Modified Duplex PSA. 2. Sharp Separation and ... - ACS Publications

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Modified Duplex PSA. 2. Sharp Separation and Process Intensification for N2-O2-5A Zeolite System S. V. Sivakumar† and D. P. Rao*,‡ Department of Chemical Engineering, IIT Kanpur, Kanpur 208016, India ABSTRACT: We present the simulation studies carried on separation of the N2-O2 mixture with the original and modified duplex PSA. The purities of products were in excess of 99 mol % with the modified duplex PSA, whereas the original duplex PSA yielded product purities of 72 mol %. For both product purities of 95 mol %, the bed size and energy requirements with the modified duplex PSA were less by 10 and 2.5 times respectively compared to the conventional PSA and were less by an order of magnitude compared to those with original duplex PSA.

’ INTRODUCTION The companion paper, Part 1, dealt with the separation of CO2-N2 mixture over 13X zeolite. We ignored the adsorption of N2 and hence it was a system with single component adsorption and the selectivity is infinity. In this Part 2, we examined the performance of the original and modified duplex PSA for the N2-O2-5A zeolite system. It is a system with competing adsorption, i.e. the amount of one component adsorbed influences the amount of the other adsorbed and the selectivity is about 3. The performance of duplex PSA for the separation of the N2O2 mixture has not been reported in the open literature. Leavitt discloses the expected performance in a duplex PSA for the fractionation of air in a patent.1 He claims that air can be fractionated in a duplex PSA employing PH of 105 kPa and PL of 70 kPa using 13X zeolite to yield a raffinate product of oxygen and argon of 99.9 mol % and extract product of 99.9 mol % nitrogen. Indeed a remarkable achievement! Unfortunately, only limited details are disclosed in the patent. Because of its commercial interest and contrasting adsorption characteristics compared to the CO2-N2-13X zeolite system, we have studied the duplex PSA’s performance for the separation of nitrogenoxygen mixture. The objective of this work is to examine the potential for sharp separation and process intensification of the modified duplex PSA for the system of competing adsorption. ’ SIMULATION OF ORIGINAL AND MODIFIED DUPLEX PSA The descriptions of the original and the proposed modified duplex PSA have been presented in the Part 1. The mathematical model and simulation are presented in the Appendix. Table 1 gives the parameters used in the simulation. Figure 1 shows the adsorption equilibria of the system at different pressures estimated using the extended Langmuir model with the parameters given in Table 1. The diagram depicts the equilibria rather comprehensively. The horizontal line anywhere within the region covering the phase envelope is a tie line. The total amount of adsorbate, qTotal, can be read from the figure for a given gas-phase mole fraction, x, or adsorbate mole fraction, r 2011 American Chemical Society

y. It may be noted that the selectivity is independent of the system pressure, which is an attribute inherited from the extended Langmuir model. The average selectivity for this system is 3.1 against infinity for the CO2-N2-13X zeolite system that was studied in Part 1 of this work. We have used the adsorption isotherms, LDF parameters, and physical properties of the adsorbent given by Farooq et al.2 The LDF parameters appears to be rather high; however, the LDF parameters reported for 10X zeolite by Singh and Jones for N2 (6.2 s-1) and O2 (35.0 s-1) were also in the same range.3 The cyclic steady state was attained after 150 cycles. However, we carried out simulations up to 300 cycles. The bed length has been divided into equispaced grids with 105 and 209 grid points for original and modified duplex PSA respectively, based on preliminary exploratory runs. The feed was introduced at the 60th grid (60/209th grid) from the extract recycle end of the bed. A run took about 1 h for original duplex PSA and 2.5 h for modified duplex PSA on Compaq P-IV PC (512 MB RAM and 2.79 GHz).

