vacuum pump cooler direct contact cooler TEG absorber membrane

sizing correlation adiabatic adiabatic utility based six-tenths rule removal eﬃciency and liquid circulation rate based area based on compartment model

ref 52 52 52 46 55 52

the dehydration superstructure (Figure 2). In this work, we used the model developed by Bahadori and Vuthaluru55 to obtain the costs of feed dehydration using TEG absorption (Figure 3). The membrane dehydration costs are obtained using the process shown in the superstructure (Figure 2), where the single-stage membrane is modeled52 with SPEEK as the membrane. The permeance values of H2O, N2, CO2, and O2 are taken to be 28 700, 0.03, 1.11, and 0.39 GPU (gas permeation unit, 1 GPU = 0.75 × 10−6 m3(STP)/m2·s·bar), respectively.53 The refrigeration and compression and cooling alternatives are simulated in Aspen Plus. The superstructure shown in Figure 2 is implemented along with each of the absorption- and membrane-based process conﬁgurations for 15647

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Figure 4. Process ﬂow diagram of the absorption process with CO2 compression.

5.1.2. Model Development. We ﬁrst state the problem and the major assumptions made for the optimization of the absorption-based CO2 capture process. Problem Statement. Given the composition, feed ﬂow rate, temperature, and pressure of the feed gas, and the process conﬁguration described in Figure 4, determine the minimum annualized cost of the heat integrated process. Modeling Assumptions. 1. Feed gas does not contain NOx, SOx, SH2, or ﬂy ash. 2. Absorption is adiabatic. 3. Pressure drops inside the absorber and stripper columns are 2 kPa per stage. 4. The electrolyte-NRTL thermodynamic package is suﬃcient to describe the thermodynamics of the process. 5. All reactions are at equilibrium56 and take place in the liquid phase. The concentration of water in liquid remains constant since it is very large compared to those of the other components in the liquid phase. 6. Ten stages are considered for both the absorption and stripper columns. 7. The stripper reboiler is in vapor−liquid equilibrium. 8. All compressors run adiabatically with 75% thermal eﬃciency.65 Six compressor units are required for the multistage compression to deliver the captured CO2 at 150 bar for sequestration, where each compressor unit has a pressure ratio of 2.3. The indices, sets, parameters, variables, assumptions, mathematical constraints, and the objective function that describe the mathematical model are presented below. Indices.

CO2 that is released from the stripper carries a signiﬁcant amount of water with it. Therefore, it is cooled and partially condensed in the partial condenser. The two-phase mixture is then ﬂashed in a ﬂash drum from which the liquid stream is sent back to the top stage of the stripper while the gaseous CO2 is sent to the multistage compressor train. The compressor train has six stages with interstage cooling. We place a second ﬂash drum just after the ﬁrst interstage cooler to remove any water droplets that escaped the ﬁrst ﬂash drum. The compressed CO2 is discharged at 150 bar for sequestration. The process also has a number of heat exchangers, along with the columns (absorber and stripper), the multistage compressor units, and the solvent pump. The heat exchangers include the heater for the rich solvent, the cooler for the lean solvent, the stripper reboiler, the stripper aftercondenser, and ﬁve interstage coolers for the multistage compressor system. Most28,30 CO2 absorption processes use an economizer that combines the heater and cooler used for the rich solvent and lean solvent, respectively. However, such a preﬁxed match may not be the optimal match. To perform a detailed heat integration to determine the optimal heat exchanger network topology for the process, we need to allow all plausible combinations of hot and cold process streams to exchange process heat. Therefore, while the overall process topology remains the same as shown in Figure 4, the heaters and coolers are further connected using a superstructure-based approach for heat exchanger networks.59−64 The superstructure is used to derive the optimal heat exchanger network topology. We discuss the detail of the synthesis of a heat exchanger network for the process in section 5.1.4. 15648

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Table 4. Reactions and Equilibrium Constants Used in the VLE Modela reaction

equilibrium constant

2H 2O ↔ OH− + H3O+

−12092.1

−36.7816

235.482

3

−12431.7

−35.4819

220.067

K2 (mol/dm ) K3 (mol/dm ) K8 (mol/dm3)

MEAH + H 2O ↔ H3O + MEA a

140.932

MEACOO− + H 2O ↔ HCO3− + MEA +

a3

−22.4773

HCO3− + H 2O ↔ CO32 − + H3O+ +

a2

−13445.9

K1 [(mol/dm ) ]

CO2 + 2H 2O ↔ HCO3− + H3O+

a1

3

3 2

3

K9 (mol/dm )

−3090.83

0.0

−5851.11

0.0

6.69425 −3.3636

ln K = a1/T + a2 ln T + a3.

Pa: absorber feed pressure, 1−10 bar Ps: stripper pressure, 1−10 bar Wj: utility requirement in unit j (kW) MW: make-up water ﬂow rate (kg/s) We also adjust the absorber and stripper column diameters to ensure that there is no ﬂooding (not more than 80%) inside the columns. Absorber and Stripper Model. The absorber and stripper are the two major units in the process for which we must select (i) an appropriate modeling approach, (ii) a reaction scheme and kinetics, and (iii) the vapor−liquid equilibrium model. Two main approaches can be used to model absorption/ desorption process in a column: the equilibrium-stage modeling approach and the rate-based modeling approach. In the equilibrium-stage approach, all segments including the reboiler of the column are assumed to be equilibrium stages where the liquid and vapor phases are well-mixed.28 Murphree eﬃciencies are assigned to CO2, water, and temperature to account for the departure from the equilibrium. This approach results in a simpler model than that derived from the rate-based approach. Only the mass, equilibrium, summation, and enthalpy (MESH) equations are considered.66 Unlike the equilibrium-stage approach, the rate-based approach considers a ﬁnite rate of absorption/desorption. Therefore, physical property relations, contactor information, and mass and heat transfer rates are crucial in the rate-based modeling approach. This approach reﬂects reality and captures actual column behavior. Zhang et al.57 demonstrated the superiority of the rate-based model over the traditional equilibrium-stage model for CO2 capture with aqueous MEA. In this work, we also use the rate-based modeling approach and select the RADFRAC model in the Aspen Plus process simulator for both the absorber and stripper. Both columns have the same packing speciﬁcations. IMTP No. 40 type metal packing is used for all stages. Next, we must choose a reaction scheme between CO2 and MEA solution. Two mechanisms are proposed in the literature, namely, the zwitterion mechanism and the termolecular mechanism.56 While the former assumes multiple reaction steps, the latter considers a single-step reaction. Lastly, we need a vapor−liquid equilibrium (VLE) model to estimate the CO2 partial pressure and the liquid bulk concentrations of all chemical species present in the solution. In this work, we use the VLE model by Aboudheir et al.56 Table 4 lists all the reactions along with the equilibrium constants used in this VLE model. These reactions determine the chemisorption of CO2 using MEA. As pointed out by Aboudheir et el.,56 the concentration of water in the MEA solution is much larger than the concentration of all other chemical species. This makes the concentration of water remain more or less constant, regardless of the feed composition and even for short contact time. The

i: component j: equipment c: cold stream h: hot stream Sets. Let IF be the set of components which are present in the feed ﬂue gas and IS be the set of components which are present in the recirculating solvent. i ∈ IF = {CO2 , N2 , O2 , H 2O} i ∈ IS = {CO2 , N2 , O2 , H 2O, MEA, MEAH+ , MEACOO− , HCO3− , CO32 − , H3O+ , OH−}

Let I be the set of all components, such that I = IF ∪ IS. Let J be the set of all utility equipment. These include all compressor units, heaters, coolers, reboilers, and condensers that are run by hot or cold utilities. Units that do not require utilities are not included in J. j ∈ J = {stage compressor units + heaters, coolers , interstage coolers, reboiler, condensers}

