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GENERAL RESEARCH Direct Measurement of Transient Concentration Profiles in Adsorbent Particles and Chromatographic Columns by MRI Nils-Karsten Ba1 r,† Bruce J. Balcom,† and Douglas M. Ruthven*,‡ MRI Centre, Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 Canada, and Department of Chemical Engineering, University of Maine, Orono, Maine 04469
Magnetic resonance imaging (MRI) was applied as an in situ imaging technique to study transient adsorption/desorption and chromatographic processes in microporous adsorbents. Transient concentration profiles were measured for several different types of systems: the diffusion of water vapor into a bed of 4A zeolite, the movement of pulses of light hydrocarbons through a chromatographic column of 5A or 13X zeolite, and the transient adsorption/desorption of propane or water vapor in a single extrudate of 13X zeolite. The profiles are approximately as predicted from nonlinear diffusion theory and the effect of isotherm nonlinearity on the form of the transient profiles is clearly apparent. The possibility of distinguishing between the concentration profiles in the gaseous and adsorbed phases by MRI methods is also examined. Introduction The adsorption and diffusion of reactants and products play an important and often dominant role in determining the kinetics of reactions catalyzed by porous solids. Chromatographic methods provide a simple and relatively straightforward approach to the measurement of adsorption kinetics and equilibria, and such techniques have therefore been widely applied to characterize both adsorption dynamics and catalytic kinetics in these systems. In a chromatographic experiment, information on the processes occurring within a packed adsorption column is deduced from measurements of the concentration response at the column outlet for a well-defined concentration perturbation at the column inlet. Although powerful, this approach necessarily provides information only on average properties; local effects such as might arise from coking or deactivation in a particular region obviously cannot be seen. More detailed information of this kind could, in principle, be obtained from direct measurement of the transient concentration profiles within the column, but that is more difficult in practice than simply monitoring the effluent concentration. A novel approach to the measurement of transient concentration profiles in adsorbent columns by “positron emission profiling” has recently been developed by Anderson and Noordhoek et al.1,2 However this approach is extremely costly as it requires a cyclotron for preparation of the radioactively labeled adsorbates. Magnetic resonance imaging (MRI) provides another obvious approach that has attracted some prior attention.3-6 In particular, it has been successfully applied to measure uptake rates in adsorbent beds6 and to study * Corresponding author. † University of New Brunswick. ‡ University of Maine.
flow patterns and measure axial dispersion in selected liquid chromatographic systems.7-10 However, in adsorption systems, the relaxation times are often too short to permit the application of traditional spin-echo imaging methods. This is particularly true when commercial adsorbents, which generally have a significant level of paramagnetic impurities, are used as, for such systems, the spin-spin relaxation time is generally very short ( 0, c ) co at z ) 0, c ) 0 at z ) z1
(2)
k(t) represents the (time-dependent) flux, and is the void fraction of the adsorbent bed. Because no adsorption occurs in this region [0 < Z < Z(t)], the gas-phase concentration profile must vary linearly, so
c ) 1 - z/z1 co
(3)
The progress of the wave front is therefore represented by
Dco z(t)
) (1 - )qs
dz1 dt
(4)
(
2 Dco z1 2 D cot t or Z(t) ) ) 1 - qs l 1 - l 2 qs
)
1/2
(5)
Evidently, the concentration wave propagates according to the parabolic law (z1 ∝ xt). Conformity of the experimental data with eq 5 is shown in Figure 5 in which the square of the penetration distance is plotted against the time. From the slope of this plot with the ratio (qs/co ) 48 500) estimated from the equilibrium isotherm and ≈ 0.5, we obtain D ) 0.055 cm2 s-1. This value can be compared with the molecular diffusivity of water vapor in air (0.22 cm2 s-1) at the experimental temperature (283 K). The ratio Dm/D should correspond to the tortuosity of the adsorbent bed. The value (4) is of the expected order of magnitude although somewhat larger than might be expected for a loosely packed assemblage of adsorbent particles.14 This might suggest some additional diffusional resistance associated with the diffusion of water vapor into the individual adsorbent particles. A very similar study of the diffusion of nitrobenzene into a bed of activated carbon particles was recently reported by Aarden et al.15 For