CO2 capture from dry flue gas by pressure vacuum swing adsorption: A systematic simulation and optimization

International Journal of Greenhouse Gas Control 51 (2016) 1–10

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International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc

CO2 capture from dry flue gas by pressure vacuum swing adsorption: A systematic simulation and optimization Haiyu Yan, Qiang Fu, Yan Zhou, Dongdong Li, Donghui Zhang ∗ The Research Center of Chemical Engineering, State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China

a r t i c l e

i n f o

Article history: Received 20 January 2016 Received in revised form 19 March 2016 Accepted 4 April 2016 Keywords: CO2 capture Process simulation Pressure swing adsorption Optimization Dry flue gas

a b s t r a c t A vacuum pressure swing adsorption process that used silica gel as adsorbent to capture CO2 from dry flue gas (85%N2 /15%CO2 ) by two-bed one-stage operation is investigated through dynamic simulation and optimization. Heavy component purge is added into schedule to improve the concentration of CO2 and light product of this step is collected and utilized for pressurization to save energy and guarantee a handsome recovery. Models of bed and sub-units all established in gPROMS and the accuracy of simulation results is verified by experiments. To decrease the energy consumption of the process, decision variables are optimized by r-SQP method within given constraints. Results show that under optimal conditions, the purity of CO2 could reach 90.77% with recovery of 76.47% and energy consumption reduced from 623.64 kWh tonne−1 at simulation to 419.99 kWh tonne−1 under optimal condition. Distribution of CO2 at the end of each step under optimal condition is given on both gas and solid phase with comparison of initial state to insight the effects of operation and decision variables on the whole VPSA process. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction It is now widely accepted that large scale emissions of CO2 into atmosphere is the major cause for anthropogenic climate change while combustion of fossil fuels contributes extensively to the CO2 emissions (Stern, 2007; Birol, 2010). Results of recent study showed that around 40% of total CO2 is discharged in the form of flue gas from the fossil fuel based power plants annually and the concentration of CO2 in flue gas usually lies between 12% and 15% (Krishnamurthy et al., 2014). Albeit CO2 of low concentration is unable to be utilized directly, a high concentration of CO2 (typically 90–95%) can be used to enhance oil and coal bed methane recovery or converted to useful products (Agarwal et al., 2010; Dowling et al., 2012). From standing point of both environmental protection and economic benefit, upgrading the low-concentration flue gas is extremely advantageous considering more stringent policies on greenhouse emissions and converts waste gas profitable. To remove N2 from flue gas as well as enrich CO2 , many chemical engineering processes like amine-based absorption, chilled ammonia, alkali-metal carbonates, membranes and adsorption have already been proven to be feasible (Hanak et al., 2015; Maas et al., 2016;

∗ Corresponding author. E-mail address: [email protected] (D. Zhang). http://dx.doi.org/10.1016/j.ijggc.2016.04.005 1750-5836/© 2016 Elsevier Ltd. All rights reserved.

Oreggioni et al., 2015; Riboldi and Bolland, 2015; Upendar et al., 2012). Among all these operations, pressure swing adsorption (PSA) or vacuum pressure swing adsorption (VPSA) is the most desirable one for its low cost in energy consumption, none hazardous byproducts and highly efficient automatic operation (Susarla et al., 2015). Adsorption-based processes for gas separations have extensively been studied and applied in air separation, hydrogen purification, hydrocarbon separation and air drying (Farooq and Ruthven, 1991; Malek and Farooq, 2000; Grande et al., 2005; Ritter and Yang, 1991). Since the Japanese power industry started using adsorption to remove CO2 from flue gas, numerous PSA or VPSA processes have been developed in both literatures and factories and proving this method to be a promising option for CO2 capture and concentration from flue gas (Hiros et al., 2005; Ito et al., 2004). Table 1 shows a summary of studies concerning CO2 capture from dry flue gas. In this table, yFeed , pCO2 , rCO2 refer to CO2 concentration in feed gas, purity of CO2 in product and recovery of CO2 through the whole process respectively. Exp. in result type means data in this line was experimental results and Sim. refers to simulation outcomes. Cho et al. (2004) studied a two-stage PSA process with zeolite 13X for a flue gas containing 15% CO2 . CO2 was firstly enriched to 63.2% with a recovery of 92.4% then 88% of CO2 was caught with purity of 99%. Major steps in their cycles are adsorption, pressure

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H. Yan et al. / International Journal of Greenhouse Gas Control 51 (2016) 1–10