We also deﬁne SCP, HU, and CU as the subsets of J as follows. j ∈ SCP = {6‐stage compressor units for CO2 compression}

j ∈ HU = {heaters, reboiler}

j ∈ CU = {coolers, interstage coolers, condensers}

Parameters. The following parameters are deﬁned: CCU: unit cost of cooling utility ($/kW) CE: unit cost of electricity ($/kWh) CHU: unit cost of heating utility ($/kW) CMW: cost of make-up water ($/kg) FCO2,IN: molar ﬂow rate of CO2 in the feed Variables. The optimization variables of the process under consideration are listed as follows. F: solvent ﬂow rate, 0.1−5000 kmol/s q: stripper reboiler duty, 0−5000 MW TC: temperature of the stripper aftercondenser, 308− 473 K TP: outlet temperature of the solvent preheater, 308− 473 K TS: outlet temperature of the ﬁrst-stage compressor, 308−1000 K La: absorber column length, 0.1−25 m Ls: stripper column length, 0.1−25 m Da: absorber diameter, 0.1−25 m Ds: stripper diameter, 0.1−25 m 15649

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C PL,s = 300.9(3.281Ds)0.63316 (3.281Ls)0.80161

eﬀect of temperature on the VLE constants is captured using the correlation shown in Table 4. The operating temperatures of the absorber and stripper are well within the range (273− 498 K) for which the constants are obtained.56 Transport Property Models. Transport property models are required to determine various physical and thermal properties such as density, viscosity, surface tension, thermal conductivity, and diﬀusivity using various empirical correlations of heat and mass transfer, interfacial area, pressure drop, liquid holdup, etc. Zhang et al.57 examined various transport property models available in Aspen Plus for CO2 capture using MEA absorption. Most of the transport property models used in this work were selected based on the suggestion of Zhang et al. These include the Clarke density model for electrolyte solutions with mixed solvents to calculate density, the Jones−Dole model for liquid solutions with electrolytes for viscosity, the Onsager−Samaras surface tension model for the liquid mixture surface tension, and the Riedel thermal conductivity model for the liquid mixture thermal conductivity. However, we used the Nernst− Hartley electrolyte model which is the default model in Aspen to calculate diﬀusivity, instead of the Wilke−Chang model. Constraints and Objective Function. Let FCO2,OUT be the molar ﬂow rate of CO2 in the product (“SEQ” stream). To ensure a minimum recovery of 90%, we impose FCO2,OUT ≥ 0.9FCO2,IN

VP,s =

EC = 3000 ∑ ∑ Ah , c 0.6 h

(5)

AOC = 8000[(3600 (7)

π VP,a = (3.281Da )2 (3.281La) 4 π C DR,a = 3·125· (3.281Da )2 4

+

Ws = (π (39.37Ds + tS)(39.37(0.8Ds + Ls))tSρ)

∑ j ∈ SCP

CHUjWj + 3600

∑

CCUjWj

j ∈ CU

CEjWj) + 3600·CMW· MW] (18)

where, CHU, CCU, and CE are the unit costs of the heating utility, cooling utility, and electricity, respectively. MW is the amount of make-up water in kg/s, and CMW is the unit water cost. 5.1.3. Model Implementation. The Aspen Plus v7.3.2 platform with the electrolyte-NRTL thermodynamic package is used to model the MEA-based absorption process. We used c = 109.902 (2009 cost index), and co = 103.263. The absorptionbased process is optimized using the “optimization” option available in Aspen Plus. A constraint set “MinRe” is created using the “Constraint” option that enforces eq 3 to be active with a tolerance of 1 × 10−3, when the ﬂow sheet is optimized. We chose the SQP method as the optimization algorithm. While the global optimality of the solution is not guaranteed by the SQP method due to the nonconvexities in the model, it is observed to be more eﬃcient and better performing than other available methods in Aspen. The input variables, which are

(8) (9)

(10)

C V,s = exp{7.2756 + 0.18255[ln(Ws)] + 0.02297[ln(Ws)]2 }

∑ j ∈ HU

where tS is the shell thickness and ρ is the density of the carbon steel. We use FM = 2.1, CPK = 40, ρ = 0.284 lb/in.3, and tS = 2 in.67 Similarly, the purchase cost of the packed stripper, SC, is obtained using the following expressions: SC = FMC V,s + C PL,s + VP,sC PK + C DR,s

(17)

c

where h and c denote hot and cold streams respectively in the absorption-based process presented in Figure 4, and include both the process and utility streams. Ah,c is the area of the heat exchanger that is used to exchange heat from a hot stream (utility) h to a cold stream (utility) c. The total annualized cost of the process includes the investment (AIC) and operating costs (AOC). The annualized investment cost, AIC, is computed using eq 2, where the above purchase costs are used along with indirect costs, installation costs, maintenance costs, and the factors as described in Table 2. The annual operating cost, AOC, is given by

C V,a = exp{7.2756 + 0.18255[ln(Wa)]

C PL,a = 300.9(3.281Da )0.63316 (3.281La)0.80161

(16)

where SCP denotes the set of all six-stage compressor units for sequestration, and Wj is the power rating in kW for the unit j (j ∈ SCP). Similar model for the six-stage compression system is presented in eqs 32−34. Parameters c = 109.902 and co = 103.263 are the yearly cost indices for the years 2009 and 2004, respectively. The total purchase cost of the heat transfer equipment (exchangers, heaters, coolers, reboilers, condensers, and interstage coolers), EC, is a function of the heat transfer areas and is computed as follows.9

(4)

(6)

(15)

0.82 ⎛ c ⎞⎛ Wj ⎞ ⎟ ⎜ CC = 3791.3⎜ ⎟⎜ ∑ ⎝ co ⎠⎝ j ∈ SCP 0.7453 ⎟⎠

(3)

Wa = (π (39.37Da + tS)(39.37(0.8Da + La))tSρ)

(14)

The compressor train that is used for CO2 sequestration has six stages. The compressor purchase cost, CC, is considered to be a function of the total power used by the compression system, and is given by52

where FM is the factor for materials of construction, CV,a is the free on board (f.o.b.) purchase cost of the empty absorber vessel with the weight Wa, CPL,a is the added cost for absorber platforms and ladders, VP,a is the absorber packing volume, CPK is the installed cost of the packing for unit volume, and CDR,a is the installed cost of high performance liquid distributors and redistributors. These are expressed as follows:

+ 0.02297[ln(Wa)]2 }

π (3.281Ds)2 (3.281Ls) 4

π C DR,s = 3·125· (3.281Ds)2 4

The purchase cost of the packed absorber, AC, is obtained using the following expressions:67 AC = FMC V,a + C PL,a + VP,aC PK + C DR,a

(13)