’ RESULTS AND DISCUSSION In the simulation studies, the feed is chosen to be of equimolar mixture. Therefore, the extract and raffinate products rates are set as equal to yield perfect separation, if feasible, if not the products would be of the same purity. Figures 2 and 3 show the massbalance sheets for Mode-E (pressure resetting from the extract end) and Mode-R (pressure resetting from the raffinate end). They present the amounts of components held in the beds at the beginning and end of Steps; the recycle between the beds in Step1 and the amount transferred in Step-2; purities of products; and the specific energy requirements for the individual steps and productivities of products. In computing energy requirement, we have considered that the feed is at 1 atm and both products are available at pressure, PH. Additional energy needed to pressurize the feed from 1 atm to 4 atm has been included in these cases. In Step-2, unlike the CO2-N2 separation, where the amount recycled in Mode-R in the pressure-resetting step was less by 7 Received: January 25, 2011 Accepted: January 28, 2011 Published: February 18, 2011 3437

dx.doi.org/10.1021/ie200175h | Ind. Eng. Chem. Res. 2011, 50, 3437–3445

Industrial & Engineering Chemistry Research

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times compared to the amount required in Mode-E, the difference was not substantial in the N2-O2 separation. It was less only by a factor of 1.4. Had there been equimolar counter diffusion and the adsorbent saturated, the amounts of gas entering and leaving the beds should have been the same.

However, they are far different. This could be attributed to the variation of qTotal with composition, a 3-fold rise in qTotal, as the mole fraction of N2 varied from 0 to 1.0 (see Figure 1). The amounts of recycle streams would have been the same had qTotal been uniform over entire composition range. There was a minor deficit in the amount of gas required in the pressure-resetting step in Mode-E, whereas it was in excess in Mode-R as shown in the figure. The extract and raffinate product purities are 78.74 and 78.75 mol % for Mode-E and 72.14 and 72.15 mol % for Mode-R. However, the specific energy requirements are 469.8 kWh/ton of O2 for Mode-E and 320.0 kWh/ton of O2 for Mode-R. Figure 4 shows the qTotal and qN2 profiles in the bed undergoing the feed, blowdown, purge, and pressurization steps for Mode-R. There is a significant shift in the qTotal and qN2 profiles in the pressure-resetting step in both the beds unlike in the case of the CO2-N2-13X system, where the change is almost negligible. Figure 5 shows a mass-balance sheet for the modified duplex PSA with operating conditions similar to the original duplex PSA shown in Figure 3. There is a dramatic improvement as the product purities are 99.3 mol % N2 and 99.6 mol % O2 for the modified duplex PSA against 72 mol % N2 and 72 mol % O2 for the original duplex PSA. The total specific energy requirement was nearly the same for both processes. Figure 6 shows the solid-phase and gas-phase concentration profiles in the beds in various steps for the modified duplex PSA case presented in Figure 5. Let us examine the profiles in Bed-1. The kink in its profiles undergoing feed step is due to the entry of feed (Figure 6a). The adsorbate in a section at the top bed reached almost pure nitrogen by the end of the feed step. The section penetrated deep into the bed in Step-2 (Figure 6b). Therefore, the extract product drawn in Step-3 is almost pure nitrogen (Figure 6c). Consider the profiles in Bed-2. At the beginning of Step-1 (purge step), a section at the bottom of Bed-2 was loaded with almost pure nitrogen (vertical broken line at 0 s in Figure 6c). As the time progressed, the bottom got enriched with oxygen as the

Table 1. Parameters Used for the Simulation Studies physical properties of the adsorbent2 bulk density of adsorbent, kg/m3

720

bed length, m

1.0

bed diameter, m

0.025

bed void fraction

0.4

tortuosity factor

3.0

particle diameter, mm particle porosity

0.707 0.33

Langmuir isotherm model parameters2 b, m3/mol

N2: 2.813 10-3 [0.114 bar-1] O2: 8.935 10-4 [0.036 bar-1]

3

qs, mol/m

N2: 5260 [4.38 mol/kg] O2: 5260 [4.38 mol/kg]

LDF parameters2 k, s-1

N2: 19.7 O2: 62.0

operating variables feed composition

50% N2

temperature, K

298.15

cycle time, s:

original duplex: 50 modified duplex: 60

feed, s:

20

intermediate blowdown, s: purge, s:

5 20

pressurization, s:

5

final blowdown, s:

5

Figure 1. The x-y- qTotal diagram for nitrogen-oxygen-5A zeolite system. 3438

dx.doi.org/10.1021/ie200175h |Ind. Eng. Chem. Res. 2011, 50, 3437–3445


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Figure 2. Mass-balance sheets with Mode-E for original duplex PSA.