Nomenclature bo c Cpg

R Rb Rp t T vg wads yi z

Adsorption affinity (1/kPa) Total gas phase concentration (mol/m3 ) Constant pressure specific heat of the gas mixture (kJ(kg K)) Specific heat of the adsorbent (kJ(kg K)) Valve constant (mol/(kPa s)) Gas phase concentration of compontent i (mol/m3 ) Axial dispersion coefficient (m2 /s) Effective diffusion co efficient of component i (m2 /s) Knudsen diffusion co efficient of component i (m2 /s) Molecular diffusion co efficient (m2 /s) Particle pore diameter (m) Molecular difussion volume (cm3 /mol) Molar flow of rates (mol/s) Molar flow rate into the pump (mol/s) Molar flow rate out of the pump (mol/s) Heat transfer coefficient between gas and column wall (W/(m2 K)) Bed height (m) Iso steric heat of absorption of component i (kJ/mol) Effective axial thermal conductivity (W/(m K)) Molecular weight of the gas (kg/mol) Total number of component Pressure (Pa) Absorbed phase concentration of component i (mol/kg) Maximum absorbed phase concentration in equilibrium with bulk gas of component i (mol/kg) Ideal gas constant (J/(mol K)) Bed radius (m) Particle radius (m) Time (s) Temperature (K) Supeficial velocity (m/s) Mass of absorbent (kg) Molar fraction of component i Axial direction

Greek εb εp p g p  

Bulk phase porosity Particle phase porosity Density of the absorbent (kg/m3 ) Density of the gas phase (kg/m3 ) Work efficiency of compressor and vaccum pump Gas visco sity (Pa s) Compressor adiabatic factor

Cps Cv ci Dax Dc,i Dk,i Dm dp Dv F Fi Fo h Hb Hi kg M N P qi qm,i

Subscripts i Species

equalization, blowdown, low pressure purge and feed pressurization. Shen et al. (2012) also used two-stage operation but vacuum step was added into their process. They simulated the VPSA process in gPROMS using activated carbon as adsorbent. With vacuum pressure of 5 kPa, 80.42% was get at concentration of 96.40%. Liu et al. (2012) used zeolite 5A to study the capture and concentration of CO2 capture from dry flue gas with a 3-bed 7-step VPSA process which involved pressurization, high pressure adsorption, concurrent depressurization, heavy component rinse, blowdown, purge and equalization. With such configuration, 79% of CO2 was captured with 81% purity and overall energy consumption was 656 kWh tonne−1 . Wang et al. (2013a,b) have demonstrated the

capture of CO2 use both two-stage and one-stage operations based on real coal-fired power plants. For the two-stage operation (Wang et al., 2013a), 13X APG was selected as adsorbent for the first unit within a 3-bed 8-step VPSA process Following it is a 2-bed 6-step VPSA process using activated carbon for the second unit. CO2 was enriched to 95.6% with recovery of 90.2% and the energy consumption was 677.78 kWh tonne−1 . Then in their following work (Wang et al., 2013b), they measured the exact energy consumption of the whole process and conclude that vacuum pumps account twothird of the total energy consumption. Flue gas with 15.5–16.5% of CO2 was passed into a 3-bed 8-step VPSA process and finally reached to 73.0–82.3% with recovery of 84.7–95.2%. Haghpanah et al. (2013) simulated a 1-bed 4-step VPSA process for CO2 capture via finite volume simulation. In their study, energy consumption can be minimized to just 149 kWh tonne−1 with no less than 90% purity-recovery constraints. Performance of a PSA process is often evaluated by a trade-off between desirable indicators (i.e. purity, productivity, profit and safety) and undesirable objectives (i.e. capital investment, operating cost, by-product disposition and environmental cost). The best operation condition should increase desirable factors and decrease undesirable ones (Ko and Moon, 2002). However, results and objectives of a VPSA process are systemic interacted with many variables like bed dimension, temperature, gas velocity, pressure, it is hardly possible to get the best solution just by experiments and pilot plants. Thus, several researchers have investigated the mathematical design and optimal of VPSA processes for ideal operating conditions. Smith and Westerberg (1991) presented a mixed-integer nonlinear programming (MINLP) method with very simplified model that contained time averaged mass and energy balances for the design of a PSA process to minimize capital and operation costs. Nilchan and Pantelides (2000) proposed a complete discretization of both spatial and temporal derivatives simultaneously and reduced partial differential algebraic equations (PDAEs) into largescale of nonlinear algebraic equations. This model is solved by a commercial NLP solver and applied in single-bed RPSA process for air separation. Jiang et al. (2003) performed a direct determination approach augmented with a hybrid trust region for Newton step improvement to accelerate the convergence for cycle steady state (CSS) and design constraints then applied it into air separation process by 1-bed 6-step operation and 5-bed 11-step units for H2 purification. Agarwal et al. (2009, 2010) performed model reduction by employing proper orthogonal collocation and reduced order models for simulation and optimization of PSA process then demonstrated it by maximizing recovery for H2 separation. They also presented superstructure-based approaches to design and optimize PSA process for CO2 capture from syngas (Agarwal et al., 2009, 2010). Although a discretization in both spatial and temporal could describe PSA models more precisely, large scale of computation would also have to be taken into account comparing with a discretization just in spatial. Our mathematical simulation and optimization work were all built on the basis of spatial discretization alone. Yang et al. (2014) optimized a 3-bed 7-step VPSA process for N2 /CH4 separation process. The r-SQP method was employed in his work to maximize the recovery of CH4 and minimized the energy consumption of the whole process. Boundary conditions and sub-models are described in details and sensitivity analyzation is given to help explain the effect of operating parameters on process. Sun et al. (2015) then applied the model and method into software gPROMS and maximized the recovery of CH4 from coal bed methane. Important PSA objectives, decision variables, and operational constraints are discussed and incorporated in optimization framework.