(11) (12) 15650

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varied during the ﬂow sheet optimization, are the variables listed in section 5.1.2, except for Wj, FCO2,IN, FCO2,OUT, and xCO2,OUT since they are intermediate variables in the model. The objective is set to minimize TAC subject to the constraint set “MinRe”. The model in Aspen Plus is complex. The complexity is mainly attributed to (i) the nonconvexities in the objective function, (ii) the presence of several electrolytes in the liquid phases, (iii) reactive absorption and desorption, (iv) multiple recycle streams (stream LEANSOL, 19 and 22), and (v) the use of rate-based nonconvex column models. These make the ﬂow sheet diﬃcult to converge, even for a simulation without any optimization. To overcome this challenge, we adopt the following two initialization strategies: 1. “Tear” the three recycle streams with the maximum tolerance value of 1 × 10−10. The convergence sequence is LEANSOL, 19 and 22. 2. Perform a sensitivity analysis on the solvent ﬂow, reboiler duty, column lengths, and temperatures to obtain tighter variable bounds, before optimizing the ﬂow sheet. Our experience suggests that tight bounds on the decision variables are critical for the convergence of the ﬂow sheet. 5.1.4. Heat Exchanger Network Optimization. The ﬂow sheet is further optimized and heat integrated by developing a heat exchanger network (HEN). One key feature of the heat integration is that we include all possible options for integration of heat from the capture plant and the compression system, and we introduce an optimization-based approach for (a) the minimum utility cost, (b) the minimum number of matches, and (c) the minimum investment cost for the ﬁrst time. Other approaches for heat integration addressed mostly the utility cost.39,68−70 Given the information provided by the optimized Aspen process ﬂow sheet, a HEN optimization framework is used to determine the hot and cold utility loads, the heat exchanger matches, the areas of each match, and the HEN topology. This can be achieved either through a decomposition of the tasks into subtasks or through a simultaneous consideration of all goals. Though approaches for the synthesis of HEN without decomposition has been developed,59−64 a decomposition framework will be used in this study. This framework has three stages, which are performed sequentially as follows: (a) Minimize the total hot/cold/power utility requirement. (b) Minimize the heat exchanger matches to meet the given utility requirement. (c) Determine the topology of heat exchangers given the matches that provide the minimum annualized cost.9,11,12,59,64 The model for part a will not consider simultaneous heat and power utilities9 due to the lack of high-temperature hot streams which could provide waste heat for a steam turbine. A restricted utility model9 will be utilized to prevent undesired heat transfer (e.g., between a hot process stream and a reboiler), and a minimum temperature approach of 10 °C is enforced. The minimum hot/cold utility model used for part a is a linear optimization problem that is solved to global optimality using CPLEX. The model for part a provides (i) the amount of hot/ cold utility needed for the process and (ii) the location of pinch points denoting the distinct subnetworks. The pinch points will mark the temperature levels across which no heat transfer will

occur. This allows the subsequent parts of the decomposition framework to be solved independently for each subnetwork and will reduce the complexity of the optimization models. Given the information from part a, the minimum heat exchanger matches necessary to meet speciﬁcations (i) and (ii) are calculated using a mixed-integer linear optimization model9,11,12,59,64 and solved to global optimality using CPLEX. Vertical heat transfer9,71 was used in the formulation to distinguish between sets of heat exchanger matches with the same number of matches. A minimum temperature approach of 10 °C is also used for this analysis. Upon solution of the minimum matches model (b), the heat exchanger topology with the minimum annualized cost can be found using the superstructure methodology.9,11,12,59,64 The resulting nonlinear optimization problem is solved to ﬁnd high-quality local solutions using CONOPT and a multistart procedure with 100 initial points. For this stage, the minimum temperature approach was relaxed to 0.1 °C. Note that the above procedure is repeated for every feed CO2 composition and every feed ﬂow rate. To illustrate, we consider the feed that contains 10% CO2 and has a total ﬂow rate of 0.1 kmol/s. The corresponding ﬂow sheet is optimized in Aspen and the information of the optimized ﬂow sheet is provided to GAMS. The HEN models are solved in GAMS using CPLEX, CONOPT, and DICOPT as the LP/MILP, NLP, and MINLP solvers, respectively. Two distinct subnetworks (SN1 and SN2) are obtained by solving the model in part a. After solving the MILP model in part b, it is found that the SN1 and SN2 must have seven and ﬁve heat exchangers, respectively, to meet speciﬁcations. In part c, we determine the network topologies of each subnetwork using superstructures for both SN1 and SN2. For illustration, only the superstructure for SN2 is shown in Figure 5 for the ﬁve heat exchangers. The hot streams are presented in red, and the cold streams are presented in blue. The input−output temperatures for each stream are also shown. The output temperature of the low pressure (LP) steam is equal to the input temperature because this utility stream is undergoing isothermal condensation. The temperature of the reboiler is also constant because this stream

Figure 5. Topological superstructure for subnetwork 2 of 10% CO2 concentration and 0.1 kmol/s total ﬂow rate. All temperatures given correspond to the inlet and outlet temperatures of each stream in the subnetwork. The hot streams are colored red, and the cold streams are colored blue. 15651

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Figure 6. Optimal heat exchanger topology for subnetwork 1 of 10% CO2 concentration and 0.1 kmol/s total ﬂow rate. All inlet and outlet temperatures given correspond to the actual stream temperature of the match. The hot streams are colored red, and the cold streams are colored blue. The minimum temperature approach used to ﬁnd the optimum topology was 0.1 °C.

is undergoing evaporation without any temperature change. Among the ﬁve heat exchanger matches provided by the minimum match model, three of them include matches between CO2 compression intercooler units. LP steam is used to heat a remaining portion of the rich solvent and provide heat to the reboiler. There are no recycle streams used for the LP steam because it is a hot utility stream. The optimal topologies for SN1 and SN2 are shown in Figures 6 and 7, respectively. The two topologies together constitute the optimal HEN for the absorption-based process. The rich solvent (stream 7 in Figure 4) is a major cold stream

in the process which is heat integrated with multiple hot streams. In the SN1 topology, the stream 7 is ﬁrst split into two substreams and heated by the two high pressure CO2 streams (11 and 13) from the compression system. Stream 7 is then heated by two hot process streams, ﬁrst by the gaseous outlet (stream TOSEQ) of the stripper and then by the lean solvent. Upon heating from 47.4 to 110.1 °C in SN1, the rich solvent (stream 7) enters SN2. The transition of the streams from SN1 to SN2 is shown as stream superscripts (1→2 and 2→1) in Figures 6 and 7. In the SN2 topology, the rich solvent is again split and heated by streams 11, 13, and 15 from the CO2 compression system. Note that, before the heat integration took place, these three streams did not exchange heat with other process streams and were cooled using the cooling utility in three intercoolers. The substream that exchanges heat with stream 11 is further heated by LP steam before being mixed with the other substreams. LP steam is also used to provide the reboiler duty needed for the stripper. Cooling water is required only in SN1, and LP steam is required only in SN2. 5.1.5. Computational Results on the Absorption-Based Process with Heat Integration. The absorption-based process is optimized and energy integrated over a range of feed compositions (1−70% CO2, 5.5−15% H2O, 5.5% O2, and the balance N2) and ﬂow rates (0.1, 1, 5, and 10 kmol/s). This is obtained sequentially, starting with optimizing the conﬁguration for feed dehydration and the Aspen ﬂow sheet (Figure 4) and then obtaining the optimal HEN. Interestingly, the feed dehydration process is the same for all cases. The feed is ﬁrst cooled to 35 °C using a direct contact cooler. This reduces the H2O composition of the feed to 5.5% (which is the composition of a saturated feed at 35 °C), irrespective of the initial H2O composition (5.5−15%). No further reduction in the moisture content is performed. Hence,

Figure 7. Optimal heat exchanger topology for subnetwork 2 of 10% CO2 concentration and 0.1 kmol/s total ﬂow rate. All inlet and outlet temperatures given correspond to the actual stream temperature of the match. The hot streams are colored red, and the cold streams are colored blue. The minimum temperature approach used to ﬁnd the optimum topology was 0.1 °C. 15652

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Figure 8. Optimized and heat integrated process ﬂow diagram of the absorption coupled with with feed dehydration and CO2 compression for the feed that contains 10% CO2, 15% H2O, 5.5% O2, and 69.5% N2, and has a total ﬂow rate of 0.1 kmol/s.