that system, the equilibrium isotherm is essentially linear, and the concentration profiles show the classic form for a onedimensional Fickian diffusion system.16 A comparison with the present profiles for water-4A provides a clear illustration of the dramatic effect of isotherm shape on the form of the transient concentration profile. (b) Chromatography of Alkanes in 5A and 13X Zeolites. In the previous experiments, the evolution of the concentration profile through the adsorbent bed is slow because the rate is controlled by diffusive flow through the interstitial gas phase with a high capacity in the adsorbed phase. An essentially similar imaging technique can be used to follow the evolution of the transient concentration profile in a chromatographic column under flow conditions using the arrangement shown in Figure 2. Beads of 5A zeolite (8-12 mesh) or extrudates of 13X zeolite (0.3 cm o.d., ∼0.8 cm length) were used as the adsorbents. They were packed into a glass tube of 3-cm diameter and 10-cm length. After dehydration, a He carrier stream was passed at a controlled flow rate through the column. A pulse of the sorbate (methane, ethane, or propane) was injected
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2323 Table 1. Details of the Experimental Conditions
experiment diffusion into bed chromatography
single-particle ads/des
a
system
experimental conditionsa
4A (20-40 mesh) + H2O 5A (8-12 mesh) + 27 mL of C2H6 5A (8-12 mesh) + 27 mL of C2H6 5A (8-12 mesh) + 50 mL of C3H8 5A (8-12 mesh) + 26 mL of C2H6 and 18 mL of C3H8 13X extrudates + C3H8 13X extrudates + H2O
SPRITE, tp ) 0.2 ms, TR ) 4 ms, FOV ) 3.5 cm, Gmax ) 20 G/cm spin-echo, TE ) 1.1 ms, FOV ) 31 cm, G ) 0.5 G/cm, flow rate ) 250 mL/min spin-echo, TE ) 1.1 ms, FOV ) 31 cm, G ) 0.5 G/cm, flow rate ) 500 mL/min SPRITE, tp ) 0.4 ms, TR ) 1 ms, FOV ) 33 cm, Gmax ) 5 G/cm, flow rate ) 200 mL/min spin-echo, TE ) 1.1 ms, FOV ) 31 cm, G ) 0.5 G/cm, flow rate ) 650 mL/min spin-echo, TE ) 1.1 ms, FOV ) 1.6 cm, G ) 11.5 G/cm spin-echo, TE ) 1.1 ms, FOV ) 1.6 cm, G ) 11.5 G/cm
aquisition time, one profile
total exp duration
spatial resolution
figure
2 min
72 h
0.5 mm
3b, 3c
0.5 min
54 min
0.14 cm
6a
1 min
27 min
0.14 cm
6b
3 min
5h
0.45 cm
6c
0.5 min
3.5 h
0.14 cm
6d
7s
1h
0.13 mm
7a, 7b
7s
3.5 h
0.13 mm
10a, 10b
Encoding time tp, echo time TE, field of view FOV, gradient G, repetition time TR.
under flow conditions at the inlet of the bed at time zero, and the evolution of the concentration profile along the column was followed by the spin-echo or SPRITE imaging method, depending on the experimental time scale and the relaxation times of the system. A summary of the experimental conditions is included in Table 1. Under conditions where the movement of the pulse was relatively fast, 1-D spin-echo profiles, each composed of 128 points with a 31-cm FOV, were acquired using an echo time of 1.1 ms at a gradient strength of 0.5 G/cm. Sixty-four scans (for processes such as methane on 13X) or 128 scans (for slower systems such as C3H8-5A) were collected in a total time of 0.5 or 1 min, respectively. 1-D SPRITE profiles composed of 64 points with a 33cm FOV were also measured to demonstrate the possibilities of using the SPRITE method to investigate systems with shorter relaxation times. Using an encoding time (tp) of 100 µs and a maximum gradient of 2.3 G/cm, 512 scans were collected in about 1 min. The time resolution is therefore comparable to the spin-echo experiments. The lower signal/noise ratio of SPRITE in comparison to the spin-echo measurements (Figure 6b,c) is caused by the single-point acquisition of the SPRITE sequence. The time scale of these experiments is much shorter than in case a (minutes rather than days) because the flow is convective rather than diffusive. Figure 6 shows some representative results from the chromatographic experiments in which the concentration profile of an adsorbate was tracked as it progressed through an adsorbent column, carried by a stream of He. In Figure 6a, each single profile shows the concentration profile of the adsorbent injected in the column at a certain time. The sequence of profiles shows how the sorbate distribution evolves. The velocity (w) with which the concentration wave propagates through a chromatographic column is given by14
w)
v 1 - dq* 1+ dc
(
)
(6)
In the low-concentration region, dq*/dc ) K, the dimensionless Henry constant, so the wave velocity should be independent of concentration. The inverse
