Dynamic Optimization of a Dual Pressure Swing Adsorption Process

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Dynamic Optimization of a Dual Pressure Swing Adsorption Process for Natural Gas Purification and Carbon Capture Seungnam Kim, Daeho Ko, and Il Moon Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04157 • Publication Date (Web): 17 Oct 2016 Downloaded from http://pubs.acs.org on October 24, 2016

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Industrial & Engineering Chemistry Research

Dynamic Optimization of a Dual Pressure Swing Adsorption Process for Natural Gas Purification and Carbon Capture Seungnam Kima, Daeho Kob*, Il Moona*

Department of Chemical and Biomolecular Engineering, Yonsei University, Yonsei-ro 50, Seodaemun-

a

gu, Seoul, 03722, Korea

e-mail: [email protected]

*

GS E&C, Gran Seoul, Jongro 33, Jongno-gu, Seoul, 03159, Korea

b

*e-mail: [email protected] or [email protected]

ACS Paragon Plus Environment


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ABSTRACT. With an increased emphasis on reduced carbon emissions, many research efforts focused on various carbon capture techniques have concurrently expanded in application. Pressure swing adsorption (PSA) is one of the key processes for carbon capture and storage (CCS). During the natural gas sweetening operation of PSA processes, a high volume of carbon dioxide is included in the waste flow (heavy product). To improve the CO2 purity of the waste flow, this work firstly performs the dynamic optimization of a general four-step dual PSA process. The objective of the rectifying unit is to maximize methane recovery while the objective of the stripping unit is to maximize carbon dioxide purity for CCS. In brief, decision variables for the rectifying unit are the step times, P/F ratios, and feeding velocities of each unit; the length of the bed is added as a decision variable for the stripping unit. Optimization results indicate that carbon dioxide purity increases from 41.4 % to 76.3 % and methane recovery increases from 78.5 % to 95.4 %.

KEYWORDS. Pressure swing adsorption (PSA), Dynamic optimization, Modeling, Dual PSA, Carbon capture


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1.

INTRODUCTION

Among several proposed strategies to reduce carbon emissions, 1 carbon capture and storage (CCS) has emerged as a key approach.2 To support CCS, pressure swing adsorption (PSA) has been widely used in separating or purifying mixed gases including natural gas, synthetic gas, landfill (LF) gas, coal bed methane (CBM), and other gases.3 PSA, generally available for carbon capture, operates over a wide range of pressure and temperature, and offers a competitive power consumption rate in the separating field.4 Given these advantages, significant research have focused on carbon capture using various PSA processes.5-6 Dantas et al. simulated a conventional four-step Skarstrom cycle PSA process to analyze carbon dioxide purity and recovery during CO2/N2 separation.7 Modified PSA processes have also demonstrated efficient carbon capture. Li et al. used a dual reflux (DR) PSA process to increase carbon purity.8 Grande and Blom analyzed the separation efficiency of a dual PSA process during carbon capture.9 In this study, we focus on this dual PSA process. This process consists of two units: (1) a rectifying unit and (2) a stripping unit. The additional PSA (stripping) unit purifies the waste flow from the conventional PSA (rectifying) unit. The feed gas is composed of 85% methane and 15% carbon dioxide. The rectifying unit produces high purity methane. The stripping unit separates the waste flow of the rectifying unit into carbon dioxide.

Optimization of PSA processes has been the significant subject of researches over the past few decades.10 In 1990, Smith and Westerberg optimized a simple PSA process by minimizing capital and



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operating costs using time-averaged values in their balance equations.11-12 Nilchan and Pantelides established one-bed rapid and two-bed PSA models to minimize average power consumption.13 Ko et al. developed PSA optimization algorithms to be easily implemented in gPROMS modeling system and performed optimizations of PSA processes to separate flue gas (CO2 and N2) in view of design and operation.14-15 In 2012, Hasan et al. optimized PSA and vacuum PSA processes using different feed compositions to minimize total annual costs.16 In contrast to these prior studies, we carried out the optimization of the dual PSA process simultaneously maximizing the purity of the heavy product (carbon dioxide) and the recovery of light product (methane) by obtaining optimal operating strategies. A general four-step Skarstrom cycle is adopted and the axial domains of the adsorption beds are discretized by using partial differential algebraic equations (PDAEs) including mass balance, momentum balance, and adsorption kinetic. To gain optimal operational strategies at the cyclic steady state (CSS), the initial values of all CSS-related variables (i.e., temperature, gaseous and solid concentrations in the bed) are treated as decision variables. In this study, CSS is defined as the differences between the initial state variables at the beginning of the cycle and the final state variables at the end of the cycle are constrained by a very small positive variable, 𝜖 in a similar way of the previous studies.17-19


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2.

