Analysis of Nonisobaric Steps in Nonlinear Bicomponent Pressure

138

Ind. Eng. Chem. Res. 2000, 39, 138-145

Analysis of Nonisobaric Steps in Nonlinear Bicomponent Pressure Swing Adsorption Systems. Application to Air Separation Ade´ lio M. M. Mendes, Carlos A. V. Costa,* and Alı´rio E. Rodrigues Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4050-123 Porto, Portugal

This paper presents a simulation study using a pressure swing adsorption unit performing an equilibrium-based bicomponent separation, running a traditional Skarstrom cycle. This study is also supported by experimental results obtained for oxygen separation from air in a 5A zeolite. The focus is on the influence on product purity and recovery of the pressure rising rate during pressurization, pressure lowering rate during blowdown, production pressure, and intraparticle viscous flow. A co-current equalization step is also considered. Within the range of tested conditions, it was found that the pressure rising rate during pressurization influences product purity and recovery whereas the pressure lowering rate during blowdown has almost no effect. It was concluded that higher pressurization rates decrease product purity and recovery. Intraparticle viscous flow can enhance or decrease product purity depending on the relationship between diffusional and intraparticle viscous flow contributions and an axial head loss. The production pressure has a complex effect on product purity and recovery, and there is some system-dependent optimal value. Use of a co-current equalization step always enhances product purity and recovery. Introduction The design and operation of an equilibrium-based pressure swing adsorption (PSA) unit involves the decision of the best operating conditions and design parameters. This work discusses issues related with nonisobaric steps (pressurization, blowdown, and equalization), intraparticle viscous flow, and production pressure. Many authors developed and studied PSA models. The first PSA models consider local equilibrium and linear isotherms (e.g., ref 1). Models including multicomponent coupled isotherms and rate intraparticle mass transport for the isobaric and nonisobaric PSA steps were developed and later used (e.g., ref 2). Doong and Yang3 published a bidisperse pore diffusion model, and Liow and Kenney4 used the Stefan-Maxwell bicomponent equation, considering molecular and Knudsen diffusivities for the isobaric steps and a homogeneous linear driving force (LDF) model with experimentally obtained parameters for the nonisobaric steps. Richter et al.5 proposed that the mass transport during PSA nonisobaric steps is a combination of molecular and Knudsen diffusion, viscous flow, and surface diffusion and so the mass transport coefficient can never be regarded as constant. Nevertheless, solving a PSA model and all of these transport mechanisms, along with bicomponent coupled isotherms, is very bulky and cumbersome so Mendes et al.6 proposed a LDF approximation for the dusty gas model (DGM) (e.g., ref 7), the LDF-DG model. This model retains all of the important features of the DGM and is much easier to solve. Farooq et al.8 and Ruthven and Farooq9 studied the oxygen separation from air using a 5A zeolite using 100 or 250 s Skarstrom cycles when the nonisobaric steps last for about 30% of the cycle time, e.g., ≈15 or 37.5 s. * To whom correspondence should be addressed. Tel.: +351 22 2041670. Fax: +351 22 2000808. E-mail: [email protected].

They observed no influence of pressurization time on product purity and recovery. Liow and Kenney4 also studied the oxygen separation from air using a 5A zeolite. They used a special sort of 5A zeolite pellets with large pores (average diameter 800 nm). With this adsorbent they concluded theoretically and experimentally that changing the pressurization rate from 27 to 69 kPag/s had no significant effect on product purity. In this work we extended these studies in order to better elucidate the influence of pressure rising/lowering rate during the pressurization/blowdown step. Lu et al.10-12 used an intraparticle model combining diffusion transport with intraparticle viscous flow to model the pressurization and blowdown PSA steps of an inert plus solute. These authors considered sufficient axial head loss for the occurrence of viscous flow across the particles and concluded that this transport mechanism always enhances product purity. In our work we studied the case of the existence of intraparticle viscous flow when the head loss is negligible. Serbezov and Sotirchos13 considered the dusty gas model along with an energy balance and studied the bicomponent loading and unloading of a single adsorbent particle in an infinite medium and in a packed bed. These authors concluded that when modeling packed beds, it is not necessary to consider the temperature difference between the particle and the surrounding gas. Farooq et al.8 and Ruthven and Farooq9 studied the production pressure effect on product purity for a Skarstrom PSA cycle. They obtained three experimental points, indicating that product purity increases with the production pressure, up to a pressure of about 2.25 atm. We revisited this issue considering a much more complex particle model. Most of the PSA studies were performed using the traditional Skarstrom cycle. The Skarstrom cycle with

10.1021/ie990355v CCC: $19.00 © 2000 American Chemical Society Published on Web 12/02/1999