dependence on the Henry constant means that, in a multicomponent system, the more strongly adsorbed species will propagate with a lower wave velocity. For a linear system, the pulse will propagate as a symmetric Gaussian curve, the spread of which increases in proportion to the square root of the distance as a result of axial dispersion and mass-transfer resistance. The behavior of ethane, which is relatively weakly adsorbed with an almost linear isotherm, appears to conform to this pattern (Figure 6a,b), although some distortion is evident at long times as the concentration wave leaves the bed. This distortion appears to arise from interference with a small stationary signal perhaps due to a small concentration of adsorbed water in the last layers of the adsorbent. At higher loadings, the isotherm slope (dq*/dc) becomes concentration-dependent, and the behavior then becomes more complex.14 Propane, which is more strongly adsorbed with a nonlinear isotherm, shows the expected pattern (Figure 6c). Because the concentration falls as the profile evolves, the initially asymmetric pulse approaches a more symmetric form that then propagates at a constant velocity, spreading as it progresses. These experiments demonstrate the practical feasibility of applying MRI to observation of dynamic processes in commercial adsorbent systems. Experiments at different flow rates were performed to show the influence of the flow rate on the shape and velocity of the concentration pulse. Provided that the equilibrium isotherm is linear, it should be possible to estimate the effective diffusivity of the sorbate in the adsorbent particles by applying the well-known method of moments.17 Figure 6d shows the development of the profile for a mixed pulse of C2H6 and C3H8 in a 5A packed column. As expected from eq 6, the less strongly adsorbed species (C2H6) migrates through the column at a much higher rate. In this case, the velocity of the propane pulse shows a distinct transition from a relatively high value in the initial region to a more or less constant but lower value further down the column. Such behavior is to be expected if the isotherm is favorable and the initial concentration extends beyond the Henry region. For a favorable isotherm, this will give a decreasing wave velocity in the initial region, approaching the characteristic value for the Henry’s law limit some distance along the column.
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(c) Transient Concentration Profiles through a Single Adsorbent Pellet. In the third series of experiments a single 13X cylindrical extrudate of 0.8-cm length was dehydrated under a He atmosphere. The preconditioned pellet was sealed by Teflon tape and special proton-free glue (Bondo Marine Epoxy Resin) on the curved outer surface so that only the ends were accessible to the ambient gas. It was then suspended in a glass tube. At time zero, a flow of propane in He or a stream of 90% relative humidity air was passed through the tube so that the ends of the extrudate were exposed to a constant sorbate concentration. When the adsorption profile had reached equilibrium the flow was switched to a pure He stream and the desorption was followed. 1D spin-echo profiles composed of 128 points with a FOV of 1.6 cm (echo time 800 µs, gradient strength 11.5 G/cm) were achieved along the length of the extrudate (see also Table 1). A time of 7 s was required to obtain one profile (repetition time 50 ms). The rate of evolution of the concentration profile depends on the strength of adsorption, so the time interval between each profile measurement was adjusted to match the particular system under investigation. Time intervals varied from 15 s for propane to 5.95 min for water on a single pellet of 13X. Propane-13X. Figure 7 shows the evolution of the propane profile through a single extrudate of NaX zeolite, exposed at both ends (at time zero) to a propane/ He mixture. In this system, the equilibrium isotherm is highly favorable although not rectangular. The masstransfer rate is controlled by diffusion of propane within the macropores of the extrudate with accumulation in the micropores of the zeolite crystals. The process can be represented by the following equations:
diffusion equation (1 - p)
∂c ∂2 c ∂q + p ) pDp 2 ∂t ∂t ∂z
(7)
Langmuir isotherm qo bc q* ; λ) ) qs 1 + bc qs
(8)
For a strongly adsorbed species (such as propane), the accumulation in the vapor phase (p ∂c/∂t) is negligible compared with the accumulation in the adsorbed phase [(1 - p) ∂q/∂t], so eq 7 can be written in the dimensionless form
[
]
∂Q ∂ ∂Q 1 ) ∂τ ∂Z (1 - λQ)2 ∂Z
(9)
where the dimensionless variables are defined as
Q(Z,τ) ) q/qo, λ ) qo/qs, Z ) z/l, τ ) pDpt/Kl2 (10) Figure 6. Chromatographic response for a pulse of hydrocarbon injected into a He carrier stream flowing through a column packed with 5A zeolite pellets. (a) 5A-ethane (27 mL), flow rate 250 mL/ min. Successive spin-echo profiles at 8-min intervals. (b) 5A + ethane (27 mL), flow rate 500 mL/min, spin-echo 60-s profiles, 27-min experiment. (c) 5A + propane (50 mL), flow rate 200 mL, SPRITE 3-min profiles, 5 h experiment. (d) 5A + mixed pulse of ethane (26 mL) and propane (18 mL), flow rate 650 mL, spinecho 30-s profiles, 3.5-h experiment.