MATHEMATICAL MODELING OF DUAL PSA

Five key steps support the PSA modeling process: (1) Describe the adsorption and desorption equilibrium using an adsorption isotherm based on reliable data and parameters. (2) Describe the flow patterns and their effects on performance indicators, such as purity and recovery of components. (3) Establish dynamic balance equations that reflect time dependent variables. (4) Establish partial differential balance equations that consider axial dispersion. (5) Confirm the existence of CSS and define it mathematically.

These steps are typical for modeling all separation processes using a kinetic adsorbent and often lead to complex models. Although a detailed mathematical description is desirable, the computational burden resulting from these complex equation–variable relationships cannot be ignored during optimization. To ease the computational burden, the following several assumptions are adopted in this study:



Ideal gas law is applied.



Radial dispersion in concentration, momentum, and temperature is neglected.



A linear driving force (LDF) model is used to describe the adsorption phenomena.



The Langmuir–Freundlich (LF) isotherm is used to describe the adsorption and desorption equilibrium.



The particle size, bed void, and catalyst porosity in the beds are constant.



All inlet flow velocities are calculated using the valve equation except the feed flow at the adsorption step and the purge flow at the regeneration step.



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

The inlet purge flow velocity is calculated using the product velocity and the P/F ratio.



The pressure at the bottom of the column is atmospheric at depressurization and regeneration steps.

The selection of proper adsorbents is still a matter of contention. 20 In this study, a carbon molecular sieve (CMS) is used. The CMS type adsorbent is already popular in PSA process and has a good pressure resistance compared to the zeolites while the zeolites has a good adsorption efficiency at the vacuum circumstance.21-24 To apply accurate adsorption isotherm to the model, the CMS from the research of Bae and Lee is adopted.25 In 2005, they analyzed adsorption isotherms of a CMS type adsorbent. They estimated the Langmuir–Freundlich isotherm parameter values and analyzed CH4/CO2 separation performance using PSA processes and their results are listed in Table S1. To apply temperature dependencies of adsorption isotherms, all parameters for two components are modified to linear algebraic equation forms in terms of the temperature. This modification is performed by least square method using MATLAB and the results are described in Figure S1 and Table S2.

Table S3 lists the governing equations commonly used to describe the adsorption process,15, 21, 26-28 which are consistent with the previous described PSA modeling process steps and assumptions. Table S4 lists the boundary conditions for adsorption.

Each unit has four flows in this dual PSA process. Equations (1) to (4) can be used to determine the total moles of each flow during a single cycle. The binary variables for each step (yPR , yAD , yDP , and yRG ) have values of 0 or 1.14-15 At its own step, the value of each variable is 1. For example, y𝑃𝑅 = 1


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when the pressurization step starts, while y𝑃𝑅 = 0 at other steps.

t

M_Light_prod(i) = ∫0 cycle yAD uL εbed Abed Ci,L dt t

M_Feed(i) = ∫0 cycle(yPR + yAD )u0 εbed Abed Ci,0 dt t

M_Purge_in(i) = − ∫0 cycle yRG uL εbed Abed Ci,L dt t

M_Heavy_prod(i) = ∫0 cycle(yDP + yRG )u0 εbed Abed Ci,0 dt

(1) (2) (3) (4)

Using the total moles of each flow, Equations (5) and (6) are used to determine the purity and recovery, respectively.