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Table 1 PSA cycles suggested in the literature for CO2 capture from dry flue gas. Process

Adsorbent

yFeed /%

pCO2 /%

rCO2 /%

Power Consumption/kWh t−1

Literature

Result type

Two-stage PSA Two-stage VPSA 3-bed 7-step VPSA Two-stage VPSA

13X AC 5A 13X APG AC 13X 13X

10.5 15 15 16

99 96.40 71–81 95.6

88 80.42 79–91 90.2

641.5–770 236.54 638.89–866.67 677.78

Cho et al. (2004) Shen et al. (2012) Liu et al. (2012) Wang et al. (2013a)

Exp. Sim. Exp. Exp.

15 15.5-16.5

73.0–82.3 90

84.7–95.2 90

497.22–602.78 149

Wang et al. (2013b) Haghpanah et al. (2013)

Exp. Sim.

3-bed 8-step VPSA 1-bed 4-step VPSA

Table 2 Schedule of the VPSA process. Time(s)

200

25

120

200

25

120

Bed1 Bed2

AD↑ VU↓

CoD↑

RP↑ PR↑

VU↓ AD↑

CoD↑

PR↑ RP↑

AD: adsorption step; CoD: co-current blowdown step; RP: replacement step; VU: vacuum step; PR: pressurization step.

In the absence of relevant researches and pilot plants about PSA based CO2 capture, most work has favored two-stage or multi-bed operation processes. In contrast, this paper presented a systemic simulation of CO2 capture from flue gas (15% CO2 /85% N2 ) by VPSA process using two-bed one-stage operation. Silica gel was selected as adsorbent for its perfect property in regeneration. To make sure purity of CO2 in product is no less than 90%, low pressure replacement (heavy component purge) step is added into the schedule meanwhile light product of this step is recycled for pressurization to guarantee a handsome recovery. The accuracy of mathematical models was then verified by a series of experiments that differ in feed flowrates. Compared with traditional operations, the simple one-stage two-bed operation showed a good performance in CO2 capture with lower energy consumption. Optimal computation is then carried out to minimize the energy consumption based on our laboratory work. All PADEs are discrete in spatial alone and the time for each step is fixed to simplify the calculation process. Energy consumption decreased to 419.99 kWh tonne−1 after optimization with purity of 90.77% and recovery of 76.47%. Finally, we analyzed the process based on operation and decision variables changes and quantitatively explained the influence of these parameters on the process. 2. PSA model and simulation 2.1. PSA models and parameters A systemic VPSA process usually contains two or more adsorption beds, filled up by adsorbent, interacting with each other via a net of solenoid valves. A two-bed and five-step VPSA process is adopted in this paper. Fig. 1 shows the flow diagram of the process while schedule of the process is listed in Table 2. Each bed is assumed to be 1 m in length and 0.3 m in diameter. Buffer tanks (T1 and T2) are all 0.14 m3 in volume. Combustion flue gas is normally at atmospheric pressures and 323.15–343.15 K due to various precapture operations, therefore, the feed flue gas (0.15%CO2 /0.85%N2 ) is assumed to be 1 bar with temperature of 325.15 K. Heat of adsorption can be an important indicator to evaluate the property of regeneration for adsorbents. Although many kind of adsorbents, like 13X, 5A, activated carbon, all showed excellent performance in CO2 /N2 separation, silica gel is selected as the adsorbent in this work because CO2 have a relatively lower adsorption heat on it, leading a good property in regeneration comparing with other adsorbents. In the first step adsorption (AD), feed gas passed into the adsorption bed after compressor (C1), part of N2 was exhausted from top meanwhile most of CO2 was adsorbed by adsorbent. Fol-