with a number of process streams as described by the HEN. In total, seven economizers, one reboiler, one heater, and four coolers are present in the process. While the reboiler and the heater use LP steam as the hot utility, the cooler uses cooling water as the cold utility. The aftercondenser of the stripper is completely heat integrated with the rich solvent. Therefore, it does not consume any utility. The economizers also do not require any utilities and contribute to the reduction in energy usage of the process. The non heat integrated process (shown in Figure 4) with one direct contact cooler, one heater, one reboiler (attached to the stripper), one aftercondenser, one cooler for the lean solvent, and ﬁve intercoolers has 10 heat exchanger units. Most of the heat required to regenerate the rich solvent for the non heat integrated process is supplied by the steam as the hot utility. In addition, the intercoolers of the compression system are not heat integrated. A major diﬀerence between the non heat integrated and heat integrated processes is that, for the latter, a signiﬁcant amount of heat required to regenerate the rich solvent is obtained through heat integration with other process streams. The economizers reduce the steam requirement of the stripper reboiler, improve the energy eﬃciency of the process, and reduce the total cost. For instance, the non heat integrated process for 10% concentration of CO2 and a total ﬂow rate of 0.1 kmol/s consumes 1.22 kg/s ($607,852/

the bypass route is chosen from the superstructure for feed dehydration. The reason behind selecting the bypass over others (refrigeration, compression and cooling, membrane or TEG absorption) is simply because this keeps the overall cost to a minimum. Furthermore, the absorber can tolerate a feed gas with 5.5% H2O without any changes required in the process ﬂow sheet. The topologies of the optimized HENs remain similar at diﬀerent inlet CO2 concentrations. As an illustrative example, Figure 8 shows the completely heat integrated and optimized absorption-based process for CO2 capture when the feed gas contains 10% CO2, 15% H2O, 5.5% O2, and 69.5% N2, and has a total ﬂow rate of 0.1 kmol/s at 55 °C. The feed, shown in a brown color, is fed to the process using a feed compressor at 1.5 bar. It is then cooled using a direct contact cooler and then fed to the absorber at 35 °C. The lean solvent ﬂow to the absorber is shown in green in Figure 8. The ﬂow of the rich solvent is shown in two colors, pink and red, respectively, for the two heat exchanger subnetworks (SN1 and SN2). The blue lines shows the ﬂow of captured CO2 through the six-stage compression system. The feed (FLUEGAS) is ﬁrst sent to the absorber (B1) where CO2 is reacted with the lean solvent (LEANSOL). The solvent (RICHSOL) exiting the absorber column is loaded with CO2 and pumped to the stripper pressure. The pumped solvent (stream 7) then exchanges heat 15653

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Figure 9. Process ﬂow diagram of the membrane process with CO2 compression.

5.2. Membrane-Based CO2 Capture and Compression. Polymeric membranes are widely used in gas separation and CO2 recovery in natural gas processing, but they are commercially less popular for postcombustion CO2 capture. This is attributed to the high capture cost and the low purity of recovered CO2. However, recent developments such as multistage separation and vacuum permeate pumping rather than compressing the feed gas to very high pressure have shown promise45 to overcome these problems. Moreover, due to their simplicity and compactness they can be easily retroﬁtted onto the tail end of any power and chemical industry for CO2 capture. 5.2.1. Process Conﬁguration. Figure 9 shows the multistage membrane process ﬂow diagram that we have considered in this work. Similar to the absorption-based process, the feed gas is dried using the dehydration superstructure conﬁguration until the H2O content of the feed gas reduces to 0.1%. In each stage, the dry feed gas is ﬁrst split into two substreams. The ﬁrst substream is sent to a compressor and then cooled to achieve the desired driving force (pressure) and temperature for separation. The compressed and cooled gas then enters the membrane module as the feed. CO2-free clean gas is collected as retentate and vented to the atmosphere, whereas CO2 is separated and extracted on the permeate side using a vacuum pump. A vacuum pump operates such that a vacuum is created at the inlet by discharging the gas at 1 atm pressure. Therefore, the vacuum pump delivers the captured CO2 only at atmospheric condition. We allow both feed gas compression and vacuum permeate pumping in our membrane process to have the provision of all possible operating conditions. While the ﬁrst substream undergoes the separation process, the second substream is merely a bypass stream which allows the feed gas to bypass the entire stage. The mixture gas after the pump outlet is then sent as the feed gas to the next stage. Each stage in the multistage membrane system has the same equipment layout and conﬁguration. Once the product CO2 comes out of the vacuum pump of the ﬁnal stage at 1 atm pressure, it is compressed along with the stage bypass to obtain the sequestration pressure of 150 bar using a six-stage compressor with interstage cooling system. Using only a single-stage membrane process may not achieve the desired CO2 purity of 90% across the membrane unit. High purity of the captured CO2 stream is desirable, since it aﬀects the compression and sequestration costs. If the purity of the recovered CO2 is less, then the compressors would need to

year) of LP steam and 27.4 kg/s ($789/year) of cooling water. When the process is heat integrated (Figure 8), it consumes 0.82 kg/s ($408,554/year) of LP steam and 17.132 kg/s ($493/year) of cooling water, achieving more than 30 and 37% improvement in hot and cold utility usage, respectively. The annual electricity cost for both the non heat integrated and heat integrated processes is $86,340. Therefore, the operating costs are $694,981/year and $495,387/year for the non heat integrated and heat integrated processes, respectively. This translates to about 29% improvement in the operating cost when the process is heat integrated. As opposed to the operating cost, we observe 17.4% increase for the annualized investment cost, from $200,494/year to $240,670/year, when the process is heat integrated. This is attributed to the increased number and area of heat exchangers used for heat integration. However, the total annualized costs for the non heat integrated and heat integrated processes are $935,651/year and $736,054/ year, respectively. This is an overall cost reduction of more than 21%, which implies that heat integration is crucial for costeﬀective absorption-based CO2 capture and compression. We have also compared the performance of the heat integrated process with the conﬁguration of a classical absorption process65 for CO2 capture with a single crossexchanger and a cooler to bring down the temperature of the lean solvent to the stipulated value before it enters the absorber. Interestingly, the classical conﬁguration is almost the same as the non heat integrated conﬁguration, except for the heater which is used to heat the rich solvent using steam. In the classical conﬁguration, this heater is replaced by the crossexchanger to heat the cold rich solvent at the pump exit using the hot lean solvent from the stripper bottom. Therefore, the classical conﬁguration for CO2 capture and compression has one cross-exchanger, one reboiler, one aftercondenser, one cooler for the lean solvent, and ﬁve intercoolers. All the exchangers are considered to be shell and tube. The exchanger purchase cost correlations and heat transfer coeﬃcients used for the heat exchanger network optimization are obtained using the method described by Elia et al.9 Again, when compared, complete integration results in a reduced overall cost of the heat integrated conﬁguration compared to that of the classical conﬁguration. The overall cost of our heat integrated process (shown in Figure 8) is about 26% less than that of the non heat integrated classical process. This can be attributed to the use of economizers which reduce the total steam requirement and heat transfer area and improve the overall energy eﬃciency. 15654