Purity(i) =

M_Prod_out(i) NoComp

∑i

Recovery(i) =

(5)

M_Prod_out(i)

M_prod_out(i)−M_purge_in(i) M_Feed(i)

(6)

In a dual PSA process, the heavy product in the rectifying unit is fed to the stripping unit where it is separated again to obtain a high-purity carbon dioxide gas. The feed flow into the rectifying unit consists of 85% methane and 15% carbon dioxide, as is the recycle flow from the stripping unit. The methane purity of the light product is given as 97% for pipeline quality.29 Similarly, the purge flows (in and out) for the rectifying unit are composed of 97% methane and 3% carbon dioxide because all beds are rinsed with part of their product. The purge flows (in and out) for the stripping unit are comprised of 85% methane and 15% carbon dioxide for the same reason. The heavy product composition from the rectifying unit determined by the optimization is the same as the feed composition entering into the stripping unit. Table S5 lists the model parameters and their associated values. The bed length (Lbed ) of the stripping unit is not fixed. Instead, it acts as a decision variable during optimizations because the



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feed flow rate into the stripping unit is often considerably less than the feed flow rate into the rectifying unit.


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3.

OPTIMIZATION STRATEGIES

As mentioned in the previous chapter, PSA bed models are established with PDAEs with a second order centered finite difference method (CFDM) in this study. Because the PSA models are highly nonlinear, transient, and spatially discretized to be used for simulation and optimization, they are difficult to converge especially in optimization calculations. To avoid the difficulties in simultaneous optimization convergences of the PSA models involving the rectifying unit and the stripping unit, we employ an optimization framework for the dual PSA processes as illustrated in Figure 1.

Although the basic mathematical models of both units are identical, they have different objective and constraints, which are added to their own models at each ‘Variable & constraint defining’ step. After the rectifying unit is optimized, select optimal values are extracted from the results to be used for the stripping unit optimization. With those optimal values and a few constraints for stripping unit, the optimization of stripping unit is performed. The simulations and optimizations are performed by using gPROMS custom modeling system (Processbuilder version 1.0.0.).

As noted previously, the purpose and features of the rectifying unit alone in a dual PSA process are the same as those of a conventional PSA process for the purification of a light product (weak adsorbate). The key performance indicator in a conventional PSA process is primary component recovery in the light product stream. Similarly, the objective for the rectifying unit in a dual PSA process is to maximize methane recovery in the light product stream.30 To maximize methane recovery, the feeding velocity at



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the adsorption step, the P/F ratio and each step time are adopted as decision variables; the methane purity in the light product stream is fixed as 97% to meet the specification for pipelines.

For the stripping unit, the methane purity constraint in the light product stream is 85% to be identical to the methane mole fraction of the rectifying feed stream. Two additional constraints are included in the stripping unit optimization procedure: (1) the total cycle time for the stripping unit is set equal to the rectifying unit cycle time for operational convenience, and (2) the total moles of feed in the stripping unit is set equal to the total moles of heavy product in the rectifying unit.

The scheme of this process is described in Figure 2. The compositions of each stream are fixed or constrained to the corresponding values, except two streams which are marked as ‘To Be Optimized (TBO)’; the feed and heavy product streams of stripping unit. Information of those streams are obtained from the optimization results of rectifying unit and transferred to the stripping unit model during the optimization.

Compared to the rectifying unit, an additional and important decision variable, i.e., the bed length (STR. Lbed ), is included in the stripping unit. Because the feed molar flow rate of the stripping unit is typically less than that of the rectifying unit, the bed length must be shorter. Therefore, an optimal bed length is determined in conjunction with other decision variables during the stripping unit optimization.

Two additional constraints are applied to both optimization procedures (for the rectifying and stripping units). First, both units are modeled as a two-bed model in which each unit is assumed to


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have interconnected twin beds that result in partial sharing of their light product as a rinsing gas. The P/F ratio determines the amount of rinsing gas from the light product flow, which subsequently affects the rinsing efficiency and product purities. For this reason, the adsorption step time and regeneration step time are assumed to be same. The pressurization step time and depressurization step time are also the same.

