Ind. Eng. Chem. Res. 1997, 36, 3769-3777
3769
Fixed-Bed Adsorption of n-Pentane/Isopentane Mixtures in Pellets of 5A Zeolite Jose´ A. C. Silva and Alirio E. Rodrigues* Laboratory of Separation and Reaction Engineering, Faculty of Engineering, University of Oporto, 4099 Porto Codex, Porto, Portugal
Breakthrough curves were measured in fixed-bed adsorbers containing pellets of 5A zeolite (Rhoˆne-Poulenc) with feed mixtures of n-pentane, isopentane, and nitrogen. The experiments covered a temperature range of 448-548 K and partial pressure of n-pentane up to 0.2 bar in a nonisothermal, nonadiabatic system. The effects of the partial pressure of the sorbate, temperature, and total flow rate of the mixture on the behavior of the system are studied. Fixedbed desorption with inert gas is also addressed. Experimental data clearly show that the shapes of the breakthrough and desorption curves are practically influenced by the adsorption equilibrium isotherm of n-pentane and the heat effects in the system. A mathematical model was developed to simulate the experimental data. Model parameters were estimated from independent experiments (adsorption equilibrium isotherm and diffusivity) and from correlations available in the literature (axial mass and heat dispersion and film mass transfer). Good agreement was found between the model predictions and experiments. The model developed is now being used for the design of cyclic VSA/PSA separation processes. Introduction The isomerization of n-paraffins to high-octanenumber branched isomers (Asselin, 1973) is a method of upgrading naphtha to improve their utility as motor fuel components. For example, the unleaded research octane number (RON) for isopentane is 93 compared with 62 for n-pentane. In the isomerization of nparaffins to isoparaffins, it is necessary to recycle the unreacted n-paraffins to the reactor. The separation of n-paraffins/isoparaffins can be done by using molecular sieves such as 5A zeolite exchanged with calcium, zeolites R or T, or the natural zeolites chabazite or erionite (Benazzi et al., 1993). A well known isomerization process using molecular sieves for the vapor phase separation of unreacted n-paraffins is the total isomerization process (TIP) (e.g., Holcombe, 1980). A recent improvement to the process is shown by Holcombe et al. (1990) and Minkkinen et al. (1993). The adsorption unit can be operated either in the liquid phase as the MOLEX process (UOP) or in the vapor phase as the IsoSiv process (UOP). A comparison of the two technologies is presented by Raghuram and Wilcher (1991a,b). The extensive research work in adsorption allows us to consider several processes to perform the n-paraffins/ isoparaffins separation in a scientific basis. Industrial processes include pressure swing adsorption (PSA) (e.g., IPSORB of IFP), temperature swing adsorption (TSA), simulated moving bed (SMB) (e.g., MOLEX of UOP using liquid phase operation), or purge stripping and displacement processes (e.g., IsoSiv of UOP). Recently, a study of SMB in the vapor phase was performed by Mazzoti et al. (1996). Reviews on selective adsorption processes can be found in Rosset et al. (1981) and Jacob (1983). The objective of this research work is to study the effect of operating variables (temperature, flow rate, n-pentane partial pressure) on breakthrough and de* To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: 351-2-2041671. Fax: 351-22041674. S0888-5885(97)00158-9 CCC: $14.00
sorption curves measured in an adsorption unit packed with commercial adsorbents of 5A zeolite and using feed mixtures containing n-pentane, isopentane, and nitrogen. A mathematical model of the unit is developed and tested. Adsorption equilibrium isotherms for n-pentane (Silva and Rodrigues, 1997) and n-hexane (Silva and Rodrigues, 1997b) were measured in independent experiments. Diffusivity measurements indicated that macropore diffusion is the controlling diffusion mechanism in the adsorbent. The information obtained in fixed-bed adsorption studies is to be used in the design of an experimental setup to study cyclic processes for n-paraffins/isoparaffins separation. Mathematical Model The adsorption system considered is a nonisothermal, nonadiabatic