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 139 Table 1. Experimental Operating Conditions experiment

production pressure (bar)

cycle time (s)

press. step (s)

prod. flow-rate setpoint (Ln/min)

purge flow-rate setpoint (Ln/min)

equalization

8.1 and 8.2 22.1 23.4 23.6 23.8 24.2 24.10

6.8 4.2 3.0 5.1 7.1 4.2 3.1

180 180 180 180 180 180 180

40 40 40 40 40 40 40

0.1 0.1 0.1 0.1 0.1 0.1 0.1

1.10 1.15 1.15 1.15 1.15 1.15 1.15

no no no no no yes yes

an equalization step was introduced soon after the first granted patents as a way to improve the energetic performance of the original cycle.14 There are a few research papers that studied the equalization step such as, for example, those published by Hassan et al.15 and Farooq and Ruthven16 that assumed frozen profiles during this step. We extended this analysis using a more complex particle model and consequently no frozen profiles. Experimental Procedure Two PSA cycles are considered in this work, the traditional Skarstrom cycle17 and the Skarstrom cycle with co-current equalization: at the end of each production step, the product end of the column at higher pressure is connected to the feed inlet of the purged column for partial or total pressure equalization. To be able to vary the equalization flow rate, a needle valve was introduced in the pipe that links both columns during this step. The experimental PSA setup has two columns 0.84 m long and 25.0 mm internal and 28.2 mm external diameter, filled with spherical 5A zeolite particles from Laporte (1.70 ( 0.02 mm diameter) regenerated at 370 °C for about 24 hours, inside an oven, at the ambient pressure. Then, the zeolite was allowed to cool down up to about 200 °C, and it was then transferred directly to the columns. The feed gas is air, assumed to be 78% nitrogen and 22% oxygen plus argon. This system is equipped with two pressure transducers, four mass flowmeters, and a mass spectrometer for concentration measurements. Several experiments were performed to evaluate the effects of the pressure rising/lowering rate during pressurization/blowdown steps, the production pressure, and the equalization step on product purity and recovery. The operating conditions are reported in Table 1. Temperature excursions were less than 5 °C, meaning that the maximum selectivity change is less than 3%,18 and thus the system behaves almost isothermally, as was already observed by Kapoor and Yang.19 The maximum observed pressure drop during the pressurization step was 0.08 bar; thus, negligible axial pressure drop can be assumed. For each set of operating conditions and after the cyclic steady state has been reached, a set of 10 cycles was recorded and averaged and a 95% confidence interval calculated for each measured variable. Mathematical Model The PSA/LDF-DG mathematical model proposed here is based on the following main assumptions: (i) the flow pattern is described by the axially dispersed plug-flow model, (ii) the intraparticle mass transfer is described by the LDF-DG model6 and the intracrystallite masstransfer resistance is considered negligible as proposed by Ruthven et al.20 for a similar system and conditions,

(iii) isothermal operation,19 (iv) equilibrium represented by a bicomponent Langmuir isotherm, (v) negligible axial pressure drop, (vi) perfect gas behavior, and (vii) variable interparticle velocity. The interparticle dimensionless component mass balances can be written as (e.g., ref 21)

(

)

2 / / ∂p j /si ∂q ∂(u*p j /i ) j /i 1 ∂ pi ∂pi + ) 0, + R + ∂z* Pe ∂z*2 ∂θ ∂θ ∂θ i ) A, B (1)

Adding these mass balance equations and considering ∂P*/∂z* ) 0, we obtain the global mass balance

P*

∂u*

+

dP*

(∑

+R

dθ

∂z*

∂p j s/i

i

∂q j /i

∑i ∂θ

+

∂θ

)

) 0, i ) A, B (2)

The intraparticle dimensionless LDF-DG mass balance is described elsewhere.6 The DGM considers three mass transport mechanisms in the macropores/mesopores network. Molecular and Knudsen diffusion is in series and convective flow in parallel. The LDF-DG model is a lumped approximation to the DGM that was developed in order to avoid the complexity of using the DGM. This simplified model proved to be quite accurate (in relation to the DGM predictions) even in the case of any cyclic perturbation. It has three tuning parameter: one related to the diffusional response amplitude, Ω h, another related to the viscous flow response amplitude, ψ h , and another related to a time delay, φ. For long PSA cycles, the time lag of the LDF-DG model becomes negligible (φ ) 0) and model equations simplify to

∂p j /si

+

∂θ

∂q j /i ∂θ

{

hi ) Rbp Ω

p/i - p j /si Ei

+ψ h iRgµp*i (P* -

Rkk + Rkkp j s/A + p j s/B Rgk

j s/A + p j s/B Rkkp 1 EB ) + Rgk Rkk P* )

i

}

i ) A, B (3)

where

EA )