Second, CSS conditions must be satisfied. Tens or even hundreds of simulated pre-CSS cycles are typically required for a PSA process to reach CSS and optimal operation.31-33 These extensive calculations result in considerable computational burden. Thus, select research have attempted to optimize PSA processes without simulating the pre-CSS cycles. Ko et al. proposed a mathematical description for CSS when optimizing PSA processes.15 Their approach eliminates the needs for pre-CSS simulations and instead, they uses an algorithm that determines initial CSS values in their optimization model. Equation (9) defines the CSS as follows:

−𝜖 ≤ 𝜙𝑡=0 (𝑖, z) − 𝜙𝑡=𝑡𝑐𝑦𝑐𝑙𝑒 (𝑖, z) ≤ 𝜖,

(9)

𝑖 = 1, ⋯ , 𝑛

where 𝜙 includes the temperature, the gaseous component concentration, and the solid component concentration—all indicators of CSS; and 𝜖 is given as a very small, positive variable (10-2 or 10-5) reflecting a sufficiently small difference between initial and final values18-19,

34

, while Ko et al.(2005)

minimize 𝜖 by including as a penalty term in the objective function. To satisfy CSS conditions, the initial values of temperature, gaseous concentration, and solid concentration of the cycle are also treated as



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decision variables in the model15. Table 1 summarizes the optimization models for the rectifying and stripping units.


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RESULTS By the aforementioned optimization framework for Dual-PSA, the optimal operating strategies and associated values are obtained. Before discussing the optimization results, the CSS should be discussed first. For smooth conversion of optimizations, the normalized value (between 0 and 1) for gaseous component (Cnorm,i ) and temperature (Tnorm,i ) are defined. The solid phase loadings for each component (qi ) are not normalized because their values are already located similar range with Cnorm,i and Tnorm,i . The differences between the initial and final value of these normalized variables are defined to check the CSS tolerance. The PSA model in this study discretized into eleven nodes along the axial direction. Except the top and bottom point, because they are one of the boundary conditions, nine nodes are participating to check the CSS. Nine nodes with gaseous concentration, solid loading for two components, and temperature make 45 individual constraints for each unit which are working for CSS analysis and the values are listed in Table S6. The absolute mean value of the CSS tolerance is 3.57 × 10−6 , therefore, the attainment of CSS is accomplished. The initial P, T values are listed in Table S7. In addition, the pressure and temperature profile and gaseous component concentration profile of both side of beds are described in Figure S2 and Figure S3, respectively.

Table 2 lists the optimized recovery and purity of components for both conventional (stand-alone rectifying unit) and dual PSA process. The dual PSA process is regarded as a rectifying unit with a supplemented stripping unit. In other words, the conventional PSA and stand-alone rectifying unit are same in this work. The performances at the dual PSA process are compared to those of the conventional



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stand-alone PSA process. In the conventional stand-alone PSA process, the methane recovery is 78.5 %, and the carbon dioxide purity and recovery in the waste flow are 41.4 % and 86.2 %, respectively. Table 3 provides the detailed optimization results of the rectifying and stripping units. The dual PSA process has substantially higher carbon dioxide purity and methane recovery than the conventional stand-alone PSA process.

The first case study is performed to ensure the optimization results, we check the effect of adsorption step time on the methane purity and recovery in rectifying, where the variables other than the adsorption step time are maintained at the fixed values as shown in Table S8.

As expected, a trade-off between methane purity and recovery of rectifying unit is observed. As the adsorption step time increases, the methane recovery also increases, but the methane purity decreases. Referring to Figure S4, the recovery in Cases 4 and 5 is higher than the optimal results (Case 3). However, neither case meets the lower purity limit of 97%. Comparatively, the purity in Cases 1 and 2 is higher than the optimal results (Case 3) but the recovery is lower in each case. Providing the optimal balance between purity and recovery, Case 3 is regarded as the optimal case.

The stripping unit optimization relies upon select optimal variable values extracted from the rectifying unit optimization results. Cycle time (394 s) and each mole of heavy product in the rectifying unit are the same with those of the feed flow in stripping unit. Whereas the rectifying unit has a fixed bed length, the bed length in the stripping unit is not fixed and determined through the optimization.


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Most notable in these results is the increased carbon dioxide purity. The optimized value of the objective is 0.763, representing a 34.9 % increase in carbon dioxide purity in the heavy product following the stripping unit process. On the other hand, the optimized carbon dioxide recovery by the poststripping is 83.3%, representing a small decrease from the 86.2 % value observed from the result of the conventional PSA process (without a stripping unit). The total mole of light product of the rectifying unit increased by the optimization, on the other hand, the total mole of carbon dioxide in heavy product of the stripping unit decreased.