column packed with pellets of 5A zeolite through which an inert gas flows in the steady state. At time zero, a mixture of n-paraffins/isoparaffins of known composition and an inert is introduced at the bottom of the column. The mixture is fed until the column is saturated; then contercurrent or cocurrent purge of the column with inert is carried out. The following additional assumptions are made: (1) the gas is ideal. (2) the total pressure is constant during the sorption process. (3) the flow pattern is described by the axial dispersed plug flow model. (4) the main resistances to mass transfer are external fluid film resistance and macropore diffusion in series as pointed out by Silva and Rodrigues (1997a). External resistance and macropore diffusion can be combined in a global resistance according to a lumped model for the adsorbent particle as suggested by Morbidelli et al. (1982). (5) A resistance to heat transfer exists in the external fluid film around the solid. (6) The temperature dependence of the gas and solid properties is neglected. (7) The adsorption equilibrium is described by Nitta et al.’s isotherm (1984) according to the data of Silva and Rodrigues (1997a). © 1997 American Chemical Society
3770 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
The model equations are as follows. Mass Balance to Sorbate Species. The equation
Energy Balance. (a) Gas Phase. The energy balance for the gas phase is
is
bDL
( )
∂〈qa〉 ∂ ∂ ∂ya ∂ F ) (Fya) + b (Fya) + (1 - b)Fs ∂z ∂z ∂z ∂t ∂t (1)
where ya is the mole fraction of sorbate in the bulk gas phase, F is the total concentration, F is the total molar flux, 〈qa〉 is the average adsorbed concentration, Fs is the apparent adsorbent density, z and t are the axial coordinate and time, respectively, DL is the axial dispersion coefficient, and b is the bed porosity. The boundary conditions are
z ) 0, t > 0
∂ya bDLF ) Fya - Ffyaf ∂z
z ) L, t > 0
∂ya )0 ∂z
∂〈qa〉 ) apKglF(ya - 〈ya〉) ∂t
∂T ) Cpg(FT - FfTf) ∂z
(5a)
∂T )0 ∂z
(5b)
(1b)
(2)
(2a)
Mass-Transfer Rate. Since the accumulation of mass in the gas phase can be neglected relative to the solid phase, the following equation is valid in a lumped particle system controlled by macropore diffusion (Morbidelli et al., 1982),
Fs
KL
z ) L, t > 0
The boundary condition is
F ) Ff
where KL is the effective heat axial dispersion coefficient, T, Ts, and Tw are temperatures in the bulk gas, solid phase, and at the wall, respectively, hp is the film heat-transfer coefficient, hw is the wall heat-transfer coefficient, Cpg is the heat capacity of the fluid phase, and ac ) 2/Rc is the specific area of the column (Rc is the internal column radius). The boundary conditions are
(1a)
Overall Mass Balance. The overall mass balance
z ) 0, t > 0
∂2T ∂T ∂T + bFgCpg + ) fCpg 2 ∂z ∂t ∂z (1 - b)aphp(T - Ts) + achw(T - Tw) (5)
z ) 0, t > 0
is
∂〈qa〉 ∂F ∂F + b + (1 - b)Fs )0 ∂z ∂t ∂t
KL
(3)
The temperature profile inside the furnace is parabolic, so Tw ) Tw(z). (b) Solid Phase. The energy balance for the solid phase is
FsCps
∂Ts ∂〈qa〉 ) aphp(T - Ts) + (-∆Hads)Fs ∂t ∂t
(6)
where Cps is the heat capacity of the adsorbent. Initial Conditions. The equations for adsorption are
ya ) 〈ya〉 ) 〈qa〉 ) 0
t ) 0, ∀z
t)0
F ) Ff F ) Ff (7a)
T ) Ts ) Tw ) Tw(z)
(7b)
The equations for desorption are
t ) 0, ∀z
ya ) 〈ya〉 ) yaf
F ) Ff
F ) Ff (7c)
where 〈ya〉 is the average mole fraction of sorbate in the macropores, ap is the specific area of the particle, and Kgl is the overall mass transfer coefficient which is defined by
t)0 t)0
〈qa〉 ) qa(yaf, Ts ) Ts(z))
T ) T(z)
Ts ) Ts(z)
(7d)
Tw ) Tw(z) (7e)
1 1 1 ) + Kgl ke pki
(3a)
where ke is the external film mass transfer coefficient, ki is the internal mass-transfer coefficient (Glueckauf, 1955), and p is the intraparticle porosity. Adsorption Equilibrium Isotherm. Neglecting the interaction term between adsorbed molecules, Nitta et al.’s isotherm (1984) is
yaP0 )
θa 1 Kads (1 - θ )n a
(4)
where θa ) qa/qmax is the coverage of the adsorbent, qa is the adsorbed-phase concentration, qmax is the maximum adsorbed concentration, and Kads ) k0 × exp((-∆Hads)/RTs) is the equilibrium constant, where -∆Hads is the heat of adsorption, R is the ideal gas constant, and Ts is the solid temperature.