∑i pj /s )

P Pref

The equilibrium equation is

+

∑i p/i

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Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000

q j /i

RQ j /si i p

)

1+

∑j

Rkj

i, j ) A, B

(4)

p j s/j

The independent variables are

θ)

t τb

z* )

and

z L

where t is the time in each cycle, z is the axial coordinate, θ is the dimensionless time, τb is the bed reference space time, and L is the column length. The dependent variables are

q j /i )

q ji qref

p j /si )

p j si

p/i )

Rref

pi Pref

u* )

u uref

ji where qref ) pPref/FRT is a reference concentration, q is the particle-averaged adsorbed i solute molar concentration, p is the particle porosity, Pref is a reference pressure, F is the particle density, R is the perfect gas constant, T is the absolute temperature, p j si is the particle-averaged i solute intraparticle partial pressure, pi is the i solute interparticle partial pressure, P is the interparticle total pressure, u is the interstitial velocity, uref is a reference interstitial velocity, and p/i is a corrected pressure that should be used to estimate the intraparticle viscous flow contribution (eq 3). This pressure is different for particle loading or unloading: j s/i and p/i ) p j s/i when P* < ∑ip j /si. p/i ) p/i when P* > ∑ip The auxiliary variables are

Deij )

p D τt ij Dei

Doij ) DeijPref

τg )

p ) Di τt

r20

τki )

τµ )

Prefr20

Be0

Dei

r20µM

Doij

τb )

Be0Pref

(P*u*)connecting pipe )

p ) B0 τt

L uref

[P*2(z* ) 1,blowdown column) - P*2(z* ) 0,pressurization column)]/R* (5)

τp ) pτg

where Dij is the molecular diffusivity, Deij is the effective molecular diffusivity, τt is the tortuosity, Di is the Knudsen diffusivity (in this model the same tortuosity is assumed for all transport mechanisms in order to have only one fitting parameter and this simplifies calculations), Dei is the effective Knudsen diffusivity, µM is the average viscosity, r0 is the particle radius, B0 is the adsorbent permeability, and Be0 is the effective adsorbent permeability. The operating variables are the duration of each step. For a traditional Skarstrom cycle, these are cycle and pressurization step durations, θcycle and θpress, respectively. When equalization is used, an equalization time is also necessary. The model parameters are

Pe )

urefL Dax

R ) p

Rkk )

τkA τkB

1-  Rgµ )

τb τp

Rgk )

RQ i )

FRT Q kL p i i

Rbp ) τg τµ

where  is the bed porosity, Dax is the axial dispersion, and Qi and kLi are parameters of the Langmuir equation. Initial and Boundary Conditions. It is considered that at startup the inter- and intraparticle gas phases have the same composition as the feed at ambient pressure and that the adsorbed phase is in equilibrium with the intraparticle gas phase. The concentration profiles at the beginning of each new step are taken to be the same as those at the end of the previous step. The boundary conditions for the traditional Skarstrom cycle in one of the columns are as follows: (i) pres/ (θ), surization, θ ∈ [0, θpress]: P*(z*)0,θ) ) Ppressurization / / / pi (z*)0,θ) ) pipressurization(θ) ∂pi /∂z*|z*)1 ) 0, and u*(z*)1,θ) ) 0. (ii) Production, θ ∈ [θpress, θpress + θprod]: / , p/i (z*)0,θ) ) pi/production, ∂p/i /∂z*|z*)1 P*(z*)0,θ), Pproduction / ) 0, and u*(z*)1,θ) ) uproduction . (iii) Blowdown, θ ∈ [θpress + θprod, 2θpress + θprod]: ∂p/i /∂z*|z*)0 ) 0, ∂p/i /∂z*|z*)1 / ) 0, P*(z*)0,θ) ) Pblowdown (θ), and u*(z*)1,θ) ) 0. (iv) Purge, θ ∈ [2θpress + θprod, θcycle]: ∂p/i /∂z*|z*)0 ) 0, / , p/i (z*)1,θ)/P/purge ) p/i (z*)1,θ,other column)/Pproduction / / P* ) Ppurge, and u*(z*)1,θ) ) upurge. θprod ) (θcycle / / / , Pproduction , Pblowdown , P/purge, 2θpress)/2, Ppressurization / / / / pipressurization, piproduction, uproduction, and upurge are given or measured. The Skarstrom cycle with equalization has two more steps. For these steps we considered that when we link the columns, the component mole fractions at the inlet of the pressurizing column are the same as those at the outlet of the blowing down column (as we usually do for the case of production/purge) and that total pressures at these column ends are related by the Poiseuille equation:

τg τkB

Rki ) kLi Pref

where R* ) RPref/uref is a dimensionless resistance. The use of this equation is justified because we are imposing a resistance in the pipe linking the columns (needle valve) that controls the flow rate between them. The value of R* is obtained using the PSA/LDF-DG model plus the former equation and a measurement of total pressure at the ends of the connecting pipe at a given time during equalization. The PSA/LDF-DG model was solved using the package FORSIM VI.22 The spatial coordinate was discretized using three-point centered finite differences and a grid of 31 points and integrated along the time using the Gear algorithm, with a truncation error of 10-4. The equalization step involves the simultaneous solution of intra- and interparticle mass balances along with the mass transport equation between the columns (eq 5). This problem was solved starting with a guessed pressure for the blowdown column for each new time step. Using the PSA/LDF-DG model, the outlet velocity is obtained for this column and, through eq 5, the pressure for the other column is calculated. Using again the PSA/LDF-DG model for the pressurizing bed, the inlet velocity is obtained and, through eq 5, a new value for the pressure of the blowdown column is obtained. This process is repeated until convergence. The Skarstrom cycle with equalization is of a much more complex

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 141 Table 2. Parameters of the Bicomponent Langmuir Equation at 293 K gas

Qi (mol/kg)

kLi (mol/kg)

oxygen nitrogen

3.3760 ( 1 × 10-4 2.2200 ( 1 × 10-4

0.035850 ( 1 × 10-6 0.159200 ( 8 × 10-6

Table 3. Effective Molecular and Knudsen Diffusivities and Effective Permeability of Zeolite 5A from Laporte (293.15 K and 1 bar) e DO (m2/s) 2-N2

e DN (m2/s) 2

e DO (m2/s) 2

Be0 (m2/s)

1.68 × 10-6

5.41 × 10-7

5.05 × 10-7

4.31 × 10-18

solution, and the CPU time per cycle increased about 6 times, because of this iterative procedure. Results and Discussion A simulation study was carried out in order to elucidate the influence of the following issues on product purity and recovery: (a) pressure rising rate during the pressurization step and pressure lowering rate during the blowdown step, (b) intraparticle viscous flow, (c) production pressure, and (d) equalization step. To support the results obtained from the simulations, some experimental runs were performed and then simulated. To simulate the experimental PSA unit, it was necessary to have the bicomponent equilibrium and transport data. The oxygen and nitrogen bicomponent Langmuir parameters, for adsorption in the 5A zeolite from Laporte, are given in Table 2. These parameters were calculated by fitting the Langmuir bicomponent equation to the data obtained by IAST (Ideal Adsorption Solution Theory) using the experimental monocomponent data by Sorial et al.23 The Knudsen diffusivity coefficients were obtained from the kinetic theory (e.g., ref 7), the molecular diffusion coefficient was calculated using the Chapman-Enskog equation (e.g., ref 24), and the permeability was calculated using the Poiseuille equation for circular cross-sectional pores (e.g., ref 7). The average viscosity was computed using a correlation by Wilke (e.g., ref 25). The PSA/LDF-DG model has only one fitting parameter, the tortuosity. This parameter was obtained by fitting the simulation results to four experimental runs (two of them are reported here: runs 22.1 and 23.8).18 The value obtained for tortuosity was τt ) 3.6. This value is inside the range suggested by Yang17 for commercial zeolites: 1.7 e τt e 4.5. The intraparticle porosity obtained by mercury porosimetry was p ) 0.31. The effective molecular and Knudsen diffusivities and the effective permeability are given in Table 3. The Peclet number estimated using the correlation presented by Langer and co-workers (referred by Ruthven26) is higher than 500 for most of the operating conditions. Once the results are nearly the same for a Peclet number higher than 500, this was the value considered in all of the simulations. The interparticle porosity was obtained from the amount of zeolite packed in each bed, the volume of the column, and the bead density  ) 0.36. The experimental and simulated cyclic steady-state product purities (oxygen plus argon mole fraction in the product) are shown in Table 4. Also the experimental amount of purging gas, the amount of gas fed, and the amount of gas produced per cycle were computed for the cyclic steady state along with the recovery (ratio between oxygen in product stream and oxygen fed in each

Table 4. Experimental and Simulated Product Oxygen + Argon Mole Fraction at the Cyclic Steady State yO2+Ar (%) experiment

column 1

column 2

average

simulation

8.1 8.2 22.1 23.4 23.6 23.8 24.2 24.10

93.7 ( 8.6 99.0 ( 0.3 96.6 ( 0.3 99.3 ( 0.2 93.2 ( 2.2 87.4 ( 0.7 98.6 ( 0.2 98.6 ( 0.2

93.8 ( 0.6 98.8 ( 0.6 96.7 ( 0.3 99.4 ( 0.1 94.7 ( 0.4 86.7 ( 0.7 98.7 ( 0.2 98.9 ( 0.2