Figure 3. Mass-balance sheets with Mode-R for original duplex PSA.

recycle was almost pure oxygen. A section was developed in which the adsorbate is almost pure oxygen (Figure 6d). This section penetrated further into the bed during pressure resetting Step-2 (Figure 6e). Therefore, the raffinate drawn

at the beginning of feed step (Figure 6a) was almost pure oxygen. Figure 7 shows the effect of feed location on the purities for modified duplex PSA. It can be seen that over a broad range of 3439



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Figure 4. Solid-phase concentration profiles in original duplex for nitrogen-oxygen system (MODE-R).

Figure 5. Mass-balance sheets with Mode-R modified duplex PSA.

feed locations, the purities were nearly constant. In the rest of the simulations we have kept the 60th grid point as the feed point location. Effect of PH and Feed Flow Rate. Figure 8 shows the effect of feed flow rate for adsorption pressures of 1 and 4 atm. The purities were higher for the higher PH for both PSA processes.

Maxima in the purities can be seen in variation of purities with feed rate for PH = 4 atm. The purities declined with feed rate for PH = 1 atm. The trend in the energy requirement of the modified duplex PSA for PH = 1 atm (Figure 8a) is opposite to the trend of the other cases because of the deep vacuum that was required to draw as the extract product. 3440



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Figure 6. Solid phase and gas phase concentration profiles in bed for modified duplex PSA (Mode-R).

Figure 7. Variation of product purity with feed location for modified duplex PSA (F = 60 mmol/half cycle, PH = 4 atm, P0 L =1.5 atm, RR = 1.0).

’ PROCESS INTENSIFICATION Table 2 shows the performances of original and modified duplex PSA and the conventional PSA for the fractionation of an equimolar N2-O2 mixture. It can be seen that the reduction in volume and energy requirement was an order of magnitude for the modified duplex PSA compared to the original duplex PSA. The PI is substantial. It is indeed possible to enhance productivity in the modified duplex PSA by a small trade-off in product purities. Knaebel4 proposed a 6-step PSA cycle for the fractionation of air to get both products of high purity. The

experimental data reported for his cycle are given in the table. It may be noted that a part of the raffinate was used for purging the bed after blowdown and the resulting effluent was discarded. We have computed the energy requirement assuming the bed to be saturated with pure nitrogen before blowdown and the effluent is compressed to 1 atm. The energy requirement was less than half of that was required for modified duplex PSA; however, the productivity was an order of magnitude less, and the recovery was also less as there is a waste stream besides two products. 3441



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Figure 8. Effect of adsorption pressure and feed flow rates on original and modified duplex PSA.

Table 2. Performance of Processes for the Fractionation of an Equimolar N2-O2 Mixture purity (mol %)

feed (mmol/half-cycle) SLPM pressure ratio PH/PL (PH-PL)

N2

O2

O2 productivity (mol/kg.h) E (kWh/ton O2)

original duplex PSA (Mode-E)

10.0

0.54

20.0 (1-0.05)

92.3

92.4

1.01

2577.3

modified duplex PSA (Mode-R)

60.0 100.0

2.98 4.97

3.1 (4-1.29) 3.5 (4-1.13)

99.2 95.8

99.5 95.1

5.46 8.67

286.1 258.6

conventional PSA for air4

-

2.45

21.2 (1-0.047)

98.9

99.2

0.535

118.8

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’ CONCLUSIONS We have proposed a modification to the original duplex PSA to improve the performance. The simulation studies were carried out on the performance of original and modified duplex PSA for the separation of the N2-O2 mixture. The performances of both modes of pressure-resetting were comparable. It was shown that modified duplex PSA yields sharp separation for mixtures with both very high as well as low selectivity. However, the performance of Knaebel’s cycle, proposed to obtain both products of high purities in separation of air, is superior to the modified PSA with respect to energy requirement and inferior with respect to productivities. Further studies are needed to evaluate the efficacy of modified duplex PSA compared to the conventional PSA cycle.