Dimensionless model equations are shown in the Appendix. Numerical Solution of the Model Equations. The set of coupled partial differential equations shown in the Appendix was reduced first to a set of ordinary differential/algebraic equations (DAEs) applying the orthogonal collocation technique (Villadsen and Michelsen, 1978) to the spatial coordinate. The collocation points were given by the zeros of Jacobi polynomials PN(R,β)(x), with R ) β ) 0. The resulting system was solved using a fifth-order Runge-Kutta code (ODE’s) in conjunction with a Gauss elimination (Algebraic equations). Sixteen collocation points appeared to give satisfactory accuracy for all calculations performed. Determination of Model Parameters Involved in the Adsorber Model The adsorbent is extrudate 5A zeolite (Rhoˆne-Poulenc) with the characteristics shown in Table 1.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3771
(1978),
Sh ) 2.0 + 1.1Re0.6Sc0.33
(10)
where Sh is the Sherwood number. Only two parameters need to be estimated: the heattransfer coefficient between solid and bulk fluid and the heat-transfer coefficient between the system and the surroundings. These parameters were obtained by matching the experimental curves. Parameter values of the model and experimental conditions are summarized in Table 2. Experimental Section Figure 1. Adsorption equilibrium isotherms of n-pentane in pellets of zeolite 5A. Points are experimental results of Silva and Rodrigues (1997a,b). Calculated isotherms of Nitta et al.’s model (s) are also shown. Table 1. Column Characteristics, Adsorbent Properties, and Parameters of Model Isotherm Column Characteristics length, cm 20 internal diameter, cm 3.35 Adsorbent Properties Fb, g/cm3 Fs, g/cm3 b p dp, mm length, mm
0.77 1.13 0.32 0.35 1.6 6
Adsorption Equilibrium Isotherm Parameters -∆Hads, kcal/mol 13.2 n 5 qmax, g/100 g 13.0 k0, atm-1 2.04 × 10-5
The study of adsorption and diffusion of n-pentane in 5A zeolite pellets used in this work was performed by Silva and Rodrigues (1997a). Table 1 shows the adsorption equilibrium parameters of Nitta et al.’s isotherm; Figure 1 shows the adsorption isotherms. The axial mass dispersion coefficient (DL) was estimated from the correlation of Hsu and Haynes (1981),
0.328 3.33 1 ) + Pe ReSc 1 + 0.59(ReSc)-1
(8)
where Pe is the particle Peclet number, Re is the Reynolds number, and Sc is the Schmidt number. The above correlation was obtained from experiments in the range 0.08 < ReSc < 1, similar to that found in our work. The Reynolds number in our system ranged from 0.6 to 1. The effective axial bed thermal conductivity (KL) was estimated according to the suggestions of Wakao (1975). Mass transfer inside the adsorbent was controlled by macropore diffusion as reported by Silva and Rodrigues (1997a). The intraparticle mass-transfer coefficient (ki) can be calculated according to a lumped model proposed by Glueckauf (1955),
5Dp ki ) Rp
(9)
where Dp is the pore diffusivity and Rp is the particle radius. The external mass-transfer coefficients (ke) were estimated with the correlation of Wakao and Funazkri
The experimental setup is shown in Figure 2. It has three major sections: preparation of gases, adsorption column in a furnace, and analysis of gases. A description of the experimental setup follows: With two Teledyne-Hastings (Hampton, VA) mass flow controllers, nitrogen is bubbled in two Scott saturators containing isopentane and n-pentane, respectively, in a controlled Techne (Cambridge, U.K.) thermostated bath. The mixture produced is analyzed before entering the adsorber with a Carlo Erba (Milan, Italy) chromatograph equipped with a FID detector. This also allows the calibration of the signal that will be measured after the mixture passes the adsorber unit. The column is in stainless steel with a diameter of 3.35 cm and is 20 cm long. It is placed inside a Termolab (Agueda, Portugal) radiant oven equipped with a Shimaden (Tokyo, Japan) PID temperature controller. Two Omega Type K thermocouples were inserted axially in the column, one near the middle of the column and the other at the top. Data acquisition from thermocouples and FID was performed by a Data Translation (Marlboro, MA) interface attached to a IBM PS/2 computer; a computer program allowed the monitoring of signals during all the operation of the adsorber unit. Before the first run, the column was activated by purging with nitrogen during 24 h from ambient temperature