To analyze the effect of variation on the bed length of stripping unit, the second case study is performed by five additional optimizations. The results are described in Figure 3. In certain, the purity of Case 8 (optimal case) has the highest value. From the results, we can infer that the decision variables have specific influence over the carbon dioxide purity. Figure 3(b) shows that the P/F ratio and feed velocity decrease as the bed length increases. Generally, a longer bed length means an extension of contact time, which increases the purity of light product. The increase of P/F ratio also leads to higher purity of light product because the adsorbent is regenerated better in high P/F ratio than in low P/F ratio. For this case, because the purity of light product is fixed value (85% for methane), the purity improvement by the extension of bed length was offset by reduced feed velocity and P/F ratio. Considering above results and detailed data in Table S8, the decreases in carbon dioxide purity on both sides Case 8 can be demonstrated by:



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1.

According to increase of the bed length from 0.593 m to 0.659 m (from Case 6 to Case 8) in the stripping unit when the CH4 purity in light product stream is fixed at 85%, the effect of bed length and feed gas velocity on the CO2 purity in heavy product stream is smaller than that of P/F ratio. Thus the CO2 purity increases as to the increase of the bed length in Case 6 to Case 8.

2.

For the Case 8 through Case 11, the influence of the P/F ratio on CO2 purity in heavy product stream is smaller than that of the bed length and feed gas velocity. So the CO2 purity decreases according to the increases of the bed length from 0.659 m to 0.757 m (from Case 8 to Case 11).

Judging from the above analyses, when we fix the purity of light product stream, the purity of heavy product stream shows different trend, as to the bed length, feed flow rate, and P/F ratio, from when the light product purity is not fixed. The general behaviors of PSA processes without fixing the CH4 purity in light product stream show that (1) methane purity of light product stream and carbon dioxide purity of heavy product stream increase as to the increase of the bed length and the decreases of the feed gas flow rate and P/F ratio, and (2) the purity of carbon dioxide in heavy product stream is proportional to the recovery of carbon dioxide in the same stream, while the purity of methane in light product stream is inversely proportional to the recovery of methane in the same stream.

To obtain optimal ratio of the bed length of the stripping unit (STR. Lbed ) to the rectifying unit (REC. Lbed ), one more case study is conducted. Additional four cases are processed through the optimization framework supposed in this study. The methane composition varies 83 % to 87 % and the


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detailed results are listed in Table S10. The ratio trend with varying feed composition is described in Figure 4. As the methane composition increases, the methane recovery and total cycle time increase whereas the carbon dioxide recovery, carbon dioxide purity of heavy product stream and bed length of stripping unit decrease. The increase of methane recovery and total cycle time comes from the higher methane composition of the feed stream. On the contrary, the higher total mole of carbon dioxide in STR.feed decreasing makes the other variables decrease.



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4.

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CONCLUSIONS

In this study, a dual PSA process for separating natural gas is modeled and optimized using various operational and design decision variables to maximize carbon dioxide purity and methane recovery. Figure 5 depicts these optimized operational strategies. Under these optimized conditions, the carbon dioxide (secondary product) purity greatly improves to 76.3 % from the feed gas consisting of the 85% methane and 15% carbon dioxide, with the 97% methane purity as the light product specification. In the rectifying unit, maximizing methane recovery in the light product stream is the objective. In the stripping unit, maximizing carbon dioxide purity in the heavy product stream is the objective. Individual optimizations are performed for each unit with different objectives and constraints. In addition, the dual PSA optimization procedure is introduced to efficiently solve the huge model including the rectifying unit and stripping unit as well as different objective functions for each unit.

As the results of the optimization, carbon dioxide purity increases from 41.4 % to 76.3 % and methane recovery increases from 78.5 % to 95.4 % compared to the stand-alone PSA process. Contributing to these operational gains, optimal values for the step times, P/F ratio, feeding velocity, and bed length are attained. To investigate the effects of decision variables on the performances, two types of sensitivity analyses are performed by simulating five cases (Cases 1 – 5) and optimizing six cases (Cases 6 – 11). The optimization and the sensitivity analyses of this work are helpful in enhancing the understanding of the effects and interactions of the variables on the performances such as the purity and recovery. In


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addition, the bed length ratio of stripping unit with varying methane composition of feed stream is optimized. Although the trend of ratio is obtained based on conceptual design of this study, these results can be applied to specific fields.