lowing AD is the co-current blowdown step (CoD), in which most N2 was excluded to air to enrich the purity of CO2 . The replacement (RP) step uses part of the product that stored in buffer tank T2 passed through compressor (C2) to increase the concentration of CO2 and exclude N2 from top. Valve VRG only turns on at this step to guarantee a relatively lower pressure for RP step and stored part of the light product for further utilization. As concentration of heavy component in light product of this step is extremely high, all light products of RP is recycled to buffer tank T1 for further utilization as well as guarantee the recovery of the whole process. Adsorbent is regenerated during step vacuum (VU) and extracted bulk of highly purity CO2 from bed into T2. VHG would turns on at this step to decrease pressure in T2 to save energy for vacuum. Pressurization step (PR) is then conducted which uses gas in T1 to raise bed pressure and make it ready for next cycle. To simulate the dynamic process of the VPSA process above, a system of mathematical models are established in gPROMS which contains bed, compressor as well as both uni-direction valve and bidirection valve. Mathematical model of adsorption bed and some sub-models are listed in Tables 3 and 4 (Da Silva et al., 1999; Grande and Rodrigues, 2005; Yang et al., 2014) respectively. Langmuir equation in Eq. (4) is used to describe the adsorption capacity and the LDF (linear driving force) model is defined in Eq. (5). Valves are the most common units in VPSA process and we use valve constant to define how flowrate is controlled by valves. Relationships between flowrate and valve constant are shown in Eq. (9). The total energy consumption of the whole process is the sum of two compressors and vacuum. Their specific power consumption is calculated by Eq. (10). Assumptions for the whole model are listed as follows: (1) Gas phase obey the role of ideal gas. (2) Gas concentration, temperature and pressure only vary in axial direction. (3) Pressure drop along the bed is calculated by Ergun equation. (4) Thermal balance is maintained between gas and solid phase. (5) Kinetics of adsorption abided by linear driving force model. (6) Porosity of both bed and adsorbent particle is uniform along the bed. Langmuir non-isothermal model parameters for CO2 and N2 on silica gel in Table 5 were the curving fitting results of pure gas adsorption quantity on silica gel at different temperature and pressure. Adsorbent parameters about silica gel in Table 6 were measured by relevant equipment and others were the value of pure N2 and CO2 sum up in proportion of their constitution. 2.2. Cycle steady state definition For a dynamic process like VPSA, cycle steady state (CSS) is often used to judge whether a process has reached to a stable condition or not. A steady state would converge in a more rapid speed and showed good stability property in optimal computations. Thus, it is worthwhile to take more time for the VPSA cycles to reach its CSS

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Fig. 1. Graph overview of two-bed PSA system.

Table 3 Model equations for adsorption bed. Parameter

Expression

Component mass balance

−

∂y ∂(v c ) ∂c ∂ (ε − Dax c ∂zi ) + ∂gz i + (εb + (1 − εb )εp ) ∂ti + p (1 − ∂z b ∂qi = 0 ∂t ∂(v c) − ∂∂z (εb − Dax ∂∂zc ) + ∂gz + (εb + (1 − εb )εp ) ∂∂ct + p (1 − εb ) ∂∂qt

(1a,1b)

εb ) Overall mass balance

0 

N

N

i=1

i=1

N

N

vg g  Cpg,i ∂∂Tz + (1 − εb ) p  i=1

i=1

2

(1 − εb ) εp ) ∂∂Pt

Langmuir isotherm

− ∂∂Pz = q =

Diffusion coefficient

∂qi ∂t

εb 3 (2Rp ) qm,i bi Pi

1+

b0i exp 15DC,i

=

− kg ∂ 2T ∂z

150(1−εb )



∗

bi = Linear driving force model

RP 2

2

2

∂qi ∂z

p b

Dc,i =

1⁄

1⁄

T



(6c,6d)

Mi

Z = 0: ␯g,z ≥ 0, Tz = Tin , yi,z = yin,i ∂y

Else, ∂∂Tzz = 0, ∂i,z = 0, z Z = Hb : ␯g,z ≤ 0, Tz = Tout , yi,z = yout,i Else,

∂Tz ∂z

= 0,

∂yi,z ∂z

= 0,

at simulation. In this paper, successive substitution is adopted to define the state of CSS and it can be expressed as Eq. (14).

ecss = |yt=Ntcycle − yt=(N+1)tcycle | < εCSS

(6a,6b)

1 + 1 MA MB

D 3 +D 3 v,B v,A

εp Dk,i Dm Dk,i +Dm

(3)

(5)

 g RpεbDm  εb 1+9.49 2g Rp  

Dk,i = 48.5Dp

(2)

(4a,4b)

qi − qi



+

=0

1−ε  vg + 1.75 ( 2R bε )3 g |vg |vg

0.01013T 1.75

∂t

b

Dax = 0.73Dm +

Dm =

 ∂ T

w Hi + 2h T −T − (εb + R

bi Pi Hi  −  ∗RT 

P

Boundary conditions



(εb + (1 − εb ) εp )  ci (Cpg,i − R) + (1 − εb )p Cps + (1 − εb )p  qi Cpg,i − R

Energy balance

Gas phase momentum balance

=

(14)

In this equation, y could represent any significant variables in model like purity, recovery or temperature. Once the value difference between any variable at one cycle and the next is less than the critical value εCSS , we would define this condition has reached to its CSS. In this work the value of εCSS is 10−5 .