to 633 K. The experiment starts by passing inert in the column upflow with a flow rate similar to the one used in adsorption. At the same time, the mixture of n-paraffins/isoparaffins was produced in the wash bottles and analyzed in the chromatograph. Once the temperature in the column was constant, the inert was replaced by the mixture through the switching of valves. The effluent of the column was sent to the chromatograph and continuously analyzed. Since isopentane does not adsorb in zeolite 5A, an increase of signal in the computer was detected practically at the space time. This signal is constant until breakthrough of n-pentane occurs. Desorption was performed in a similar manner by switching of valves that allow cocurrent or countercurrent purge with inert. Results and Discussion Experimental adsorption runs were performed in order to study the influence of temperature, adsorbate partial pressure, and flow rate on the performance of the adsorption unit. At the same time, validation of the model is tested relative to the experiments made. Effects of Temperature. Figure 3 shows the effect of temperature in adsorption breakthrough curves for bed inlet temperatures of 548, 498, and 448 K. The total
3772 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 2. Experimental Conditions and Model Parameters experimental conditions run
fig
11 12 13 21 22 31 33 41 51
3a 3b 3c 4a, 5c 4b, 6b 5b 5a 6a, 7a, 8 7b
F, mol/(m2 s) Tf, K 0.15 0.15 0.15 0.11 0.11 0.11 0.10 0.10 0.14
548 498 448 548 498 548 548 498 498
yaf 0.19 0.17 0.18 0.04 0.05 0.09 0.19 0.09 0.11
model parameters
yiC5 P0, bar 105DL, m2/s KL, W/(m K) 102ki, m/s 102ke, m/s 102Kgl, m/s hp, W/(m2 K) hw, W/(m2 K) 0.33 0.33 0.31 0.45 0.49 0.44 0.29 0.40 0.40
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
9.1 9.0 8.4 6.9 6.4 7.1 6.5 5.8 8.6
0.35 0.35 0.35 0.34 0.34 0.34 0.34 0.33 0.35
4.4 3.9 3.4 4.4 3.9 4.3 4.3 3.9 3.9
3.5 3.1 2.8 3.4 3.0 3.4 3.3 2.9 3.1
1.06 0.95 0.83 1.05 0.94 1.05 1.03 0.93 0.95
9.2 7.8 6.7 8.7 7.5 8.9 8.6 7.3 7.8
15 15 14 14 14 14 14 14 14
Figure 2. Experimental setup used for breakthrough experiments. c, computer with data-acquisition board; Cr, chromatograph; f, furnace; fb, fixed bed; FID, detector of gas chromatograph; fm, flowmeters; fmc, flowmeter unit control; m, pressure manometer; p, PID control of furnace; t, thermocouples; tb, thermostated bath; wb, wash bottles; 1-9, on-off valves; 10-12, needle valves.
flow rate (190 mL/min at 298 K), partial pressure of n-pentane (yaf ) 0.19), and total pressure (P0 ) 1 bar) were kept constant during the experiments. The time evolution of the bed temperature profile during the sorption process at two locations, x ≈ 0.6 and column outlet, is also shown. Here we should note that a symmetric parabolic profile (relative to x ) 0.5) inside the oven was found at the beginning of the experiments. The existence of a parabolic profile inside the column apparently does not affect the sharp nature of breakthrough curves, which is expected since the isotherm of n-pentane is highly favorable at the partial pressure studied and the global mass transfer coefficient is quite high (apKgl ) 30 s-1 at 548 K to apKgl ) 24 s-1 at 448 K). The adsorbed concentration increases when the temperature decreases as a consequence of a high heat of adsorption of n-pentane of 13.2 kcal/mol predicted by Nitta et al.’s isotherm. As the temperature decreases, more heat is generated during sorption as we can see from the evolution of temperature at the two locations selected; temperature at x ≈ 0.6 increases near 7 K at 548 K and 20 K at 448 K. The final approach of the breakthrough curve to the equilibrium value is slow as a consequence of the temperature increase owed to adsorption; only when temperature reaches its equilibrium value does the breakthrough curve reach the feed composition. Nevertheless, the equilibrium theory for
Figure 3. Effect of temperature on experimental breakthrough curves of n-pentane (O), temperature histories at bed exit (0), and temperature profiles 12 cm from bed inlet (4) for adsorption of a mixture of n-pentane/isopentane/N2 in pellets of zeolite 5A. (a, top) Tf ) 548 K, yaf ) 0.19, Q ) 190 mL/min (at 298 K), P0 ) 1 atm. (b, middle) Tf ) 498 K, yaf ) 0.17, Q ) 197 mL/min (at 298 K), P0 ) 1 atm. (c, bottom) Tf ) 448 K, yaf ) 0.18, Q ) 200 mL/min (at 298 K), P0 ) 1 atm. Lines are numerical solutions of the dynamic model with parameters given in Table 3.