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Supporting Information Prediction results for LF isotherm parameters and linearized equation form in terms of temperature; trade-off between purity and recovery; initial pressure and temperature profiles; dynamic pressure and temperature profile of both side of the beds; PSA modeling governing equations and boundary conditions; model parameters; CSS tolerance checking data; case study results for varying bed length and feed composition This information is available free of charge via the Internet at http: //pubs.acs.org.

ACKNOWLEDGEMENT

This research has been supported by Korea Evaluation Institute of Industrial Technology (KEIT) under the Ministry of Trade, Industry & Energy (MOTIE) of Korea government and GS E&C.


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NOMENCLATURE

Abed

bed area, m2

Ci

gas concentration of component i, mol/m3

Cini,i

initial gas concentration of component i, mol/m3

Cfianl,i

final gas concentration of component i, mol/m3

Dx

axial dispersion coefficient, m2 /s

uI

interstitial velocity of flow, m/s

uS

superficial velocity of flow, m/s

ρbed

bed density, kg/m3

εbed

bed void

μgas

gas viscosity, kg/(m ∙ s)

R particle

particle radius, m

ρparticle

particle density, kg/m3

εparticle

particle void

ρgas

gas density, kg/m3

ki

mass transfer coefficient for component i

Ci

gaseous concentration for component i, mol/m3

Cini,i

initial gaseous concentration for component i, mol/m3

qi

solid phase loading for component i, mol/kg



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qini,i

initial solid phase loading for component i, mol/kg

qfinal,i

final solid phase loading for component i, mol/kg

qeq,i

adsorbed phase concentration in equilibrium of component i, mol/kg

Cpg

gas-phase heat capacity, J/(kg ∙ K)

Cps

adsorbent heat capacity, J/(kg ∙ K)

Kl

effective axial thermal conductivity, J/(m ∙ s ∙ K)

∆Hi

adsorption heat of component i, J/mol

hwall

heat transfer coefficient between gas phase and wall, J/(m2 ∙ s ∙ K)

M_Light_prodi

total mole of component i in light product, mol

M_Feedi

total feed mole of component i, mol

M_Purge_ini

total purge-in mole of component i, mol

M_Heavy_prodi

total mole of component i in heavy product, mol

yPR

a binary variable for pressurization step

yAD

a binary variable for adsorption step

yDP

a binary variable for depressurization step

yRG

a binary variable for regeneration step

yprod,CH4

methane purity in light product

yprod,CO2

carbon dioxide purity in heavy product

T

gas temperature, K

Tini

initial gas temperature, K


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Tfinal

final gas temperature, K

t cycle

total cycle time, s



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REFERENCES

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(12) Smith, O. J.; Westerberg, A. W. The Optimal-Design of Pressure Swing Adsorption Systems. Chem. Eng. Sci. 1991, 46, 2967. (13) Nilchan, S.; Pantelides, C. C. On the Optimisation of Periodic Adsorption Processes. Adsorption 1998, 4, 113. (14) Ko, D.; Siriwardane, R.; Biegler, L. T. Optimization of a Pressure-Swing Adsorption Process using Zeolite 13X for CO2 Sequestration. Ind. Eng. Chem. Res. 2003, 42, 339. (15) Ko, D.; Siriwardane, R.; Biegler, L. T. Optimization of Pressure Swing Adsorption and Fractionated Vacuum Pressure Swing Adsorption Processes for CO2 Capture. Ind. Eng. Chem. Res. 2005, 44, 8084. (16) Hasan, M. M. F.; Baliban, R. C.; Elia, J. A.; Floudas, C. A. Modeling, Simulation, and Optimization of Postcombustion CO2 Capture for Variable Feed Concentration and Flow Rate. 1. Chemical Absorption and Membrane Processes. Ind. Eng. Chem. Res. 2012, 51, 15642. (17) Agarwal, A.; Biegler, L. T.; Zitney, S. E. Simulation and Optimization of Pressure Swing Adsorption Systems Using Reduced-Order Modeling. Ind. Eng. Chem. Res. 2009, 48, 2327. (18) Dowling, A. W.; Vetukuri, S. R. R.; Biegler, L. T. Large-Scale Optimization Strategies for Pressure Swing Adsorption Cycle Synthesis. AIChE J. 2012, 58, 3777. (19) Khajuria, H.; Pistikopoulos, E. N. Optimization and Control of Pressure Swing Adsorption Processes Under Uncertainty. AIChE J. 2013, 59, 120. (20) Fatehi, A. I.; Loughlin, K. F.; Hassan, M. M. Separation of Methane-Nitrogen Mixtures by Pressure Swing Adsorption Using a Carbon Molecular-Sieve. Gas. Sep. Purif. 1995, 9, 199. (21) Ko, D. Development of a Simulation Model for the Vacuum Pressure Swing Adsorption Process To Sequester Carbon Dioxide from Coalbed Methane. Ind. Eng. Chem. Res. 2016, 55, 1013. (22) Ko, D. Optimization of Vacuum Pressure Swing Adsorption Processes to Sequester Carbon Dioxide from Coalbed Methane. Ind. Eng. Chem. Res. 2016, 55, 8967. (23) Jayaraman, A.; Chiao, A. S.; Padin, J.; Yang, R. T.; Munson, C. L. Kinetic Separation of Methane/Carbon Dioxide by Molecular Sieve Carbons. Sep. Sci. Technol. 2002, 37, 2505. (24) Stanciu, V.; David, E.; Stefanescu, D. Carbon Dioxide Separation from Carbon in the Natural Gas, by Carbon