(8a) (8b) (8c) (8d)

2.3. Discretization method As it has already mentioned in introduction part, we have converted partial differential equations (PDEs) into differential algebraic equations (DAEs) at spatial alone by method of lines (MOL) and central finite difference method (CFDM). The DAE system was dynamically simulated by intergrading over time in a DAE integrator and the optimizer (gOPT) in gPROMS could receive results of CSS as initial values for all variables in model. Great changes in variables only happened at initial cycles so that 20 cycles is chosen as the time horizon for this VPSA dynamic optimization studies.

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Table 4 Model equations for sub-models. Parameter

Expression

Buffer tank

energy balance:



∂T

ni Cpi

 −

∂t

∂n



N

Fi Ti



yk Cpg,i +



i=1

N

Fo To



yk Cpg,i = 0

Fi yi + FO y0 = 0 mass balance: ∂ti − Uni-direction valve: if Pin > Pout F = Cv (Pin − Pout )/106 else F = 0 Bi-direction valve: F = Cv (Pin − Pout )/106

Valve

If Pout > Pin dW =

Compressor

Pout Vin  p −1



tcycle dw o tcycle Fout yout dt 0 purityCO2 = tcycle F dt 0 tcycle out Fout yout dt recoveryCO2 = 0 t cycle F y dt 0 intcyclein

Pout Pin

 −1 

(10) (11)



−1

(12)

Wcycle =

Performance indicators

3600

productivityCO2

0

(9)

o=1

(13) (14)

(15)

Fout yout dt

(16)

tcycle wads wads = p (1 − εb ) Hb Rb2

Table 5 Langmuir nonisothermal model parameters. Parameters

CO2

N2

qm /mol kg−1 H/J mol−1 b0 /kPa

4.4386 −23,138 4.4158 × 10−7

3.11838 −17,082 2.0347 ×10−5

(17)

showed good accuracy and proved its validation for further optimal work. Feed flowrate of 32 m3 h−1 is chosen as the initial state for further optimization. Parameters of this condition are shown in Table 7 while further comparison and analyzation are given afterwards. 3. Optimization 3.1. Optimization framework

Table 6 Parameters for gas-solid system. Parameter

Value

Cpg /kJ kg−1 K−1 Cps /kJ kg−1 K−1 dp /m Rp /m ␳p /kg m−3 DvCO2 /cm3 mol−1 DvN2 /cm3 mol−1 kg /W m−1 K−1 ␧p ␧b

0.7582 0.920 5.0 × 10−9 7.0 × 10−4 825.97 26.9 18.5 0.02452 0.1429 0.3125

2.4. Experimental verification To verify the accuracy of the mathematic model and simulation results, experiments were carried out based on the two-bed experimental set-up instructed as Fig. 1. Schedule in Table 1 was realized via series of solenoid valves that controlled by S7-200 Micro PLC process. Raw material of flue gas was made by pure N2 and CO2 mixing up in a proportion of 85%:15%, the same as simulation constitution. Table 6 displays purity and recovery of CO2 at both simulation and experimentation under five different feeding flowrates. Although these experiments were various in feed flowrate, they all keep a pressure of 1.5 bar, 1.2 bar for step AD and RP respectively and 0.4 bar at the end of VU step. As it can be seen above, both results of simulation and experimentation showed the same trend that the bigger the feed flowrate, the higher purity we could get and the lower recovery it behaves. Experiments are affected by series of realistic confines like the control of flux, distribution of adsorbent and time for solenoid valves to turn on and off which would not be that ideal like it calculates in computer thus it would show little difference comparing with results of simulations. In short, as the mean deviation for purity and recovery are 0.94% and 0.85% respectively, simulation results

CO2 capture and concentration (CCC) from power plants is an energy intensive process which means that most energy is consumed at certain part of the process. Studies showed that nearly 75–80% of total cost for CCC was spent on capture part (Wang et al., 2011). Thus, minimize energy consumption has been settled as the objective function for optimal computation. Besides, by making the best of light product, energy consumption could be an absolute advantage for one-stage operation. Goal Programming (GP) method is chosen to establish the framework for our optimal work because it is quite useful for the condition that only one goal is chosen as objective function. The mathematical structure can be expressed as Obj:

min

f1 (x) x ∈ ˝ s.t.fi (x) ≤ εi

(15)

where obj represents the objective function that need to be optimized and s.t. refers to the constraints for both operation and realistic demand. Precisely in this paper, f1 (x) stands for energy consumption and fi (x) represents purity, recovery and pressure constraints for each step. Variables like valve constant and flux of pumps in models need not only an upper boundary, but a lower one as well because these two boundaries can help process performs better in convergence and make performance indicators changing in a reasonable range. Thus constraints like these can be expressed as follows. VarLB ≤ Var ≤ VarUB

(16)