adiabatic processes (Pan and Basmadjian, 1970) could not be tested since our column is nonisothermal and nonadiabatic. It is clearly seen from Figure 3 that both thermal and concentration waves appear at the end of the column at the same time. This is expected since the parameter ξm/ξh (which measures the relative velocity of the thermal and concentration waves in an
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3773
Figure 4. Effect of temperature on experimental breakthrough curves of n-pentane (O), temperature histories at bed exit (0), and 12 cm from bed inlet (4) for adsorption of a mixture of n-pentane/ isopentane/N2 in pellets of zeolite 5A. (a, top) Tf ) 548 K, yaf ) 0.04, Q ) 141 mL/min (at 298 K), P0 ) 1 atm. (b, bottom) Tf ) 498 K, yaf ) 0.05, Q ) 144 mL/min (at 298 K), P0 ) 1 atm. The lines are theoretical curves calculated according to the numerical solution of the dynamic model with parameters given in Table 3.
adiabatic system with a favorable isotherm) is lower than 1 at least in the experimental conditions used. The values of ξm/ξh in this system are reported in Table 3. In Figure 4, a similar analysis of the temperature effect is performed except that a small partial pressure (yaf ) 0.05) of n-pentane is used. The breakthrough curves are less abrupt than in the previous case, which confirms that the shape of the isotherm is relevant in the system under study. Also, temperature changes in the column are less important since lower adsorption occurs. Model predictions are in close agreement with experimental results as shown in Figures 3 and 4. The values of the parameters concerning heat transfer at the wall and from the solid to the bulk fluid are determined in order to match the experimental curves, which range from 13 to 15 W/(m2 K) and from 6.7 to 9.2 W/(m2 K), respectively. Effect of Partial Pressure of n-Pentane in the Feed. The effect of n-pentane partial pressure in the feed at Tf ) 548 K and constant feed flow rate is shown in Figure 5 for partial pressures of yaf ) 0.19, yaf ) 0.09, and yaf ) 0.04. The adsorbent capacity decreases at lower n-C5 partial pressure; breakthrough curves are sharper when the partial pressure of n-C5 increases. The stoichiometric time decreases when n-C5 partial pressure increases as a consequence of the favorable nature of the adsorption equilibrium isotherm. In fact, a simple global mass balance over the adsorption column leads to tst ) (L/vi)(1 + ξm). Sharper profiles with increasing partial pressures are observed and are a consequence of the favorable isotherms which have their origins in compressive waves according to the equilibrium theory. However, this effect is less pronounced as the partial
Figure 5. Effect of partial pressure of n-pentane on experimental breakthrough curves of n-pentane (O), temperature histories at bed exit (0), and 12 cm from bed inlet (4) for adsorption of a mixture of n-pentane/isopentane/N2 in pellets of zeolite 5A. (a, top) Tf ) 548 K, yaf ) 0.19, Q ) 130 mL/min (at 298 K), P0 ) 1 atm. (b, middle) Tf ) 548 K, yaf ) 0.09, Q ) 141 mL/min (at 298 K), P0 ) 1 atm. (c, bottom) Tf ) 548 K, yaf ) 0.04, Q ) 141 mL/min (at 298 K), P0 ) 1 atm. The lines are theoretical curves calculated according to the numerical solution of the dynamic model with parameters given in Table 3.
pressure increases since the isotherm becomes more favorable. A sharper breakthrough curve is also the consequence of velocity changes due to adsorption as pointed out by Yang (1987). The same information is retained from the temperature data: higher partial pressures lead to higher and narrow peaks; in contrast, lower partial pressures originate from smaller and wider peaks. Figure 6 shows the same effect at Tf ) 498 K for a constant feed flow rate and for partial pressures of yaf ) 0.095 and yaf ) 0.056. For a similar partial pressure, the breakthrough curves are sharper than in the case of Tf ) 548 K since the isotherm is more favorable at 498 K. Model results are also shown in Figures 5 and 6, predicting with good accuracy the observed adsorber behavior. Effect of Total Flow Rate. Figure 7 shows the influence of the total flow rate on breakthrough curves
3774 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 6. Effect of partial pressure of n-pentane on experimental breakthrough curves of n-pentane (O), temperature histories at bed exit (0), and 12 cm from bed inlet (4) for adsorption of a mixture of n-pentane/isopentane/N2 in pellets of zeolite 5A. (a, top) Tf ) 498 K, yaf ) 0.09, Q ) 127 mL/min (at 298 K), P0 ) 1 atm. (b, bottom) Tf ) 498 K, yaf ) 0.05, Q ) 144 mL/min (at 298 K), P0 ) 1 atm. The lines are theoretical curves calculated according to the numerical solution of the dynamic model with parameters given in Table 3.