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Molecular Sieves Adsorption. Revista De Chimie 1996, 47, 19. (25) Bae, Y. S.; Lee, C. H. Sorption Kinetics of Eight Gases on a Carbon Molecular Sieve at Elevated Pressure. Carbon 2005, 43, 95. (26) Chou, C. T.; Huang, W. C. Incorporation of a Valve Equation into the Simulation of a Pressure Swing Adsorption Process. Chem. Eng. Sci. 1994, 49, 75. (27) Nikolic, D.; Giovanoglou, A.; Georgiadis, M. C.; Kikkinides, E. S. Generic Modeling Framework for Gas Separations using Multibed Pressure Swing Adsorption Processes. Ind. Eng. Chem. Res. 2008, 47, 3156. (28) Santos, M. P. S.; Grande, C. A.; Rodrigues, A. E. Dynamic Study of the Pressure Swing Adsorption Process for Biogas Upgrading and Its Responses to Feed Disturbances. Ind. Eng. Chem. Res. 2013, 52, 5445. (29) Shao, P. H.; Dal-Cin, M.; Kumar, A.; Li, H. B.; Singh, D. P. Design and Economics of a Hybrid MembraneTemperature Swing Adsorption Process for Upgrading Biogas. J. Membr. Sci. 2012, 413, 17. (30) Fong, J. C. L. Y.; Anderson, C. J.; Xiao, G. K.; Webley, P. A.; Hoadley, A. F. A. Multi-objective Optimisation of a Hybrid Vacuum Swing Adsorption and Low-temperature Post-combustion CO2 Capture. Journal of Cleaner Production 2016, 111, 193. (31) Kvamsdal, H. M.; Hertzberg, T. Optimization of PSA systems - Studies on Cyclic Steady State Convergence. Comput. Chem. Eng. 1997, 21, 819. (32) Ko, D.; Moon, I. Optimization of Start-up Operating Condition in RPSA. Sep. Purif. Technol. 2000, 21, 17. (33) Zilinskas, A.; Fraga, E. S.; Beck, J.; Varoneckas, A. Visualization of Multi-Objective Decisions for the Optimal Design of a Pressure Swing Adsorption System. Chemom. Intell. Lab. Syst. 2015, 142, 151. (34) Jiang, L.; Fox, V. G.; Biegler, L. T. Simulation and Optimal Design of Multiple-Bed Pressure Swing Adsorption Systems. AIChE J. 2004, 50, 2904.