All initial values of variables are the same as they behave in simulate CSS to speed up the convergence for dynamic optimization. Then r-SQP method is employed to solve the optimization problems in software gPROMS. It is worth noticing that the standard solver of nonlinear optimization problems in gPROMS was updated from SRQPD to NLPSQR in versions 4.0 to make it a stronger solver for

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Table 7 Experimental and simulation results under different feed flowrates. Qfeed /m3 h−1

29 30 31 32 33

Purity of CO2 in product gas/% simulations

experiments

87.96 89.22 90.12 90.72 91.25

86.93 88.45 89.20 90.08 90.42

Relative error/%

1.19 0.87 1.03 0.71 0.92

Table 8 Solver and convergence statistic for optimal system. Parameter

Value

Number of axial nodes Discretization scheme DAE solver absolute tolerance DAE solver relative convergence tolerance NLP solver convergence tolerance Number of NLP iterations Number of NLP line searches CPU times Fraction of CPU spend on sensitivity integration Machine details

20 CFDM 10−5 10−5 10−5 24 45 14.84 h 57.61% Intel Core i5-2100@ 3.10 GHz

nonlinear programming problems. Lower boundary for CO2 purity is fixed in constraints as no less than 90% like most studies to make it available for further utilization. With addition of pressure limitation, optimization framework for the following three optimization problems can be expressed as follows. Obj : Min − Energy Consumption s.t. F(y, y’, q, t) = 0 PAD ≤ 1.5bar PRP ≤ 1.2bar

(17)

PVU ≥ 0.4bar PurityCO2 ≥ 90 % VarLB ≤ Var ≤ VarUB Here F is the DAEs models in Table 2, y is the state variables, q represents decision variables and t refers time. Pressure for step AD, RP and VU all have been set a boundary as no more than 1.5 bar, 1.2 bar and no less than 0.4 bar respectively. Lower boundary(LB) and Upper boundary (UB) for all decision variables are listed in Table 8. In the following part, V refers to the valve’s opening constant and Fc1 , Fc2 , Fvu refers to the flowrate of compressor C1, C2 and vacuum VU.

Recovery of CO2 /%

Relative error/%

simulations

experiments

82.40 81.96 81.39 80.86 79.74

81.75 81.27 80.75 80.02 79.10

0.79 0.85 0.79 1.04 0.80

on a higher feed reflux, there would be a raise in energy consumption. Optimal computation would take a balance between feed flowrate change and valve opening constant variation so as to get the best condition with lowest energy consumption. Although there’s a decrease in Fc1 , VAD also turned down a little to keep a higher adsorption pressure. As we can see from Fig. 2(a), the optimum adsorption pressure increased to 1.5 bar much more rapidly than initial state. Temperature variation at this step also went down a little after optimization as less gas is blow into bed at the first 200 s and a lower temperature at optimal condition is favored for CO2 separation. Opening constant of VCoD turned up from 8.5 to 11.62, which means that more N2 is excluded from bed after optimization. As desorption at CoD step was a heat absorption process, temperature variation after optimization is larger than it was at initial condition. CoD step is the only step that enhance the purity of CO2 without any energy consumption thus it should be utilized sufficiently at the premise of keeping a considerable recovery. The increases in Fc2 lead to more quantity of gas blown in at RP step and pressure at this step goes higher at optimal condition, more favorable for CO2 adsorption than the pressure tendency at initial. CO2 has a great adsorption heat on silica gel. Once large amount of CO2 was pumped into the bed, the average temperature would increase conspicuously, just as it shows in Fig. 2(b). Following it is the VU step where pressure dropped to the lowest pressure of the whole cycle at a fast speed after optimal and this is of beneficial for adsorbent regeneration. Pressurization step make the utmost of light product of RP step that stored in T1 and pressure raised higher at optimal condition comparing with initial condition. By feeding gas from bottom of the bed, bed pressure could raises automatically under the impulse of pressure difference and avoiding polluting the silica at top of bed so as to get a higher CO2 recovery and purity. From above changes in all steps, objective function been minimized towards our ideal direction. In the following part, analyzation is given in details for each step to further understanding effect of each step on the better VPSA process.

3.3. Process analyzation

3.3.1. Adsorption step Raw gases feed into the VPSA system at AD step and the adsorption front moving forward as time goes on. Fig. 3 shows the CO2 concentration and adsorption quantity on gas phase (a) and solid phase (b) under different number of iteration at the end of AD step respectively. As iteration times increases, Fc1 dropped from 32 m3 /h to 26.95 m3 /h and VAD also decreased from 2.9 to 1.88 so as to maintain the adsorption pressure. But the decrease in FC1 means less gas was compressed into bed at AD step so that adsorption front went backward from 0.3 in axial at initial condition to 0.25 at optimal condition, which could be easily drawn from Fig. 3. CO2 concentration at top of the bed dropped to a lower value and adsorption front became sharper after optimization. These changes could contribute to a higher CO2 recovery and left more spaces for co-current blowdown and replacement for further enhance on CO2 purity.