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handle more volumetric ﬂow and the compression cost would increase. If we increase the number of stages to increase the CO2 purity, then it would decrease the compression cost; however, the investment cost for additional equipment would add to the total cost. While we use a multistage conﬁguration, it is possible that the optimal conﬁguration uses a smaller number of stages than speciﬁed. Stream bypass is extremely important for such cases, since it allows the CO2 stream to disregard the extra stages. If there is no bypass, the captured CO2 must ﬂow through each of the speciﬁed stages, which would unnecessarily increase the investment cost. Therefore, stream bypass also implies that as long as the minimum number of stages is speciﬁed, the optimal conﬁguration would remain unchanged. 5.2.2. Model Development. In this section, a nonlinear optimization (NLP) model for the optimization of the abovedescribed membrane process for CO2 capture is presented. Features of this model include multistage and multicomponent separation of CO2 from industrial ﬂue gas and gas mixtures. The problem can be described as follows. Given 1. feed gas characteristics (e.g., ﬂow rate, composition, pressure, temperature) 2. membrane properties (e.g., component membrane permeability and membrane thickness) 3. CO2 sequestration pressure Determine 1. feed pressure and temperature of each stage 2. stage membrane area 3. stage permeate pressure 4. utilities (electricity, cooling water, etc.) 5. operating and investment costs Aiming to minimize the total annualized cost of the process The assumptions, indices, sets, parameters, variables, assumptions, mathematical constraints, and the objective function that describe the mathematical model of the membrane process are presented below. Modeling Assumptions. 1. Each retentate and permeate compartment of a membrane unit in a stage can be divided into multiple subcompartments.52 Mass transfer occurs between the retentate and the permeate subcompartments only through diﬀusion. 2. No reactions are present. 3. Component permeability does not depend on feed pressure and concentration. 4. Concentration polarization on the membrane surface is negligible. 5. Pressure drop along the subcompartment is negligible. 6. All membranes operate at isothermal condition. 7. All compressors run adiabatically with 75% thermal eﬃciency. 8. All movers (compressors and vacuum pumps) run by electricity which is purchased from the grid. 9. The stage vacuum pumps deliver the gas at atmospheric pressure and temperature. The following indices are used throughout the mathematical model: s: stage

i: component j: equipment n: subcompartment Sets. Let S be the set of all stages. We have run the model for diﬀerent numbers of stages, and our computational experience suggests that three stages are suﬃcient to achieve the desired recovery and purity of CO2. Therefore, we ﬁx S = 3. The set of all components, I, is given as follows: i ∈ I = {CO2 , N2 , O2 , H 2O}

Note that I can include other chemical components (e.g., H2) also. However, we assume that only the above-mentioned four components will be present in the feed gas. The set of general equipment, J, is given as j ∈ J = {stage compressor, stage cooler , stage vacuum pump, 6 sequestration compressor units, 5 interstage coolers}

where one stage compressor, one stage cooler, and one stage vacuum pump are present along with a membrane unit in each stage of the multistage process conﬁguration. Each membrane unit has two compartments, namely, the retentate (high pressure) compartment and the permeate (low pressure) compartment. To better predict the mass transfer, we use an approximate modeling approach proposed by Uppaluri et al.52 In this approach, each of the two compartments of a membrane unit at a stage s is further divided into a number of small subcompartments, denoted by the set Ns. This compartmentalization is illustrated in Figure 10. Here, we consider

Figure 10. Subcompartmentalization of a membrane module.

cocurrent ﬂow pattern. Note that countercurrent and crossﬂow patterns are also used in the literature.72 However, cocurrent is the most common ﬂow pattern for CO2 capture. We also deﬁne MV and CU respectively for the movers and coolers as the subsets of J as follows. j ∈ MV = {stage compressor, stage vacuum pump, and 6 sequestration compressor units}

j ∈ CU = {stage cooler, 5 interstage coolers}

Parameters. The following parameters are deﬁned: xfi: molar fraction of component i in feed gas Ff: molar ﬂow of component i in feed gas (kmol/s) Pf: feed pressure (bar) Tf: feed temperature (K) Cp: speciﬁc heat (kJ/kmol·K) Patm: atmospheric pressure (1 bar) Tatm: atmospheric temperature (298 K) (P/δ)i: permeance of component i (kmol/m2·s·bar) Tmem: operating temperature for membrane (K) Pseq: sequestration pressure (bar) UCmem: purchase cost of unit membrane area ($/m2) 15655

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UCMVj: unit operating cost for the mover j ∈ MV ($/kWh) UCCUj: unit operating cost for the cooler j ∈ CU ($/kW) Pmin: minimum pressure allowed (bar) Pmax: maximum pressure allowed (bar) Amin: minimum membrane area allowed (m2) Amax: maximum membrane area allowed (m2) αj: capital cost per unit horsepower for unit j βj: exponent of power cost function for unit j γ: speciﬁc heat ratio ηj: eﬃciency of unit j ϕ: annualization factor Variables. The following variables are deﬁned to model the multistage membrane process. As: membrane area of stage s (m2) P1,s: retentate pressure in stage s (bar) P2,s: permeate pressure in stage s (bar) FFi,s: molar ﬂow rate of component i in the stream that enters compressor in stage s (kmol/s) FBi,s: molar ﬂow rate of component i in the stream that bypasses stage s (kmol/s) FRi,n,s: molar ﬂow rate of component i in retentate phase of subcompartment n of stage s (kmol/s) FPi,n,s: molar ﬂow rate of component i in permeate phase of subcompartment n of stage s (kmol/s) Fi,n,s: ﬂow of i from retentate to permeate phase of subcompartment n of stage s (kmol/s) xri,n,s: molar fraction of component i in retentate phase of subcompartment n of stage s xpi,n,s: molar fraction of component i in permeate phase of subcompartment n of stage s Ts: compressor outlet temperature in stage s (K) Wj,s: heat (kW) or power (hp) consumed in unit j at stage s As, P1,s, and P2,s are the decision variables to be optimized, while the others are intermediate variables required to describe the system appropriately. Constraints. Constraints include mass balances for each stage, mass balances for both the retentate and permeate sides in each stage, mass transfer equations that govern the gas separation, minimum recovery constraints, temperature− pressure relations, and heat and power equations to compute the equipment duties. The feed gas in each stage is divided into two substreams, namely, FFi,s and FBi,s. To model the bypass, we use the following mass balances around the splitter. Ff xfi = FFi , s + FBi , s

∀ (i , s )| s = 1

FFi , s

FPi , Ns−1, s + FBi , s − 1

=

∑ FFi , s

∀ ( i , s) | s > 1

∑ FPi , Ns , s + FBi , s − 1

FBi , s ∑ FB(i , s)

=

(20c)

FPi , Ns−1, s + FBi , s − 1

∀ (i , s)| s > 1

∑ FPi , Ns , s + FBi , s − 1

(20d)

For the retentate side of each subcompartment n in stage s (see Figure 10), we must satisfy the component mass balances given by eq 21. FR i , n , s = FR i , n − 1, s − Fi , n , s

∀ (i , n , s )| n > 1

(21)

We consider a cocurrent ﬂow pattern on the permeate side. Component mass balances for the permeate side yield FPi , n , s = Fi , n , s

∀ (i , n , s )| n = 1

FPi , n , s = FPi , n − 1, s + Fi , n , s

(22a)

∀ (i , n , s)|n = 1, s > 1 (22b)

The driving force to ﬂow a component across the membrane module is given by its partial pressure diﬀerential between the feed or retentate side and the permeate side. The mass transfer model for gas permeation52,73 is given by eq 23. ⎛P⎞ Fi , n , s = As ⎜ ⎟ (P1, s xri , n , s − P2, s xpi , n , s ) ⎝ δ ⎠i

∀ (i , n , s )

(23)

where xri , n , s =

FR i , n , s ∑i FR i , n , s

FPi , n , s

xpi , n , s =

∀ (i , n , s ) (24)

∀ (i , n , s )

∑i FPi , n , s

(25)

The duties of stage compressors and vacuum pumps are given by eqs 26 and 27, respectively: 1 Wj , s = η

(γ − 1)/ γ ⎤ ⎡ ⎛ 8314 ⎞ γ ⎢⎛ P1, s ⎞ ⎜ ⎟ − 1⎥ Tf ∑ FFi ,s⎝ ⎜ ⎟ ⎥ 745.3 ⎠ γ − 1 ⎢⎣⎝ Pf ⎠ i ⎦

∀ (j , s)|j = stage compressor

Wj , s =

1 η

∑ (i , n =|Ns|)

⎛ 8314 ⎞ γ ⎟T FPi , n , s⎜ mem ⎝ 745.3 ⎠ γ−1

⎡⎛ ⎤ ⎞(γ − 1)/ γ ⎢⎜ Patm ⎟ − 1⎥⎥ ⎢⎜⎝ P ⎟⎠ ⎣ 2, s ⎦

(19a)

(26)