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List of Tables

Table 1. Optimization models for the rectifying and stripping units Table 2. Optimized performance indicators for conventional and dual PSA processes Table 3. Optimized decision variables for the rectifying and stripping units



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Table 1. Optimization models for the rectifying and stripping units

Objective

Decision vari ables

Rectifying unit

Stripping unit

max z = recoveryCH4

max z = yprod,CO2

t PR (s) t AD (s) t DP (s) t RG (s) uad (m/s) P/F ratio

Lower Boun d

Upper Bo und

1 30 1 30 1.16 0.01

30 400 30 400 1.74 0.30

−0.00001 ≤ yprod,CH4 − 0.97 ≤ 0.00001

Constraints

t PR (s) t AD (s) t DP (s) t RG (s) uad (m/s) P/F ratio STR. Lbed (m)

Lower Boun d

Upper Boun d

1 30 1 30 0.12 0.01 0.5

100 400 100 400 0.81 0.30 1.5

−0.00001 ≤ yprod,CH4 − 0.85 ≤ 0.00001 −0.0001 ≤ t PR − t DP ≤ 0.0001

−0.0001 ≤ t PR − t DP ≤ 0.0001

−0.0001 ≤ t AD − t RG ≤ 0.0001

−0.0001 ≤ t AD − t RG ≤ 0.0001

−ε ≤ Cini,i,z − Cfinal,i,z ≤ ε

−ε ≤ Cini,i,z − Cfinal,i,z ≤ ε −ε ≤ Tini,z − Tfinal,z ≤ ε

−ε ≤ Tini,z − Tfinal,z ≤ ε −ε ≤ qini,i,z − qfinal,i,z ≤ ε −0.0001 ≤ STR. M_feed(i) − REC. M_Heavy_prod(i)

−ε ≤ qini,i,z − qfinal,i,z ≤ ε (i = CH4 , CO2 )

≤ 0.0001 −0.0001 ≤ t cycle,STR − t cycle,REC ≤ 0.0001


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Table 2. Optimized performance indicators for conventional and dual PSA processes LP: Light Product

Conventional PSA process

HP: Heavy Product

(stand-alone rectifying unit)

Dual PSA process

Difference

Product

CH4 (LP)

78.5%

95.4%

16.9%

recovery

CO2 (HP)

86.2%

83.3%

-2.97%

Product

CH4 (LP)

97.0%

97.0%

-

purity

CO2 (HP)

41.4%

76.3%

34.9%

Table 3. Optimized decision variables for the rectifying and stripping units Rectifying unit

Stripping unit

CH4 recovery

CO2 purity

78.5%

76.3%

𝐭 𝐏𝐑 (s)

9

8

𝐭 𝐀𝐃 (s)

187

188

𝐭 𝐃𝐏 (s)

9

8

𝐭 𝐑𝐆 (s)

187

188

𝐭 𝐜𝐲𝐜𝐥𝐞

394

394

P/F ratio

0.109

0.045

𝐮𝐚𝐝 (m/s)

1.160

0.339

𝐋𝐛𝐞𝐝 (m)

1.55

0.659

Objective



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List of Figures Figure 1. Optimization procedure for dual PSA process Figure 2. Scheme of Dual PSA process including stream information and cycle diagram Figure 3. Comparative optimization results for various bed lengths in stripping unit: (a) CO 2 purity trends and (b) optimal P/F ratio and feed velocity trends Figure 4. Ratio of optimal bed length of Stripping unit to Rectifying unit Figure 5. Optimal dual PSA operational strategies that maximize CH4 recovery and CO2 purity


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Figure 1. Optimization procedure for dual PSA process



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Figure 2. Scheme of Dual PSA process including stream information and cycle diagram


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(a)

0.06

0.342 0.341

0.05

0.339 0.338

0.03

0.337

0.02

0.336

P/F ratio

0.335

Feed velocity

0.01

Feed Velocity

0.34

0.04 P/F ratio

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0.334

0

0.333

CASE6

CASE7

CASE8

CASE9

CASE10

CASE11

(b) Figure 3. Comparative optimization results for various bed lengths in stripping unit: (a) CO2 purity trends and (b) optimal P/F ratio and feed velocity trends



0.470 0.460

STR L_bed ratio

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0.450 0.440 0.430 0.420 0.410 0.400 0.83

0.84

0.85

0.86

Feed CH4 composition Figure 4. Ratio of optimal bed length of Stripping unit to Rectifying unit


0.87

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Figure 5. Optimal dual PSA operational strategies that maximize CH4 recovery and CO2 purity



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For Table of Contents Only


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Dynamic Optimization of a Dual Pressure Swing Adsorption Process

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