Fig. 2 shows the pressure and temperature curve over one cycle under initial and optimal condition. Higher pressure is better for CO2 purity in product, but if pressure increase was only relied

3.3.2. Co-current blowdown step Co-current blowdown is the only steps that enrich CO2 without any energy consumption so that VCoD ought to be enlarged to

3.2. Computational results To further analyze the performance of the VPSA process under optimal conditions, details of optimal computation and changes of design variables are shown in Tables 8 and 9. It can be seen from Table 8 that the process endured 24 times iteration to reach the minimum value of power consumption and the optimal process satisfied all constraints that listed in Table 9. Under optimal conditions, the energy consumption for one-stage operation could drop significantly from 623.64 kWh tonne−3 to 419.99 kWh tonne−3 although there’s a little decrease in productivity.

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Table 9 Optimal decision variables,their upper and lower boundaries and optimal performance for PSA optimization at certain number of interation. Decision variables

Initial value

LB

UP

No. of interation 10

process design VAD VCoD VHG VRP VRG VRB

2.9 8.5 3.5 1.75 2.96 0.3

operational variables FC1 FC2 FVU

32 13 35

performance variables purityCO2 recoveryCO2 power consumption productivity

90.72 80.86 623.64 0.062

25 6 25

55 25 60

b

1.6

Average bed pressure/bar

6.0 16 8.0 5 6.0 1

1.4 1.2

VU

PR

1.0 0.8

AD

CoD

RP

0.6

24

2.92 8.77 4.08 2.21 2.39 0.32

2.09 11.25 5.79 2.15 1.54 0.32

1.88 11.62 6.01 2.12 1.27 0.32

29.62 13.44 32.18

26.17 15.34 30.38

26.95 15.24 30.22

90.49 78.73 553.70 0.056

90.73 76.66 426.46 0.048

90.77 76.47 419.99 0.049

345

initial condition optimal condition

Average bed temperature/K

a

0.3 2.0 0.3 0.2 0.3 0.1

20

initial condition optimal condition

340 335 330

PR

VU

325 320 315 CoD

AD

310

RP

305

0.4

300 0

100

200

300

400

500

0

600

100

200

300

400

500

600

Times/s

Times/s

Fig. 2. (a) Comparison of pressure under initial and optimal condition over a cycle. (b) Comparison of temperature under initial and optimal condition over a cycle.

a 0.25

b 0.9 0.8

initial condition No. 20 iteration No. 24 iteration

0.20

initial condition No. 20 iteration No. 24 iteration

0.7 0.6

qCO2mol/kg

yCO2

0.15

0.10

0.5 0.4 0.3 0.2

0.05

0.1

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.0

1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Axial

Axial

Fig. 3. (a) Axial distribution of CO2 on gas phase at the end of AD step. (b) Axial distribution of CO2 on solid phase at the end of AD step.

a 0.25

b 0.9 0.8

initial condition No. 20 iteration No. 24 iteration

0.20

initial condition No. 20 iteration No. 24 iteration

0.7 0.6

qCO2mol/kg

yCO2

0.15

0.10

0.5 0.4 0.3 0.2

0.05

0.1 0.00 0.0

0.1

0.2

0.3

0.4

0.5

Axial

0.6

0.7

0.8

0.9

1.0

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Axial

Fig. 4. (a) Axial distribution of CO2 on gas phase at the end of CoD step. (b) Axial distribution of CO2 on solid phase at the end of CoD step.

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H. Yan et al. / International Journal of Greenhouse Gas Control 51 (2016) 1–10

b 1.35

a 1.0 0.9

1.20

initial condition No. 20 iteration No. 24 iteration

0.8 0.7

0.90

qCO2mol/kg

yCO2

0.6 0.5 0.4 0.3

0.75 0.60 0.45

0.2

0.30

0.1

0.15

0.0 0.0

initial condition No. 20 iteration No. 24 iteration

1.05

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.00 0.0

1.0

0.1

0.2

0.3

0.4

Axial

0.5

0.6

0.7

0.8

0.9

1.0

Axial

Fig. 5. (a) Axial distribution of CO2 on gas phase at the end of RP step. (b) Axial distribution of CO2 on solid phase at the end of RP step.

a

b 0.10

1.0 0.9

initial condition No. 20 iteration No. 24 iteration

0.08

0.8 0.7

qCO2mol/kg

yCO2

0.6 0.5 0.4

initial condition No. 20 iteration No. 24 iteration

0.3 0.2

0.06

0.04

0.02

0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.00 0.0

0.1

0.2

0.3

0.4

Axial

0.5

0.6

0.7

0.8

0.9

1.0

Axial

Fig. 6. (a) Axial distribution of CO2 on gas phase at the end of VU step. (b) Axial distribution of CO2 on solid phase at the end of VU step.