Equation 9 has the form of the diffusion equation for a one-dimensional system in which the diffusivity increases strongly with concentration according to D ) Do/(1 - q/qs)2 where Do ) pDp/K. For adsorption into an initially clean adsorbent, the relevant initial and boundary conditions are
Q(Z,0) ) 0; Q(0,τ) ) 1.0
(11a)
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2325
∂Q (0,τ) ) 0 ∂Z
(11b)
During the initial period of the process, before the concentration waves reach the center of the extrudate, the system will behave as diffusion into a semi-infinite medium, and the gradient boundary condition (eq 11b) can be replaced by the simpler condition characteristic of a semi-infinite medium, Q(l,t))0. A formal solution for the transient concentration profile for such a system has been given by Fujita18 and summarized by Crank.16 The profile assumes the form of a wave that penetrates into the extrudate (from both ends) according to the parabolic law z ∝ xt. Fujita’s solution applies only to a semi-infinite system and is therefore applicable to the present system only in the initial region before the two concentration fronts meet at the center. A numerical solution for the profiles in a finite system has been given by Garg and Ruthven.19 As the isotherm becomes increasingly favorable (λ f 1.0), the concentration profile approaches the form of a shock front (the limiting form for a rectangular isotherm) that penetrates with a velocity that varies inversely with the square root of time.20 The experimental profiles shown in Figure 7 are approximately of the expected form, although they show a distinct asymmetry. This might be because there is a significant uptake of propane by the adsorbent and the flow was not high enough to ensure that both ends of the extrudate were always exposed to the same propane concentration level. Disturbances due to inhomogeneties within the sample, especially at the ends, could also account for this asymmetry. For a linear adsorption system, adsorption and desorption are symmetric processes so the concentration profiles obtained during adsorption and desorption are mirror images. However, this is no longer true when the diffusivity is concentration-dependent, and when the concentration dependence is strong, the difference in the profiles becomes dramatic. The qualitative form of the desorption profiles in the propane-NaX system can be easily understood from simple theoretical considerations. Because propane is removed from the external surfaces of the extrudate (at z ) 0), the concentration at that point falls quickly to 0. In the central region of the extrudate the propane concentration is high, and the diffusivity is correspondingly high so, for a given flux, the gradient of concentration is very small. At the surface, the concentration is low, and the diffusivity is therefore very small, so that the concentration gradient is very large. The profile thus assumes the form seen in Figure 7b, with a more or less uniform concentration in the central region falling rapidly at the surface. As time progresses, the concentration level decreases, but the form of the profile remains the same. A formal solution for the concentration profile during desorption requires solution of eq 9 with the boundary conditions
Q(Z,0) ) 1.0; Q(0,τ) ) 0;
∂Q (1,τ) ) 0 ∂Z
(12)
in place of eq 11. However, a much simpler approximation is available because the strong concentration dependence of the diffusivity ensures that the concentration is always almost uniform in the central region of the extrudate. The system can therefore be regarded
Figure 7. Diffusion profiles for propane in a single 13X zeolite extrudate showing (a) the adsorption profiles and (b) the desorption profiles as an offset stack plot. Individual profiles were acquired in 7 s with the adsorption and desorption experiments requiring 1 h in total. The field of view was 1.6 cm.