93.7 ( 0.6 98.9 ( 0.4 96.6 ( 0.3 99.4 ( 0.1 93.9 ( 1.3 87.0 ( 0.7 98.7 ( 0.2 98.8 ( 0.2

95.3 99.5 96.1 96.4 94.8 91.8 98.7 98.8

cycle) and compared with the simulated amount of gas fed per cycle and the recovery and are presented in Table 5. The simulated product purity follows the experimental results except for experiment 23.4, performed at low production pressure. The experimental value is 99.4%, while the simulated one is 96.4%. The corresponding experimental value for the Skarstrom cycle with equalization, experiment 24.10, is 98.8%. This difference, which is not observed for run 24.10 carried out under the same conditions with equalization, can only be explained by an abnormal accuracy problem, probably in the mass spectrometer measurements. Recovery and feed flow rate are reasonably predicted by the model. Also we note that despite only four experiments being taken to estimate the tortuosity, this value was used with success to simulate all other experiments in different operating conditions. Pressure Rising Rate during the Pressurization Step and Pressure Lowering Rate during the Blowdown Step. A set of simulations was performed to study the influence on product purity and recovery of the pressure rising rate during the pressurization step and of the pressure lowering rate during the blowdown step. The traditional Skarstrom PSA cycle for oxygen separation from air was considered in all simulations and experimental runs. In the set of simulations the values of the parameters are in the range of the experimental runs. Further, it was considered that the pressure rising rate was constant in view of the experimental data represented in Figure 1. The parameters common to all simulations are Rgk ) 0.317, Rgµ ) 1.34 Q k × 10-2, Rkk ) 1.07, RQ A ) 10.7, RB ) 31.2, RA ) 3.71 × k -2 10 , RB ) 0.138, and Rbp ) 351. It is also considered that the purge pressure is the atmospheric pressure. The operating conditions for the present simulations are / ) 6.8, θprod ) 1.08, u/prod ) 1, and u/purge ) Pproduction -6.24. Three simulations are reported: (1) case 1.1, θpress ) 4.33 × 10-2 (tpress ) 2 s in the experimental unit); (2) case 1.2, θpress ) 0.216 (tpress ) 10 s in the experimental unit); (3) case 1.3, θpress ) 0.735 (tpress ) 34 s in the experimental unit);. The cyclic steady-state average product purity and recovery and the dimensionless productivity (amount of product produced per cycle referred to in case 1.1) for this set of simulations are shown in Table 6. It can be seen from this table that the purity increases 11% when the pressurization time increases 2.4 times: cases 1.1 and 1.2. The recovery also increases, and the productivity attains its maximum value for a pressurization step duration between cases 1.1 and 1.3. The simulated cyclic steady-state profiles, at the end of the pressurization step, are shown for each case in

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Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000

Table 5. Cyclic Steady-State Experimental and Simulated Recovery and Feed, Purge, and Product Volumes per Cycle (1 bar and 293 K) experimental

simulated

experiment

F purg (Ln/cycl)

F feed (Ln/cycl)

F prod (Ln/cycl)

recovery (%)

F feed (Ln/cycl)

recovery (%)

8.1 8.2 22.1 23.4 23.6 23.8 24.2 24.10

1.99 ( 0.22 1.97 ( 0.21 2.04 ( 0.12 2.04 ( 0.09 2.02 ( 0.15 2.10 ( 0.34 2.01 ( 0.11 2.00 ( 0.08

21.0 ( 0.4 17.6 ( 0.2 12.0 ( 0.2 9.1 ( 0.3 13.7 ( 0.3 17.8 ( 0.5 11.0 ( 0.2 8.8 ( 0.3

0.18 ( 0.03 0.18 ( 0.04 0.18 ( 0.04 0.18 ( 0.04 0.18 ( 0.04 0.17 ( 0.03 0.19 ( 0.05 0.18 ( 0.04

3.6 4.6 6.6 8.9 5.8 3.7 7.6 9.2

16.6 16.9 12.6 9.8 14.3 17.9 10.9 8.9

4.7 4.8 6.3 8.1 5.5 4.2 7.5 9.2

Figure 1. Experimental pressure (95% confidence interval), measured at the column’s entrance, as a function of the cycle time, at cyclic steady state and averaged over 10 cycles. Experiments 8.1 and 8.2. Table 6. Average Product Purity, Product Recovery, and Productivity case

pressurization time (s)

average product purity (%)

recovery (%)

productivity

1.1 1.2 1.3

4.33 × 10-2 0.216 0.735

85.7 95.4 99.5

4.4 4.8 4.9

1.00 1.01 0.74

Figure 2. Cyclic steady-state profiles at the end of the pressurization step. Case 1.1: pressurization time θ ) 4.33 × 10-2. Case 1.2: pressurization time θ ) 0.216. Case 1.3: pressurization time θ ) 0.735.