b 0.35

a 0.125

0.25

qCO2mol/kg

0.075

yCO2

initial condition No. 20 iteration No. 24 iteration

0.30

initial condition No. 20 iteration No. 24 iteration

0.100

0.050

0.20 0.15 0.10

0.025 0.05 0.000 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Axial

1.0

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Axial

Fig. 7. (a) Axial distribution of CO2 on gas phase at the end of FR step. (b) Axial distribution of CO2 on solid phase at the end of FR step.

minimize the energy consumption of the VPSA process. Distribution of CO2 at the end of CoD step is displayed in Fig. 4. Adsorption front at the end of CoD step was push forward based on where it was at the end AD step. Although initial condition has an advanced adsorption front, the VCoD of it is less than optimal comparing 8.5 with 11.62. This means that less N2 was expelled from bed at initial condition but much more after optimization, leading to nearly the same position of adsorption front at both conditions by the end of CoD step. Besides, optimal condition also enjoyed a shaper adsorption front and lower concentration of heavy component at outlet of bed so that CO2 could be enriched with less loss and none energy consumption.

in bed and exclude N2 from top of column most effectively. Bed pressure is the key element that determined the effectiveness of RP step. A lower RP pressure could save energy for the process and benefit for desorb of N2 , but also accelerate the breakthrough of CO2 . Fig. 5 displays the CO2 concentration profiles after RP step. To enrich CO2 with just two-bed one-stage operation, RP step has to be proceeded sufficiently to guarantee the purity of CO2 in product. It can be seen that there is a significant reduction in the CO2 concentration at the out let of bed after optimal. The increase in FC2 leads to an advanced adsorption front and bigger temperature variation. Both changes contribute to an adequate heavy component purge with less CO2 dissipation.

3.3.3. Replacement step The replacement step, also called heavy component or product purge step, is the step that could increase the concentration of CO2

3.3.4. Vacuum step The regeneration of adsorbent and recovery of heavy component all relay on one energy consumed step, that is the VU step.

H. Yan et al. / International Journal of Greenhouse Gas Control 51 (2016) 1–10

Effects of optimization on VU step could be observed directly in Fig. 6. The decrease in Fvu is accompanied with a decreased in FC1 and little increase in FC2 as less vacuum reflux is needed when less gas is compressed into the bed. It can be seen that CO2 remaining on adsorbent at optimal condition is much more less than initial condition. This indicates most heavy component has been recovered from bed to T2 and the adsorbent has made a better preparation for next cycle. Moreover, the better gas desorption also benefit by the former steps in which a sharper adsorption front kept more CO2 accumulated at the inlet of column then mutual benefit also did on the next cycle that a clearer adsorbent contributes to the sharpness of the adsorption front by reducing the pre-stored amount of the heavy component.

3.3.5. Pressurization step Fig. 7 displays the concentration distribution after the pressurization step. Feed gas that used to raise bed pressure is part of the light product of RP step that stored in T1so as to recycle the CO2 contained light product and save energy for the whole process. By the end of RP step, concentration of CO2 at the outlet of bed is smaller under optimal condition than that is at initial condition, thus CO2 concentration and adsorption quantity distribution in bed after FR step under optimal condition was reduced to a lower level, leaving more clean adsorbent for a sharper front in AD step to enrich CO2 with less loss.

3.4. Process performance comparison With constraints added in the calculate process, CO2 could be concentrated to no less than 90% with a relatively higher CO2 recovery and lower energy consumption comparing literatures in Table 1. In premise that purity of CO2 can be enriched to the standard concentration, the energy consumption required in this study is in the same magnitude as that in other works and smaller than some of two-stage or multi-bed operations. Besides, as fewer adsorption beds and other equipment are needed in the two-bed one-stage operation, such operation would still show strong competitiveness.

4. Conclusions A systemic simulation and optimization of VPSA process for CO2 capture from dry flue gas by one-stage two-bed operation has been demonstrated and discussed in this work. Models of bed and summodels that contains valves and compressors were established in software gPROMS. By recycling light product of heavy component step, CO2 can be enriched to more than 90% with recovery of no less than 79%. Experiments were carried out to testify the accuracy of models and parameters. Lower energy consumption is the biggest advantage for one-stage operation. The operating conditions have been discussed for minimizing the energy consumption under specific constraints using the r-SQP method. Energy consumption can be minimized from 623.64 kWh tonne−3 to 419.99 kWh tonne−3 after optimization with purity and recovery of 90.77% and 76.47% respectively and little decrease in productivity. These results indicated that the performance of VPSA process can be improved through optimization. Analysis then carried out to provide an insight observation and comparison into effects the influence of the decision variables on the process performance. Distribution of CO2 on both gas and solid phase showed that optimal condition could form a sharper adsorption front, desorbed more sufficiently and save energy for the whole process.

9

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ijggc.2016.04. 005.

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