at 548 K. The total flow rate practically does not affect the shapes of the breakthrough curves, which is an indication that the axial and heat mass dispersion coefficients are not limiting mechanisms in the system. This analysis can be clearly seen if we normalize the real time by the respective stoichiometric time; similar breakthrough curves are then obtained. Clearly, breakthrough curves occur faster at higher flow rates, as indicated by the relation tst ) (L/vi)(1 + ξm); the proportionality between the breakthrough time and flow rate indicates that constant pattern conditions are valid. Again, model predictions are in good agreement with experimental data relative to concentration and temperature evolution. Effect of Purge Flow Rate in Desorption Curves. Figure 8 shows the effect of purge flow rate in the desorption of a bed saturated with n-pentane at a partial pressure of 0.1 bar at 498 K. In the figure, we also show the adsorption curve that was previously performed with a total flow rate of 130 mL/min. If desorption were performed with a flow of inert similar to the total flow rate used in the adsorption, the wash out of column practically doubles the time of adsorption. To reach a cycle time of the same order, one has to double the purge flow rate, as could be clearly seen in Figure 8. This is expected for a system with a favorable isotherm since in desorption, concentration waves are dispersive. In Figure 8, we show the comparison of heat effects at the middle of the column in adsorption and desorption. It is clear that heat effects are rather small in desorption compared to the ones in adsorption due to the dispersive effect caused by the unfavorable nature of the isotherm in desorption.
Figure 7. Effect of flow rate on experimental breakthrough curves of n-pentane (O), temperature histories at bed exit (0), and 12 cm from bed inlet (4) for adsorption of a mixture of n-pentane/ isopentane/N2 in pellets of zeolite 5A. (a, top) Tf ) 498 K, yaf ) 0.09, Q ) 127 mL/min (at 298 K), P0 ) 1 atm. (b, bottom) Tf ) 498 K, yaf ) 0.11, Q ) 185 mL/min (at 298 K), P0 ) 1 atm. The lines are theoretical curves calculated according to the numerical solution of the dynamic model with parameters given in Table 3.
Figure 8. Effect of flow rate on desorption with nitrogen of a bed saturated with n-pentane (yaf ) 0.1) at Tf ) 498.15 K, P0 ) 1 atm, and Q ) 130 mL/min (at 298 K). (]) Desorption curve with Q ) 275 mL/min (at 298 K); (0) desorption curve with Q ) 130 mL/ min (at 298 K). The adsorption breakthrough curves with Q ) 130 mL/min (at 298 K) (O) are also shown. Temperature profiles 12 cm (adsorption) and 8 cm (desorption) from the bed inlet are also shown. The lines are theoretical curves calculated according to the numerical solution of the dynamic model with parameters given in Table 3.