Figure 2. The lines between dots were drawn for better visualization; only dots are simulation results. It is visible that their dispersion decreases when passing from case 1.1 to case 1.3, because of a larger contact time. This dispersion is responsible for the observed lower product purity and recovery. In parallel with these simulations, some experimental runs were also performed and later simulated. The experimental pressure as a function of the cycle time, at cyclic steady state, and averaged over 10 cycles is

Figure 3. Experimental and simulated recovery and product purity as a function of the rising pressure time. Experiments 8.1 and 8.2.

shown in Figure 1 for two experiments. In experiment 8.1 the pressure rising took about 10 s, while in experiment 8.2 it took about 34 s. In both cases tpress ) 40 s. The experimental and simulated cyclic steady-state recovery and product purity are shown in Figure 3 and in Tables 4 and 5 and confirm the trend in terms of the influence of the pressure rising rate on recovery and purity already observed in the simulation study. These conclusions are different from the ones presented by Farooq et al.8 and Ruthven and Farooq9 probably because they only used very large pressurization times, 30 and 75 s, and particles with a small diameter (0.707 mm) and thus are in a region of very low sensitivity. Also Liow and Kenney4 did not observe any influence of the pressure rising rate because they used an adsorbent with large average pore diameter (about 40 times larger than the one used in this study) and so they always worked close to equilibrium conditions. In equilibrium-based PSA separations, if the interparticle gas-phase velocity is too high for the equilibrium to be reached, dispersion phenomena will make the product purity decrease.17 The feed volume per cycle is always about 5-10 times larger than the product plus purge volumes (Table 5). This indicates that the interparticle gas-phase velocity should be about 10 times higher during the pressurization step than during the production step. The pressurization step is then quite important for good product purity and recovery. In fact, it was verified that higher pressurization rising rates lead to lower product purities. On the other way around, PSA productivity decreases when the pressurization time increases, because the pressurization/blowdown steps are not productive. Any difference in the product purity or recovery was not observed when the pressure lowering time was

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 143 Table 7. Average Product Purity and Product Recovery for Varous Intraparticle Viscous Flow Contributions case

Rgµ

average product purity (%)

recovery (%)

2.1 2.2 2.3

1.00 × 10-5 1.34 × 10-2 1.00

96.2 96.0 94.7

6.3 6.3 6.2

changed from 4 to 20 s for a 40 s blowdown step. This can be explained by the dispersive characteristics of blowdown. Intraparticle Viscous Flow. The parameter Rgµ takes into account the intraparticle viscous flow contribution. The intraparticle mass transport rate increases with the particle pore diameter because of the increase of the molecular diffusion and of the permeability. Three simulations were performed with increasing intraparticle viscous flow contributions in order to study its effect: (1) case 2.1, Rgµ ) 1.00 × 10-5; (2) case 2.2, Rgµ ) 1.34 × 10-2 (base case); (3) case 2.3, Rgµ ) 1.00. In these simulations we kept all of the parameter values as in case 1 except for Rbp now equal to 211. The / ) 4.2, θcycle ) 6.55, operating conditions are Pproduction θpress ) 1.46 (tpress ) 40 s in the experimental unit), and u/purge ) -3.87. The simulation results are summarized in Table 7. It is possible to verify from this table that the higher the viscous flow contribution, the lower is the product purity. Recovery is almost not affected. In our model we assumed negligible axial head loss (≈0.1 bar/m), and so the mechanism for intraparticle viscous flow results from the existence of different total pressures outside and inside the adsorbent particles; these differences can arise because we are changing the bulk total pressure during nonisobaric steps and/or the intraparticle total pressure due to adsorption. The decrease in product purity when the intraparticle viscous flow contribution increases can be explained by the bulk transport to the interior of adsorbent particles especially during pressurization, which slightly increases the penetrating distance. Lu et al.10 studied the pressurization step for an inert plus solute when the pressure drop across the bed is not negligible; that is, there is flow across the particles. They concluded that in this situation the purity is always enhanced. This apparent discrepancy can be explained as follows: in the high head loss region the system evolves from diffusion controlled to equilibrium controlled by increased flow across the particles. Thus, the purity always increases when the flow across the particles increases. For low or very low pressure drop, the system evolves from diffusion controlled to bulk transport to the particles controlled (our case), and so the purity decreases when the bulk flow to the particles increases. For some intermediate value of head loss, the system should evolve from diffusion controlled, to bulk transport, to the particles controlled, and finally to equilibrium controlled. That is, the purity initially decreases and then increases with intraparticle viscous flow. Production Pressure. Two simulations were performed to study the production pressure effect on the product purity and recovery. In the first simulation the dimensionless production pressure considered was / / ) 4.26, while in the second, it was Pproduction ) Pproduction 7.19. In both cases the dimensional cycle time and the product mass flow rate were the same. In these simulations we kept all of the parameter values as in case 1