∀ (j , s)|j = vacuum pump (27)

FPi , Ns , s − 1 + FBi , s − 1 = FFi , s + FBi , s

∀ (i , s)|s > 1

Every stage has a feed gas cooler before the membrane unit, the duty of which is given by

(19b)

To ensure when the feed stream is split into two substreams (FFi,s and FBi,s), each substream compositions must be the same; we use FFi , s ∑i FFi , s

= xfi

FBi , s ∑i FB(i , s)

= xfi

Wj , s =

∑ FFi ,sCp(Ts − Tmem)

∀ (j , s)|j = stage cooler

i

(28)

To get Ts, which is the temperature of the gas at the outlet of the stage compressor, we have

∀ ( i , s) | s = 1 (20a)

⎛ P1, s ⎞(γ − 1)/ γ Ts = Tf ⎜ ⎟ ⎝ Pf ⎠

∀ ( i , s) | s = 1 (20b) 15656

s=1 (29a)

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Figure 11. Optimized process ﬂow diagram of the membrane process coupled with feed dehydration and CO2 compression for the feed that contains 10% CO2, 15% H2O, 5.5% O2, and 69.5% N2, and has a total ﬂow rate of 0.1 kmol/s.

⎛ P1, s ⎞(γ − 1)/ γ Ts = Tatm⎜ ⎟ ⎝ Patm ⎠

P min ≤ P2, s ≤ Patm

s>1 (29b)

The minimum CO2 recovery and purity constraints are imposed using eqs 30 and 31, respectively. FPi , n , s + FBi , s ≥ 0.9Ff xfi

i ∈ CO2 , s = |S| , n = |Ns| (30)

FPi , n , s + FBi , s ≥ 0.9 ∑ (FPi ′ , n , s + FBi ′ , s) i′

∀s

(35b)

⎛ P max ⎞(γ − 1)/ γ Tf ≤ Ts ≤ Tf ⎜ s=1 ⎟ ⎝ Pf ⎠

(35c)

⎛ P max ⎞(γ − 1)/ γ Tatm ≤ Ts ≤ Tatm⎜ s>1 ⎟ ⎝ Patm ⎠

(35d)

Amin ≤ As ≤ Amax

∀s

(35e)

(31)

0 ≤ xri , n , s ≤ 1

∀ (i , n , s )

(35f)

Six-Stage CO2 Compression System. We consider six-stage compression with interstage cooling for sequestering the captured gas. To compute the total duty of the sequestration compressor system, we use

0 ≤ xpi , n , s ≤ 1

∀ (i , n , s )

(35g)

i ∈ CO2 , s = |S| , n = |Ns|

Wj , s =

⎛ 8314 ⎞ 1 ⎟T (6 ∑ (FPi , n , s + FBi , s))⎜ ⎝ 745.3 ⎠ mem η (i , n =| Ns |)

∑

(32)

∀ (i , n , s )

∀ (i , n , s )

∀ (i , n , s )

(35j) (35k) (35l)

(36)

where TIC is the total investment cost, ϕ is the annualizing factor, and OC is the annual operating cost of the membranebased CO2 capture process. TIC is given by TIC =

∑ (j ∈ J , s ∈ S)

αj(Wj , s)βj +

∑ UCmemAs s∈S

(37)

In eq 37, the ﬁrst term represents the investment cost of the movers (all compressors and vacuum pumps), while the second term represents the investment cost of the membrane units. The operating cost, OC, is the sum of the costs of total electricity consumption and cooling water usage, and is given by

(34)

Bounds. The following variable bounds are applied. ∀s

(35i)

min[ϕTIC + OC]

(33)

where Tmem and TC are respectively the inlet and outlet gas temperatures of each compression stage. It is assumed that the outlet gas of each compression stage is cooled to Tmem. Furthermore, a compression ratio of 2.3 is used for all six stages. All these ensure that TC is the same at each stage outlet and is computed as follows:

Patm ≤ P1, s ≤ P max

∀ (i , n , s )

Objective Function. The objective is to minimize the total annual cost of the membrane process that includes CO2 capture and compression, and has the following expression:

(FPi , n , s + FBi , s)Cp(TC − Tmem)

TC = [2.3(γ − 1)/ γ − 1]Tmem

0 ≤ FBi , s ≤ Ff xfi

0 ≤ Fi , n , s ≤ Ff xfi

(i , n =|Ns|)

∀ (j , s)|(j = seq cooler, s = |S|)

(35h)

0 ≤ FPi , n , s ≤ Ff xfi

The total duty of ﬁve interstage coolers is given as follows: Wj , s = 5

∀ (i , n , s )

0 ≤ FR i , n , s ≤ Ff xfi

γ [2.3(γ − 1)/ γ − 1] γ−1 ∀ (j , s)|(j = seq compressor, s = |S|)

0 ≤ FFi , s ≤ Ff xfi

(35a) 15657

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OC = (0.746·8000)

Article

vacuum (about 0.04 bar) for regeneration. The regenerated TEG solvent is pumped back to the absorption column after being cooled to 65 °C. The dehydrated feed is then sent to the two-stage membrane-based capture process. The major operating variable values are shown in Figure 11. In each step, the feed is ﬁrst compressed (up to 4.1 bar in the ﬁrst stage and 3.4 bar in the second stage) and then cooled to 35 °C before it enters the membrane module. A vacuum pump in each stage draws the concentrated CO2 in the permeate side. The gas from the permeate side of the ﬁrst stage is sent to the compressor to the second stage. The product from the vacuum pump of the second stage is then compressed to 150 bar using the six-stage compression system.

UCMVjWj , s

(j ∈ MV, s ∈ S)

+ (3600 ·8000)

∑ (j ∈ CU, s ∈ S)

UCCUjWj , s (38)

Equations 19a−38 deﬁne the NLP model for the optimization of membrane process for CO2 capture with compression. 5.2.3. Model Implementation. The NLP model for the membrane-based process is a nonconvex model, and a feasible starting point is critical when solving the model. However, it is not trivial to generate a feasible solution for the model. We ﬁnd the ﬁrst feasible solution using the following strategy. Let M1 be the original NLP model. We note that eqs 19a−25 and 29a−38 constitute a reduced model M2, which is a relaxed version of M1, but has the same feasible region as that of M1. The reason is that M2 includes all the mass balances, mass transfer equations, performance constraints, and bounds. The advantage of M2 is that it can be solved easily, since the size of M2 is much smaller than that of M1. Therefore, we get the ﬁrst feasible solution by solving M2. Once the feasible solution is obtained, we start solving M1 using the solution of M2 as the starting point. This strategy is implemented in GAMS74 using CONOPT as the NLP solver. We set Tmem = 298.15 K, Tmin = Tmem, Tmax = 1000 K, Pseq = 150 bar, Pmin = 0.01 bar, Pmax = Pseq, Amin = 5 m2, Amax = 50 000 m2, γ = 1.4, and η = 0.75. The gas permeance values for CO2, N2, O2, and H2O are 2.7 × 10−5, 6.7 × 10−7, 6.7 × 10−7, and 1.323 × 10−5 kmol/m2·s·bar, respectively. 5.2.4. Computational Results on the Membrane-Based Process. Similar to the absorption-based process, the membrane-based process is optimized over a range of feed compositions (1−70% CO2, 5.5−15% H2O, 5.5% O2, and the balance N2) and ﬂow rates (0.1, 1, 5, and 10 kmol/s). As an example, Figure 11 shows the optimized membrane-based process when the feed gas contains 10% CO2, 15% H2O, 5.5% O2, and 69.5% N2 and has a total ﬂow rate of 0.1 kmol/s at 55 °C. The feed is ﬁrst cooled to 35 °C using a direct contact cooler, and the H2O content reduces to 5.5%. Further dehydration of the feed to 0.1% H2O is achieved using the TEG absorption process. TEG absorption is selected based on the fact that the total cost of dehydration is the lowest for TEG absorption among those of the dehydration alternatives shown in Figure 2. Note that we cannot use a bypass, since we must dehydrate the feed to 0.1% H2O. We also cannot use compression and cooling and refrigeration, since the loss of CO2 from these two dehydration alternatives is more than the allowable limit of 10%. Therefore, the feasible alternatives for feed dehydration are SPEEK-based membrane and TEG absorption. Now, the annualized investment and operating costs of the SPEEK-based-membrane process plus the direct contact cooler to dehydrate the feed from 15 to 0.1% H2O are $739,000 and $213,000, respectively, when the feed ﬂow rate is 0.1 kmol/s. For TEG absorption, the investment and operating costs for the same are $146,000 and $67,000, respectively. Therefore, we select TEG absorption for feed dehydration for the membrane-based CO2 capture process. Here, as shown in Figure 11, H2O in the feed gas is absorbed in liquid TEG solvent ﬂowing countercurrently in the TEG absorber. The dry gas leaves the column from the top. The H2O-rich solvent from the bottom of the column is pumped and then heated in a heater to about 73 °C. The heated solvent is then ﬂashed under