as equivalent to desorption from a semi-infinite medium for which the zero-gradient boundary condition is replaced by Q(1,t) ) 1.0. By using the Boltzmann approximation (y ) z/2xDot), eq 9 is reduced to the ordinary differential equation
[
]
dQ d 1 dQ + 2y )0 dy (1 - λQ)2 dy dy
(13)
which must be solved subject to the boundary conditions
Q(0) ) 0; Q(yf∞) ) 1.0
(14)
to yield the profile Q(y). The integration of eq 13 is straightforward. Theoretical profiles calculated in this way for various values of λ are shown in Figure 8. If the profiles are plotted as q/qs()λQ) vs y, it becomes clear that the slope of the profile at the surface of the extrudate is essentially independent of λ and is given by
λ
1 dQ | ) dy y)0 4
(15)
Because the concentration profile is flat over most of
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Figure 8. Theoretical concentration profiles for desorption from a semi-infinite medium calculated from eqs 13 and 14: (a) Q vs y and (b) q/qs vs y.
the range of y, one can equate the desorption rate to the rate of change of concentration in the central region of the extrudate
-Do
x
qs dq | ) dz z)0 8
dqo Do )-l t dt
(16)
or, upon integration from q ) qoo at t ) 0
qo 1 )1qoo 4λ
x
Dot l2
(17)
where λ ) qoo/qs. Conformity with this expression is shown in Figure 9 in which the ratio qo/qoo from the experimental profiles (Figure 7b) is plotted against the square root of time. The plot is linear and passes through the point qo/qoo ) 1.0 at t ) 0, as required by eq 17. From the slope, we find Do/l2 ≈ 7.1 × 10-4 s-1 (assuming λ ≈ 1). With l ) 0.4 cm, K ) 800,21 and p ) 0.3, this gives Do ) pDp/K ≈ 1.1 × 10-4 cm2 s-1 and Dp ≈ 0.3 cm2 s-1, which can be compared with the molecular diffusivity of propaneHe at ambient temperature (∼0.45 cm2 s-1). The desorption data are evidently quite consistent with the assumption that transport of propane is controlled by diffusion within the relatively open macropore network of the 13X extrudate. Water-NaX. The profiles for this system, shown in Figure 10, are of the same general form as the profiles for propane, but they differ in several important details. The differences can be accounted for by two key
Figure 9. Desorption from 13X zeolite extrudate. The plots show qo/qoo vs xt for (a) propane (data from Figure 7) and (b) water (data from Figure 10).
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2327
dependence of the plateau concentration conforms to eq 17 (see Figure 9b). From the slope of this plot we find Do/l2 ≈ 10-4 s-1, and hence, with K ≈ 105(22) and p ) 0.3, Dp ) KDo/p ≈ 5 cm2 s-1. This value is substantially greater than the molecular diffusivity for H2O-He (∼0.9 cm2 s-1 at ambient conditions). The most obvious explanation is a substantial contribution from surface diffusion in the macropores, which, at these relatively high humidity levels, is not unreasonable. Future Challenges
Figure 10. Diffusion profiles for water-13X in a single extrudate showing (a) the adsorption profiles and (b) the desorption profiles as an offset stack plot. Individual profiles were acquired in 7 s with the adsorption and desorption experiments requiring 3.5 h in total. The field of view was 1.6 cm.
factors; the equilibrium isotherm for water is more favorable (closer to rectangular) than the propane isotherm, and the water loading experiments were run at a higher relative pressure (∼90% relative humidity). As a consequence of the more favorable isotherm, the adsorption profiles are closer to the limiting shrinkingcore pattern in which the concentration wave penetrates as a rectangular shock from both ends of the extrudate. Superimposed on this, we see an additional uptake in the later stages resulting from capillary condensation in the macropores. When the flow is switched to a pure He stream, the capillary condensed water, which is relatively weakly held, is easily and rapidly removed, leading to the initial sharp drop in the concentration level. The water that is adsorbed within the zeolite crystals is held much more strongly and desorbs only very slowly, so that the profile appears to approach a limiting form. In fact, this is not a true asymptote as the decline will continue, eventually to zero, but the rate of desorption becomes extremely slow for such a strongly held species. The form of the desorption profiles is similar to the corresponding profiles for propane, and the time