Table 8. Influence of Production Pressure on Average Product Purity and Recovery case

dimensionless production pressure

average product purity (%)

recovery (%)

3.1 3.2

4.26 7.19

96.0 91.5

6.3 4.2

Figure 4. Experimental and simulated recovery and product purity as a function of the production pressure. Experiments 23.4, 22.1, 23.6, and 23.8.

except for Rbp that is now 211 for case 3.1 and 355 for case 3.2. The operating conditions are as follows: (1) case 3.1, u/purge ) -3.71, θcycle ) 6.55, θpress ) 1.46 (tpress ) 40 s and tproduction ) 180 s); (2) case 3.2, u/purge ) -6.25, θcycle ) 3.89, θpress ) 0.864 (tpress ) 40 s and tproduction ) 180 s). The results of these simulations are summarized in Table 8. It is apparent from these results that the product purity and recovery decrease when the production pressure increases. Some experimental runs were also performed and later simulated, to support the above conclusions. The operating parameters are shown in Table 1. The production pressures considered were as follows: experi/ / ) 3.0; experiment 22.1, Pproduction ment 23.4, Pproduction / ) 4.2; experiment 23.6, Pproduction ) 5.1; and experi/ ) 7.1. ment 23.8, Pproduction Figure 4 compares the cyclic steady-state experimental product purity and recovery results with the simulated ones. It is apparent from this figure that the higher the production pressure, the worse the PSA unit performs, considering both the experimental or the simulated results. In this example, the optimal production pressure should be lower than 3 bar. Increasing the production pressure while maintaining all of the other variables constant has a complex effect on the PSA product purity and recovery. It affects the mass transport mechanism, the adsorption selectivity, the pressure rising/lowering rates during the pressurization/blowdown steps, the temperature excursion inside the columns, the energy consumption and the fraction of the product stream of one column used to purge the other column undergoing the regeneration step. The Knudsen diffusivities are independent of the total pressure, while the molecular diffusivity is approximately inversely proportional and the intraparticle viscous flow directly proportional to it. Increasing the production pressure in the molecular diffusion regime will decrease the adsorbent separation ability, once the intraparticle viscous flow contribution will increase and the diffusive contribution will decrease.

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Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000

Table 9. Influence of the Equalization Step on the Average Product Purity and Recovery case

θequal./R*

average product purity (%)

recovery (%)

4.1 4.2 4.3 4.4

0 0.011/0.25 0.028/0.25 0.011/0.10

96.0 98.5 99.0 98.5

6.3 7.3 8.1 8.4

The equilibrium selectivity decreases when the total pressure increases, for nonlinear favorable isotherms. The PSA performance increases as the isotherms approach linearity.27-29 The higher the production pressure, the lower is the fraction of product flow rate used to purge the column undergoing the regeneration step, increasing the PSA performance. The optimum production pressure is a complex compromise among all of these different effects. Equalization Step. Four simulations were performed to study the equalization step effect on the product purity and recovery. The parameters considered in these simulations are the same as those in case 2, / and the operating conditions are Pproduction ) 4.2, θcycle / ) 6.55, θpress ) 1.46, and upurge ) -3.87. The equalization step is controlled by the equalization step duration and by the flow resistance of the connecting pipe. The four cases considered are as follows: (1) case 4.1, no equalization step θequal ) 0; (2) case 4.2, dimensionless equalization time θequal ) 0.11 and resistance R* ) 0.25; (3) case 4.3, dimensionless equalization time θequal ) 0.18 and resistance R* ) 0.25; (4) case 4.4, dimensionless equalization time θequal ) 0.11 and resistance R* ) 0.10. We selected two equalization times: case 4.2, where the system attains 50% of the maximum equalization pressure, and case 4.3, where it attains 80% of the maximum equalization pressure. Case 4.4 has the same equalization time as case 4.2, but the equalization rate is higher, allowing also for 80% of the maximum equalization pressure to be reached. The simulation results are summarized in Table 9. These results confirm that the equalization step always increases product purity and recovery. Case 4.3 attained a higher purity than case 4.2, because the equalization step is longer. The product purity of case 4.4 is smaller than that of case 4.3, because equalization is faster, but its recovery is higher, once less product is vented out during the blowdown step. We also report an experimental run, experiments 24.2, using the same operating conditions as those for experiment 22.1 but including an equalization step of 2 s. The experimental and simulated product purity and recovery proved to be very close to each other, as can be see from Tables 4 and 5. Experiment 24.2 performs better than experiment 22.1. The equalization step was introduced to increase product purity and recovery and to conserve the compression energy of the traditional PSA Skarstrom cycle. The equalization step can be made longer or shorter, and the equalization flow rate can be controlled by a needle valve. While the gas leaving the equalization/ depressurization column is richer than the feed in the product component, the equalization step is advantageous for purity, recovery, and energy conservation. These effects should be balanced with the productivity requirements as the equalization step is a nonproductive step and so it should be made as short as possible.