6. RESULTS AND DISCUSSION The absorption-based process does not use feed dehydration and the bypass route is chosen, once the H2O content reaches 5.5% after the direct contact cooler. However, the membranebased process usually uses TEG absorption for feed dehydration, since TEG absorption provides dehydration at the lowest cost. The costs obtained for the fully optimized processes are shown in Figures 12−18. [While the investment and operating

Figure 12. Annualized investment costs for the optimized and heat integrated absorption process.

costs for variable feed CO2 compositions and feed ﬂow rates are shown in logarithmic scale for clarity (as the ranges for the costs are very high) in Figures 12−15, the same are shown in linear scale in Figures 16 and 17.] The optimal annualized investment and operating costs of the absorption-based process for variable molar composition of CO2 from 0.01 to 0.70 (i.e., feed CO2 molar content of 1−70%) and also for 0.1, 1, 5, and 10 kmol/s feed ﬂow rates are shown in Figures 12 and 13, respectively. A signiﬁcant increase in costs is observed as the feed ﬂow rate increases. This shows the importance of the scale of a process for CO2 capture. It is also clear from the plots that, for any feed ﬂow rate, the investment and operating costs increase with CO2 composition. This is expected, since the net CO2 ﬂow rate also increases with CO2 composition, for ﬁxed total feed ﬂow rate. It is important to note that each cost curve represents a constant total feed ﬂow. Therefore, when the CO2 composition is increased, the total CO2 ﬂow in the feed is also 15658

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Figure 13. Annual operating costs for the optimized and heat integrated absorption process.

Figure 15. Optimized annual operating costs for the membrane process.

increased. Increased CO2 ﬂow requires increased solvent ﬂow and reboiler duty of the stripper in the absorption-based process. Moreover, it increases the compression cost for CO2 transportation. While increased CO2 composition reduces the operating cost of the membrane units by increasing the partial pressure driving force through the membrane materials, the savings is oﬀset by the increased compression cost. The optimized annualized investment and operating costs for the membrane-based CO2 capture process are shown in Figures 14 and 15. Similar trends are observed for costs with those of

Second, absorption is the technology of choice when the feed gas has a low CO2 composition, as the investment and operating costs for the absorption-based process are lower than those of the membrane-based process in the low composition region for all four ﬂow rates. At low CO2 compositions, the investment costs (Figure 16) for the membrane-based process are more than twice of those of the absorption-based process. The operating costs (Figure 17) for the membrane-based process are even higher. Third, the investment and operating costs of the absorption-based process increase more sharply than those of the membrane-based process. The operating costs of the membrane-based process are much higher than those of the absorption-based process at low CO2 compositions. This is because of the larger feed compression required to achieve the desired driving force for separation in the membrane-based process. On the other hand, the operating costs of the absorption-based process are much higher than those of the membrane-based process at high CO2 compositions, largely due to the costly solvent regeneration for the former. Interestingly, there exists a critical CO2 composition for which crossover is present between the investment and/or operating costs of the two technologies for each ﬂow rate. This crossover happens when the feed CO2 composition is about 10−20% and 35% for the investment and operating costs, respectively. The membrane-based process becomes competitive with the absorption-based process as the feed CO2 composition approaches these crossover compositions. In fact, the membrane-based process is more economical at high feed CO2 compositions. While the crossover compositions are diﬀerent for the annualized investment and operating costs for the two technologies, we compute the total costs for better selection. The reason is that there will be a single crossover composition for each ﬂow rate when the total cost is considered. Figure 18 shows the total costs for each ton of CO2 captured and compressed, when the feed ﬂow rate is 0.1, 1, 5, and 10 kmol/s. The total cost ($/ton of CO2 captured and compressed) decreases with CO2 composition. At low compositions, the absorption-based process is the technology of choice. Furthermore, there is a crossover in cost for each feed ﬂow rate at about 27−30% of feed CO2 composition. This means that when the feed CO2 composition is less than 27%, the

Figure 14. Optimized annual investment costs for the membrane process.

the absorption-based process. However, the cost values are not the same for the two technology alternatives. This is evident from Figures 16 and 17, which compare the investment and operatings costs, respectivley, for the two technologies at four feed ﬂow rates. Several interesting observations can be made from these plots. First, as a general trend, the investment and operating costs, except for the membrane-based process at low CO2 compositions, show almost linear relations with feed CO2 composition. For the membrane process, costs increase nonlinearly with CO2 composition at very low concentrations. 15659

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Figure 16. Investment cost comparisons between the absorption- and membrane-based processes.

absorption-based process is the technology of choice for postcombustion CO2 capture. After this, the membrane-based process is preferred over the absorption-based process. Signiﬁcant cost reduction in the CCS chain is possible by capturing CO2 from highly concentrated ﬂue gases, using the membrane-based process. The eﬀect of feed ﬂow rate is also evident from the results shown in Figure 18. Costs are higher at low feed ﬂow rates and vice versa. Interestingly, the cost increases more sharply with decreasing feed ﬂow rate at low CO2 compositions. This highlights the beneﬁts of economy of scale. It also suggests that capturing CO2 from larger sources would be more economical for any given sector. Although we set the purity targets for the capture processes to be 90% or more, the absorption-based process captures CO2 at high purity (almost 99% pure), thereby posing no challenges for the subsequent pipeline transportation (the pipeline speciﬁcations for CO2 transport may require 95% pure CO2 after the capture and compression75). The membrane-based process failed to capture CO2 with 95% purity and 90% recovery when the CO2 composition in the feed was less about 5%. On the basis of the above results, in section 6.1, we propose a simple parameter estimation based input−output model to

explicitly derive the cost expressions as a function of the feed CO2 composition and feed ﬂow rate. 6.1. Input−Output Model. Our goal in this section is to develop explicit expressions for costs of each of the capture processes as function of feed CO2 composition and feed ﬂow rate. This provides a quantitative approach toward scaling up a CO2 capture process for any CO2-emitting chemical and power industries. We propose the following simple functional expression for the investment (IC) and operating costs (OC) as function of feed CO2 composition (xCO2) and feed ﬂow rate (F). IC or OC = α + (βxCO2 n + γ )F m

(39)

where α, β, γ, n, and m are parameters which we can obtain by ﬁtting. The rationale of selecting an explicit functional form shown in eq 39 is that we can easily incorporate the cost functions into a process synthesis model for technology selection. To illustrate, let yt be the binary variable that represents the selection of capture technology t, and is deﬁned as ⎧1 if technology t is selected yt = ⎨ ⎩ 0 otherwise 15660

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Figure 17. Operating cost comparisons between the absorption- and membrane-based processes.