Conclusions The mathematical model developed represents well the behavior of the laboratory adsorption unit for n-pentane/isopentane separation using zeolite 5A. The effects of temperature, partial pressure of sorbate, and total flow rate in breakthrough curves were experimentally analyzed and compared with model predictions.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3775
Both approaches are instructive with regard to the influence of the nature of the isotherm in the dynamic behaviour of fixed-bed adsorbers. This model is currently in use for the description of cyclic processes in order to design a small laboratory pilot plant and for the prediction of the behavior of a multicomponent system involving a n-C5/n-C6 mixture. Acknowledgment J. A. C. Silva acknowledges financial support from Junta Nacional de Investigac¸ a˜o Cientifica e Tecnolo´gica (Research Fellowship Praxis XXI/BD/3148/94). Nomenclature ap ) specific area of the pellet (m-1) ac ) specific area of the column (m-1) B ) adiabatic temperature rise ()-∆Hadsqaf/CpsTf) Cpg ) heat capacity of the gas (J/(mol‚K)) Cps ) Heat capacity of the solid (J/(kg‚K)) dp ) pellet diameter (m) DL ) axial mass dispersion coefficient (m2/s) Dm ) molecular diffusivity (m2/s) Dp ) pore diffusivity (m2/s) F ) total molar flux (mol/(m2‚s)) Ff ) total molar flux of feed (mol/(m2‚s)) F ˜ ) dimensionless molar flux ()F/Ff) ∆Hads ) isosteric heat of adsorption (J/mol) hp ) film heat-transfer coefficient (W/(m2‚K)) hw ) wall heat-transfer coefficient at the wall (W/(m2‚K)) Kgl ) global mass-transfer coefficient (m/s) ki ) internal mass-transfer coefficient (m/s) ke ) external mass-transfer coefficient (m/s) Kads ) adsorption equilibrium constant (bar-1) Kads(Tf) ) adsorption equilibrium constant at Tf (bar-1) KL ) effective axial bed thermal conductivity (W/(m‚K)) L ) length of column (m) n ) coefficient of model isotherm Nhf ) number of film mass-transfer units ()(1 - b)apLhp/ bvifFfCpg) Nhw ) number of wall heat-transfer units ()acLhw/bvifFfCpg) Nf ) number of film mass-transfer units ()(1 - b)apLKgl/ bvif) P0 ) total pressure of column (bar) Pe ) particle Peclet number ()vidp/DL) Pemf ) mass Peclet number at feed conditions ()vifL/DL) Pehf ) heat Peclet number at feed conditions ()FfCpgvifL/ KL) 〈qa〉 ) average adsorbed-phase concentration (mol/kg) qaf ) sorbed phase concentration at equilibrium with yaf (mol/kg) qmax ) maximum adsorbed-phase concentration (mol/kg) q˜ a ) dimensionless sorbed-phase concentration ()qaf/qmax) Q ) volumetric flow rate (m3/s) R ) ideal gas law constant (J/(mol‚K)) Rc ) internal radius of the column (m) Re ) Reynolds number ()Fvdp/µ) Rp ) Pellet radius (m) Sc ) schmidt number ()µ/FgDm) Sh ) Sherwood number ()kedp/Dm) t ) time (s) tst ) stoichiometric time (s) T ) temperature in the bulk gas phase (K)
Ts ) temperature in the solid phase (K) T ˜ ) dimensionless temperature in the bulk gas phase ()(T - Tf)/Tf) T ˜ s ) dimensionless temperature in the solid ()(Ts - Tf)/ Tf) Tf ) feed gas temperature (K) Tw ) temperature at the column wall (K) T ˜ w ) dimensionless temperature at the column wall ()(Tw - Tf)/Tf) v ) superficial velocity (m/s) vi ) interstitial velocity (m/s) vif ) interstitial velocity at feed conditions (m/s) x ) dimensionless axial coordinate in the bed ()z/L) ya ) mole fraction of the sorbate in the bulk phase yaf ) mole fraction of the sorbate at the inlet of the column yiC5 ) mole fraction of isopentane at the inlet of the column 〈ya〉 ) average mole fraction of sorbate in the pores of the pellet z ) axial coordinate in the bed (m) Greek Letters ξh ) heat capacity factor ()(1 - b)FsCps/bFfCpg) ξm ) mass capacity factor ()(1 - b)Fsqaf/byafFf) b ) bed porosity p ) solid porosity F ) total gas concentration (mol/m3) Ff ) total gas concentration of the feed (mol/m3) y˜ ) dimensionless total gas concentration ()F/Ff) Fb ) bulk density (kg/m3) Fs ) apparent density of the pellet (kg/m3) θa ) coverage of adsorbent θaf ) coverage of adsorbent at yaf ()qaf/qmax) τ ) dimensionless time ()vift/L) µ ) gas viscosity (kg/(m‚s)) γf ) Arrhenius number ()(-∆Hads)/RTf)