Conclusions The pressure rising rate during the pressurization step and pressure lowering rate during the blowdown step, the production pressure, and the intraparticle viscous flow effects on product purity and recovery of an equilibrium-based PSA for bicomponent separation using the traditional Skarstrom cycle were studied. Experimental results were obtained for oxygen separation from air, using a 5A zeolite. The PSA model is based on the LDF-DG intraparticle mass transport model presented by Mendes et al.6 It was concluded that higher pressure rising rates, during the pressurization step, increase dispersion in the PSA columns conducting to lower product purity and recovery. On the other way around, any difference in the product purity or recovery was not observed when the pressure blowing down time was decreased to 4 s. For negligible axial pressure drop, the interparticle viscous flow is due to pressure gradients during the nonisobaric steps and/or to adsorption. The intraparticle viscous flow is a nonselective transport mechanism, and in these circumstances, it contributes to a product purity decrease. The production pressure has a complex effect on the product purity and recovery: it affects the mass transport mechanism, the adsorption selectivity, the pressure rising/lowering rates during the pressurization/ blowdown steps, and the fraction of the product stream of one column used to purge the other column. For the operating conditions considered, it was concluded that there is a production pressure that optimizes the product purity and recovery. The traditional PSA Skarstrom cycle performance can be improved by adding an equalization step. This step was also modeled, and few experimental runs were done. The model fits the experimental results quite well. We observed that the introduction of an equalization step improves product purity and recovery. Although these effects should be balanced against productivity losses, this should hold as far as the gas leaving the blowdown column is richer than the feed in the light component. Nomenclature B0 ) adsorbent permeability (m2) Be0 ) adsorbent effective permeability (m2) Di ) i solute Knudsen diffusivity (m2/s) Dei ) i solute Knudsen effective diffusivity (m2/s) Dij ) molecular diffusivity (m2/s) Deij ) effective molecular diffusivity (m2/s) Dax ) axial dispersion (m2/s) kLi ) i solute Langmuir constant (Pa-1) L ) column length (m) pi ) i solute interparticle partial pressure (Pa) p j si ) i solute intraparticle volume-averaged partial pressure (Pa) P ) interparticle total pressure (Pa) Pref ) reference pressure (Pa) Pe ) Peclet number qref ) reference concentration for normalization (mol/kg) q j i ) i solute particle averaged adsorbed concentration (mol/ kg) Qi ) i solute Langmuir isotherm constant (mol/kg) r0 ) particle radius (m) R* ) pipe dimensionless mass transport parameter, eq 5 (kg/m2/s) Rbp ) ratio between bed and particle time constants

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 145 Rgk ) ratio between component B molecular and Knudsen diffusion time constants Rbµ ) ratio between component B molecular diffusion and intraparticle viscous flow time constants Rkk ) ratio between components A and B Knudsen diffusion time constants k RQ i , Ri ) dimensionless parameters for the bicomponent Langmuir isotherm R ) perfect gas constant (Pa‚m3/mol/K) t ) time (s) T ) absolute temperature (K) u ) interstitial velocity (m/s) upurge ) inlet interstitial velocity during the purge step (m/ s) uref ) reference interstitial velocity (interstitial velocity at the column’s outlet during the production step)(m/s) yi ) product i solute mole fraction (m) z ) axial coordinate (m) Greek Letters R ) parameter  ) bed porosity p ) adsorbent porosity φi ) LDF-DG model parameter, normalized phase lag µM ) average viscosity (kg/m/s) θ ) dimensionless time θcycle ) dimensionless cycle time θpress ) dimensionless pressurization step time θprod ) dimensionless production step time F ) particle density (kg/m3) τb ) bed time constant (s) τg ) molecular diffusion time constant (s) τki ) i solute Knudsen diffusion time constant (s) τp ) particle time constant (s) τt ) tortuosity τµ ) intraparticle viscous flow time constant (s) Ω h i ) LDF-DG model parameter related to the diffusion mass transport ψ h i ) LDF-DG model parameter related to intraparticle viscous flow Superscript * ) dimensionless variable

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Received for review May 24, 1999 Revised manuscript received September 28, 1999 Accepted October 6, 1999 IE990355V