The studies reported here illustrate the exciting potential of MRI measurements as a tool for studying adsorption or reaction systems. However, in these measurements, we did not attempt to distinguish between the adsorbed and vapor phases within the column or particle. The profiles are, in fact, dominated by the adsorbed phase because the molecular density is much higher than for the gas. It would be interesting to determine the individual profiles for gaseous and adsorbed species as this would allow, inter alia, a direct measurement of the mass-transfer resistance (or HETP). As the relaxation behaviors of the adsorbed and gaseous species are distinctly different, such a goal can, in principle, be achieved. However, the low signal intensity from the gas phase (because of the low molecular density) makes this a challenging task. One approach that appears promising is the use of T2- and ir-weighted spin-echo profiles. Figure 11a,b shows weighted profiles of a sealed glass vial containing NaA extrudates in the left-hand half and free methane gas in the right-hand portion. Methane was selected for this experiment because it is relatively weakly adsorbed so that the disparity in molecular densities between the adsorbed and gas phases is not too large. It is clear that, with increasing observation time TE, the T2-weighted profile of the adsorbed phase is suppressed, leaving only the response from the gas phase (right-hand peak in Figure 11a). Similarly, by varying τir, the characteristic time constant of the ir/spin-echo sequence, the inversion-recovery-weighted spin-echo profiles of either phase can be reduced because of the spin-lattice relaxation time (T1) effects, although not totally suppressed because T1 depends strongly on the loading in the zeolites. To carry out such measurements under transient conditions to allow both profiles to be seen remains a challenging goal. Conclusions This study has demonstrated the practical feasibility of applying MRI with SPRITE and spin-echo sequences to measure transient concentration profiles in adsorbent systems containing commercial zeolite-based adsorbents on the scale of either a single adsorbent particle or a packed adsorbent column. The measured profiles conform broadly to theoretical expectations and provide a clear illustration of the rich variety of diffusional behavior that can be obtained depending on the form of the adsorption isotherm. In particular, the profiles for adsorption and desorption of propane and water vapor in a single adsorbent pellet (Figures 7 and 10) are striking. They show clearly the dramatic difference between the form of the concentration profiles in adsorption and desorption and provide direct evidence of the onset of capillary condensation at high loading.
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approach that might prove more cost-effective. Even though the equipment required for MRI measurements is not inexpensive, it is substantially cheaper than that for positron imaging, which requires a cyclotron to generate the necessary short-lived isotopes. Notation b ) Langmuir constant c ) gas-phase concentration co ) initial (steady) value of c D ) diffusivity Do ) limiting value of D at low concentration Dp ) pore diffusivity Dm ) molecular diffusivity K ) dimensionless equilibrium constant () bqs) based on gross particle volume l ) half-length of extrudate q ) adsorbed-phase concentration q* ) equilibrium value of q qo ) value of q at equilibrium with co qs ) saturation capacity qoo ) initial value of q for desorption Q ) q/qo (dimensionless concentration) t ) time v ) interstitial gas velocity w ) wave velocity y ) dimensionless distance variable z ) distance z1 ) distance to concentration front Z ) dimensionless distance z/l Z1 ) dimensionless distance z1/l τ ) dimensionless time ) voidage of adsorbent bed p ) porosity of pellet or extrudate λ ) nonlinearity parameter () qo/qs) Common MRI Abbreviations
Figure 11. Suppression of gas phase on adsorbed-phase profiles from methane-sodium A by use of T2- and T1-weighted measurements. (a) Suppression of adsorbed phase using T2 spin-weighted profiles at observation times TE larger than 2 ms. (b) Suppression of adsorbed phase on gas-phase profiles by use of ir-weighted profiles at values of τir in the range 5- 500 ms.
In principle, profiles of this kind could be calculated by solving the (nonlinear) diffusion equation together with the appropriate isotherm and boundary conditions. However, the ability to measure such profiles directly provides not only a verification of our understanding of such processes but a useful tool for future experimental measurements. It would clearly be straightforward to extend these studies to measure either transient or steady-state concentration profiles in a flow reactor. Extension to the measurement of both gas- and adsorbed-phase concentration profiles in a chromatographic column is a more challenging but, we believe, achievable goal. Considerable efforts have recently been devoted to developing experimental techniques based on positron emission imaging to measure transient concentration profiles in adsorbent columns and catalytic reactors.1,2 We believe that MRI offers a competitive alternative
FOV ) image field of view G ) magnetic field gradient strength TE ) echo time in spin-echo experiment TR ) repetition time, time between RF excitation pulses τir ) recovery time after inversion of sample magnetization tp ) phase encode time in SPRITE T1 ) spin-lattice relaxation time T2 ) spin-spin relaxation time T2* ) effective spin-spin relaxation time
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Received for review October 1, 2001 Revised manuscript received February 4, 2002 Accepted February 12, 2002 IE010821S