By summing up eq 5 over components, we have 2 N DP D2 P DP ð1 - εÞ Dqi ¼ KP RT i ¼ 1, 2 ð6Þ þK Dt DZ 2 DZ ε i ¼ 1 Dt

∑

Substitution eqs 6 in 5 yields Dxi DL0 D2 xi DP Dxi ¼ þK Dz Dt P Dz2 Dz N

ð1 - εB Þ RT Dqi Dqi xi þ εB P Dt i ¼ 1 Dt

∑

Dqi ¼ ki ðqei - qi Þi ¼ 1, 2 Dt

Mathematical Model. In modeling of this PSA, we assumed

D2 xi P Dðvxi PÞ Dxi P ð1 - εB Þ Dqi þ þ ¼ 0 for i ¼ 1, 2 RT - DL 2 þ Dz Dz Dt εB Dt

ð1Þ (see Nomenclature for the symbols). The interstitial velocity is given by the Blake-Kozeny equation ν¼ -

dp2 εB 2

DP 150μð1 - εB Þ Dz 2

where K ¼

150μð1 - εB Þ2

qe i ¼

DLo P

∑ bj xj

i ¼ 1, 2 & n ¼ 2

ð9Þ

j¼1

I:C: : xðz, 0Þ ¼ xf ; qi ðz, 0Þ ¼ qe if ; Pðz, 0Þ

ð2Þ

¼ PH for all z Dx B:C: : at z ¼ 0 Dz ð3Þ

Dx B:C: : at z ¼ L Dz

ð10Þ

z¼0

z¼L

DP ¼ 0, Dz

¼0

ð11Þ

z¼0

DP ¼ 0, vf ¼ - K Dz

ð12Þ z¼L

• Purge step

ð4Þ

I:C: at t ¼ tpu- : xðz, tpu- Þ ¼ xðz, tbþ Þ; qðz, tpu- Þ ¼ qðz, tbþ Þ; Pðz, tpu- Þ ¼ Pðz, tbþ Þ ð13Þ Dx B:C: : at z ¼ 0 Dz

! Dxi DL0 D2 xi D2 P xi DP 2 DP Dxi ¼ þ K xi 2 þ þ Dz Dz Dz Dt P Dz2 P Dz xi DP ð1 - εB Þ RT Dqi for i ¼ 1, 2 εB P Dt P Dt

n

The partial differential eqs 6, 7, 8a, and 8b along with eq 9 have to be solved with the appropriate boundary conditions to obtain the various profiles. The following initial and boundary conditions are used for the different steps of the duplex PSA: • Blowdown step

Substituting eq 3 for v and eq 4 in eq 1 we get

-

qsi bi xi 1þ

The pressure effect on axial dispersion coefficient can be expressed as DL ¼

ð8bÞ

The concentrations of the adsorbate at equilibrium were estimated by the extended Langmuir isotherm

DP Dz

dp2 εB 2

ð7Þ

ð8aÞ

The LDF coefficient, ki, in eq 8 was estimated by ! 60εp DM dc ki ¼ dq τp dp2

which can be put in the form v ¼ -K

for i ¼ 1, 2

The interphase transport rate is given by

’ APPENDIX the following: isothermal operations, the gas obeys the ideal gas law, the adsorption equilibria for mixtures can be represented by the extended Langmuir isotherm, the gas phase pressure drop across the bed is governed by the Blake-Kozeny equation, the flow in the bed can be represented by the axial dispersed-plug flow model, the LDF model holds good for intraparticle mass transfer, and the external film mass-transfer resistance is negligible. A mass balance of species ‘i’ for the gas phase is (see Nomenclature for notation)

!

DP ¼ -K Dz

ð5Þ 3443

¼ z¼0

v ðxR - xjz ¼ 0 Þ, vf DL ð14Þ

z¼0


Industrial & Engineering Chemistry Research Dx B:C: : at z ¼ LPðL, tÞ ¼ PðL, 0Þ Dz

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¼0

The axial dispersion coefficient is estimated from6

ð15Þ

DL ¼ 0:75DM þ

z¼L

ð25Þ

and DM is calculated using the Chapman-Enskog equation7

• Pressurization step I:C: at t ¼ tpr- : xðz, tpr- Þ ¼ xðz, tpuþ Þ; qðz, tpr- Þ ¼ qðz, tpuþ Þ; Pðz, tpr- Þ ¼ Pðz, tpuþ Þ ð16Þ Dx B:C: : at z ¼ 0 Dz DP ¼ -K Dz