IC or OC = αt yt + βt xCO2 nF m + γtF m L U xCO y ≤ xCO2 ≤ xCO y, 2 t 2 t

y = [0, 1]T

(40a)

F Lyt ≤ F ≤ F Uyt , (40b)

Here, xLCO2 and xUCO2 are respectively the lower and upper bounds on the feed CO2 composition, and FL and FU are respectively the lower and upper bounds on the feed ﬂow rate. Equation 40a ensures that when technology t is selected (i.e., yt = 1), the cost function reduces to eq 39, for a given feed CO2 composition xCO2 and feed ﬂow rate F. Otherwise, IC and OC are zero. Equation 40b ensures that a technology is selected only when the feed CO2 composition and total feed ﬂow rate are within their valid ranges. To obtain α, β, γ, n, and m for the absorption- and membrane-based technologies discussed in this work, we use our optimized cost data and apply the maximum likelihood parameter estimation for the best ﬁt. The resulting parameters are presented in Table 5. On average, the prediction errors are less than 5%. For the low ﬂow rates, the prediction errors are much less. Note that errors as high as 10−20% are not uncommon in scale-up. This justiﬁes the proposed model, which has only ﬁve parameters. Due to its explicit form, it can be easily used for process scale-up, parametric study, process

Figure 18. Total costs for the absorption- and membrane-based CO2 processes.

t ∈ T |t = {absorption, membrane}

With this, we can reformulate the cost model (eq 39) as follows: 15661

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Table 5. Estimated Parameters for the Input−Output Based Cost Model [α + (βxCO2n + γ)Fm] process

α

β

γ

n

F (mol/s)

0.01 < xCO2 < 0.70

100 < F < 10 000

0.01 < xCO2 < 0.70

100 < F < 10 000

absorption

7,719

67,871

177,500

16,505

absorption

0

24,088

Operating Cost ($/year) 0 1 1

0.01 < xCO2 < 0.70

100 < F < 10 000

membrane

0

11,619

0

0.01 < xCO2 < 0.70

100 < F < 10 000

18,912

0.88

0.21

0.77

1

(2) Metz, B.; Davidson, O.; De Coninck, H. C.; Loos, M.; Meyer, L. A. IPCC Special Report on Carbon Dioxide Capture and Storage: Prepared by Working Group III of the Intergovernmental Panel on Climate Change; IPCC, Cambridge University Press: Cambridge, U.K., 2005. (3) Davis, S. J.; Caldeira, K.; Matthews, H. D. Future CO2 emissions and climate change from existing energy infrastructure. Science 2010, 329, 1330−1333. (4) DOE. Carbon Sequestration: Research and Development; U.S. Department of Energy Report; Oﬃce of Science, Oﬃce of Fossil Energy, U.S. Department of Energy; Washington, DC, 1999. (5) Pires, J. C. M.; Martins, F. G.; Alvim-Ferraz, M. C. M.; Simões, M. Recent developments on carbon capture and storage: An overview. Chem. Eng. Res. Des. 2011, 89, 1446−1460. (6) Chu, S. Carbon capture and sequestration. Science 2009, 325, 1599. (7) Deutch, J.; Moniz, E. J. The Future of Coal: Options for a CarbonConstrained World; Massachusetts Institute of Technology: Cambridge, MA, 2007. (8) Baliban, R. C.; Elia, J. A.; Floudas, C. A. Toward novel biomass, coal, and natural gas processes for satisfying current transportation fuel demands. 1. Process alternatives, gasification modeling, process simulation, and economic analysis. Ind. Eng. Chem. Res. 2010, 49, 7343−7370. (9) Elia, J. A.; Baliban, R. C.; Floudas, C. A. Toward novel hybrid biomass, coal, and natural gas processes for satisfying current transportation fuel demands. 2. Simultaneous heat and power integration. Ind. Eng. Chem. Res. 2010, 49, 7371−7388. (10) Elia, J. A.; Baliban, R. C.; Xiao, X.; Floudas, C. A. Optimal energy supply network determination and life cycle analysis for hybrid coal, biomass and natural gas to liquid (CBGTL) plants using carbonbased hydrogen production. Comput. Chem. Eng. 2011, 35, 1399− 1430. (11) Baliban, R. C.; Elia, J. A.; Floudas, C. A. Optimization framework for the simultaneous process synthesis, heat and power integration of a thermochemical hybrid biomass, coal, and natural gas facility. Comput. Chem. Eng. 2011, 35, 1647−1690. (12) Baliban, R. C.; Elia, J. A.; Floudas, C. A. Simultaneous process synthesis, heat, power, and water integration of thermochemical hybrid biomass, coal, and natural gas facilities. Comput. Chem. Eng. 2012, 37, 297−327. (13) Floudas, C. A.; Baliban, R. C.; Elia, J. A. Global optimization of a MINLP process synthesis model for thermochemical based conversion of hybrid coal, biomass, and natural gas to liquid fuels. Comput. Chem. Eng. 2012, 42, 64−86. (14) Floudas, C. A.; Elia, J. A.; Baliban, R. C. Hybrid and single feedstock energy processes for liquid transportation fuels: A review. Comput. Chem. Eng. 2012, 41, 24−51. (15) Elia, J. A.; Baliban, R. C.; Floudas, C. A. Nationwide energy supply chain analysis for hybrid feedstock processes with significant CO2 emissions reduction. AIChE J. 2012, 58, 2142−2154. (16) Rao, A. B.; Rubin, E. S. A technical, economic, and environmental assessment of amine-based CO2 capture technology for power plant greenhouse gas control. Environ. Sci. Technol. 2002, 36, 4467−4475. (17) Yang, H.; Xu, Z.; Fan, M.; Gupta, R.; Slimane, R. B.; Bland, A. E.; Wright, I. Progress in carbon dioxide separation and capture: A review. J. Environ. Sci. 2008, 20, 14−27.

7. CONCLUSION Two major CO2 capture technologies, namely the MEA-based chemical absorption and the multistage membrane, are rigorously modeled, optimized, and energy integrated over a range of feed CO2 compositions and feed ﬂow rates. Key components of each of the two processes include a feed dehydration section, a separation plant to capture at least 90% of CO2 from the feed, and a multistage compression system to compress the captured CO2 to separate pure CO2 for sequestration at 150 bar. A simulation-based optimization approach is presented for the absorption-based process. The process is further optimized and heat integrated using a heat exchanger network approach. One key feature of the heat integration is that it is expanded beyond the capture plant to include the compression system for the ﬁrst time. A novel multistage superstructure model is also presented for the membrane-based process to minimize the total annualized cost. This model can be easily used for many other gas separation applications including natural gas upgrading, H2 puriﬁcation, air separation, and oxy enrichment, and also for screening membrane materials. A cost-based comparison between the absorption- and membrane-based CO2 capture processes suggests that CO2 composition and ﬂow rate can play signiﬁcant roles and should be considered in selecting capture technologies for diverse emission scenarios. Results suggest that while absorption is cost-eﬀective at low CO2 compositions, signiﬁcant cost reduction is possible using membrane-based technology when the CO2 compositions are about 30% or more in the feed gas. Finally, the explicit expressions developed for the investment and operating costs is a contribution to the CO2 capture literature which we believe would help in decision and policy making for global carbon management. AUTHOR INFORMATION

Corresponding Author

*Tel.: (609) 258-4595. Fax: (609) 258-0211; E-mail: ﬂoudas@ titan.princeton.edu. Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS The authors gratefully acknowledge partial ﬁnancial support from the National Science Foundation (NSF EFRI-0937706 and NSF CBET-1158849).

■

xCO2

membrane

optimization, and process synthesis of CO2 networks for carbon capture.

■

m

Investment Cost ($/year) 901 0.66 0.80

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Modeling, Simulation, and Optimization of Postcombustion CO2

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