Appendix Dimensionless Model Equations. Introducing dimensionless variables for space x ) z/L, time τ ) tvif/L, molar flux F ˜ ) F/Ff, adsorbed-phase concentration q˜ a ) 〈qa〉/qaf, total concentration y˜ ) F/Ff, and fluid, solid, and wall temperatures T ˜ ) (T - Tf)/Tf, T ˜ s ) (Ts - Tf)/ Tf, T ˜ w ) (Tw - Tf)/Tf, respectively, dimensionless model equations become as follows
overall mass balance ∂q˜ a ∂F˜ ∂F ˜ + yafξm + )0 ∂x ∂τ ∂τ
(A1)
where yaf is the mole fraction of sorbate in the feed gas phase and ξm is the mass capacity factor
boundary conditions x ) 0, τ > 0;
F ˜ )1
(A1a)
sorbate mass balance 2 ∂q˜ a ˜ ya) ∂(F˜ ya) F˜ ∂ ya ∂(F + + yafξm ) 2 Pemf ∂x ∂x ∂τ ∂τ
(A2)
3776 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
where Pemf is the mass Peclet number
Model parameters are defined as follows:
mass Peclet number
boundary conditions 1 ∂ya 1 ) (F ˜ ya - yaf) Pemf ∂x F˜
x ) 0, τ > 0
(A2b) Pehf )
mass-transfer rate yafξm
∂q˜ a ) NfF(ya - 〈ya〉) ∂τ
(A3)
FfCpgbvifL KL
mass capacity factor ξm )
where Nf is the number of film mass transfer units
1 - b Fsqaf b yafFf
heat capacity factor
adsorption equilibrium isotherm yaP0 )
vifL DL
heat Peclet number
∂xa )0 ∂z
x ) 1, τ > 0
Pemf )
(A2a)
θafq˜ a 1 Kads (1 - θ q˜ )n af a
ξh )
(A4)
1 - b FsCps b FfCpg
number of film mass-transfer units where θaf is the coverage of adsorbent at yaf and Kads(T ˜ s) ) Kads(Tf) exp(-γf(T ˜ s/(1 + T ˜ s))), where γf ) (-∆Hads)/ RTf) is the Arrhenius number
energy balance for the gas phase
Nf )
number of film heat-transfer units
∂T ˜ 1 ∂2T ∂T ˜ ˜ + F˜ + Nhf(T )F ˜ ˜ -T ˜ s) + Nhw(T ˜ -T ˜ w) Pehf ∂x2 ∂x ∂τ (A5)
Nhf )
Nhw )
˜ 1 ∂T )F ˜ (T ˜ + 1) - 1 Pehf ∂x
B)
(A5a) (A5b)
γf )
energy balance for the solid phase ∂T ˜s ∂q˜ a ) Nhf(T ˜ -T ˜ s) + ξhB ∂τ ∂τ
(A6)
θaf )
adsorption ya ) 〈ya〉 ) 0 τ ) 0;
Table 3. Dimensionless Model Parameters
F)1
F ) 1 (A7a)
T ˜ )T ˜s ) T ˜w ) T ˜ w(x)
(A7b)
desorption ya ) 〈ya〉 ) yaf
F ˜ )1
y˜ ) 1 (A7c)
τ)0
qaf qmax
Table 3 shows the dimensionless model parameters used in the numerical simulations of all the experiments performed.
initial conditions
τ)0
-∆Hads RTf
nonlinearity parameter of isotherm
where ξh is the heat capacity factor and B is the dimensionless adiabatic temperature rise
τ ) 0, ∀x
(-∆Hads)qaf CpsTf
Arrhenius number
∂T ˜ )0 ∂x
x ) 1, τ > 0
τ ) 0, ∀x
achwL bFfCpgvif
adiabatic temperature rise
boundary conditions
ξh
1 - b aphpL b FfCpgvif
number of wall heat-transfer units
where Pehf is the heat Peclet number, Nhf is the number of film heat transfer units, and Nhw is the number of wall heat-transfer units
x ) 0, τ > 0
1 - b apKglL b vif
˜ )T ˜ (x)) q˜ a ) q˜ a(yaf, T
T ˜ )T ˜ (x)
T ˜s ) T ˜ s(x)
(A7d)
T ˜w ) T ˜ w(x) (A7e)
run
fig
11 12 13 21 22 31 33 41 51
3a 3b 3c 4a, 5c 4b, 6b 5b 5a 6a, 7a, 8 7b
Pemf Pehf 44 44 44 44 44 44 44 44 44
3.0 3.0 2.8 2.3 2.4 2.5 2.1 2.1 2.9
Nf 655 596 565 839 803 821 821 879 620
Νhf Nhw ξm 221 192 175 283 234 266 302 269 196
21 21 22 27 25 25 28 29 21
ξh
θaf
γf
222 998 0.21 12.1 333 968 0.32 13.3 404 919 0.45 14.8 462 1040 0.09 12.1 672 906 0.21 13.3 329 982 0.15 12.1 221 1059 0.21 12.1 493 974 0.26 13.3 451 953 0.28 13.3
102B 3.7 6.1 9.8 1.6 4.0 2.6 3.6 5.0 5.3
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Received for review February 17, 1997 Revised manuscript received May 19, 1997 Accepted May 19, 1997X IE9701581
X Abstract published in Advance ACS Abstracts, August 1, 1997.