0:5dpv 9:5DM 1þ dpv

¼ z¼0

v ðxR - xjz ¼ 0 Þ, vf DL ð17Þ

z¼0

Dx B:C: : at z ¼ L Dz

z¼L

DP ¼ 0, Dz

¼0

ð18Þ

z¼L

• Feed at intermediate position I:C:at t ¼ tf _ : xðz, tf _ Þ ¼ xðz, tprþ Þ; qðz, tf _ Þ ¼ qðz, tprþ Þ; Pðz, tf _ Þ ¼ Pðz, tprþ Þ

B:C: : at z ¼ 0 & z ¼ zF

Dz

ð19Þ

þ Dx z

v DP ¼ - ðxF - xjz Þ, vf ¼ - K DL Dz

ð20Þ z

DP Dx B:C: : at z ¼ L & z ¼ zF- ¼ 0, ¼ 0 Dt Dz z

ð21Þ

z

In the blowdown and pressurization steps, the flow into the bed should be such that the bed reaches the desired pressure in the given step time. The following equation represents the flow through a valve5 ΔP 2fLe v2 ¼ F dpipe gc On rearranging eq 22, we get dpipe gc 1=2 v¼ ðΔPÞ1=2 ¼ CðΔPÞ1=2 2fLe F

ð22Þ

ð23Þ

where C = ((dpipegc)/(2fLeF))1/2. The above equation has been modified as v ¼ kCðΔPÞ1=2 where ‘k’ is a parameter.

ð24Þ

DM ¼

1:86 10-3 T 3=2 1 1 1=2 þ M1 M2 pσ212 Ω

ð26Þ

Energy Equation. The energy required for the compression or evacuation of a gas stream is obtained by numerically integrating the equation " #! Z nðPL Þ γRTavg PH γ - 1=γ - 1 dnðPL Þ ð27Þ W ¼ γ-1 PL 0

Equation 27 was used to estimate individual energy consumption for various steps (Step 1 and 2 of duplex PSA; Steps 1, 2, and 3 of modified duplex PSA). The specific energy requirement reported is then obtained by summing all individual steps together and normalizing with the product drawn per cycle. We have defined productivity in our analysis as the ratio of the moles drawn as product to the total adsorbent mass used multiplied with the cycle time. Method of Simulation. The governing eqs 6, 7, 8a, and 8b were solved with appropriate initial and boundary conditions given in eqs 10-21 to obtain pressure and compositions of the gas and adsorbate phases for all steps in a duplex cycle. The PDEs were discretized in the space domain using the central-difference scheme of the finite difference approximation. Thus, they were reduced to a set of ordinary differential equations. The discretized form of the governing equations and the boundary conditions for each step are given elsewhere.8 These were stiff equations. They were integrated using the DDASPG subroutine available in IMSL library of Fortran Power Station 4.0. It employs the Petzold-Gear method.9 We have set the ratio of the heavy and light products to be the same as the ratio of the heavy and light components in the feed to ensure near ideal separation; that is pure A and pure B as products. In the simulation, we have used the recycle ratio of A-rich stream, RE, and recycle ratio of B-rich stream, RR, to fix the recycle streams in Step-1 and -3 of the duplex PSA. The grid numbers were swapped at the end of purge step to initialize the conditions for calculations of the pressurization. Likewise, the grid numbers are swapped after the feed to initialize the conditions for blowdown calculations. The pressure-resetting steps (Step-2 and -4) were treated as blowdown from PH to PL for the bed at high pressure and as pressurization from PL to PH for the bed at low pressure. The effluent from blowdown was used to pressurize the other bed. The calculations were started with the blowdown by considering the bed being saturated with almost pure A at PH. The ‘k’ parameter in eq 24 was adjusted to ensure that the blowdown was complete in preset step time. The profiles and average effluent composition of blowdown were calculated. Then the profiles, effluent amount, and its composition for the purge step were calculated by assuming the end condition of blowdown as the initial condition. Likewise, the parameter ‘k’ was adjusted 3444



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using the regula-falsi method to ensure that the pressurization was complete in the pre-set time using the effluent from the blowdown. Resetting the end conditions of pressurization as the initial conditions, the calculations were performed for the feed step. This completes the calculation for one cycle. The calculations for subsequent cycles were performed using the profiles and the average effluent compositions of the previous steps until periodic steady state is attained.

v, vf xF xi W y z zFzFþ

’ AUTHOR INFORMATION

Greek letters

Corresponding Author

*Phone: þ 91 512 2597432. Fax: þ91 512 2590104. E-mail: [email protected]. Present Addresses †

Shell Projects and Technology, Shell Technology Centre Amsterdam, Grasweg 31, 1031 HW Amsterdam. ‡ Process Intensification Consultants, 201, Varshini Mansion, Deepthisri Nagar, Miyapur, Hyderabad 500049, India.

’ NOMENCLATURE bi Langmuir’s constant of component i (mol/m3)-1 dpipe diameter of pipe (m) axial dispersion coefficient (m2/s) DL axial dispersion coefficient at reference pressure of 1 DL0 atm (m2/s) molecular diffusivity (m2/s) DM diameter of the particle (m) dp E moles of extract product F moles of feed, feed rate (mmol/half-cycle) f fanning friction-factor conversion factor from Newton’s second law of motion gc i component index k tuning parameter for adjusting flow rates in blowdown and pressurization K Kozeny constant linear driving force mass transfer coefficient (s-1) ki equivalent length of the valve (m) Le M molecular weight, (g/mol) M1,M2 molecular weight of components 1 and 2, (g/mol) initial moles of heavy component in the bed, (mmol) MAi initial moles of light component in the bed, (mmol) MBi final moles of heavy component in the bed, (mmol) MAf final moles of light component in the bed, (mmol) MBf initial total moles in the bed, (mmol) MTi final total moles in the bed, (mmol) MTf N number of components, (-) n moles of gas, (mmol) P pressure (atm) adsorption pressure (atm) PH desorption or final-desorption pressure (atm) PL intermediate-desorption pressure (atm) P0 L amount of component i in the adsorbate, (mol/m3) qi saturation constant of component i (mol/m3) qs,i total solid-phase molar concentration (mol/m3) qTotal R moles of raffinate product R universal gas constant, (N.m.kmol-1.K-1) raffinate recycle ratio RR extract recycle ratio RE t time (s) T temperature, (K)

εB εp γ Ω F σ12 τp μ

superficial velocity of the gas, (m/s) mole fraction of heavy component in the feed mole fraction of component i in gas phase work done, (J) mole fraction of component in solid phase distance measured from the bed inlet (m) bed position just before the feed inlet bed position just after the feed inlet bed voidage particle porosity ratio of heat capacities cp/cv Lennard-Jones Potential function density of fluid mixture, (kg/m3) collision diameter, Å particle tortuosity viscosity of fluid mixture (kg/m.s)

Subscripts

b bbþ f fi,j pr prprþ pu pupuþ

blowdown start of blowdown end of blowdown feed start of feed component number pressurization start of pressurization end of pressurization purge start of purge end of purge

Superscripts

e

equilibrium condition

’ REFERENCES (1) Leavitt, F. W. Duplex Adsorption Process. US Patent 5,085,674. 1992. (2) Farooq, S; Ruthven, D. M.; Boniface, H. A. Numerical Simulation of a Pressure Swing Adsorption Oxygen Unit. Chem. Eng. Sci. 1989, 44, 2809. (3) Singh, K; Jones, J. Numerical simulation of air separation by piston-driven pressure swing adsorption. Chem. Eng. Sci. 1997, 52, 3133. (4) Knaebel, K. S. Pressure Swing Adsorption. US Patent 5,032,150. 1991. (5) Perry, R. H.; Green, D. W. Perry’s Chemical Engineering Handbook, 7th ed.; McGraw-Hill Co.: 1997. (6) Huang, W. C.; Chou, C. T. A Moving-Finite Element Simulation of a Pressure Swing Adsorption Process. Comput. Chem. Eng. 1997, 21, 301. (7) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: Cambridge, 1997. (8) Sivakumar, S. V. Sharp separation and process intensification in adsorptive separation processes. Ph.D. Thesis, Indian Institute of Technology Kanpur: India, 2007 (9) Brenan, K. E.; Campbell, S. L.; Petzold, L. R. Numerical Solution of Initial Value Problems in Differential-Algebraic Equations; SIAM: 1996.

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Modified Duplex PSA. 2. Sharp Separation and ... - ACS Publications

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