Scale-up analysis of a twin-bed PSA pilot plant

The first factor influencing the dissimilarity between the PSA performance obtained from the pilot- and the full-scale plant is the axial and/or radial mass dispersion, which refers to column geometry as well as gas velocity along the adsorber. Three main sources of dispersion arise during PSA operation; namely (1) gas channelling at the adsorber wall and/or in the kernel part of the packed-bed due to non-uniform interparticle voidage, (2) turbulent mixing of gas caused by flow disturbances around adsorbent pellets, and (3) molecular diffusion which occurs even in absence of a gas flow [15]. As the volume of the column increases, both the adsorbent-to-adsorber diameter ratio d/D and the surface-to-volume ratio of the fixed-bed S/V decline exponentially. Therefore, it is expected that large-scale adsorbers exhibit reduced dispersion effects and consequently improved performance figures in relation to the PSA pilot plants. Nevertheless, the challenge remains in finding an adequate mathematical representation of the mass dispersion originating from the three mentioned different sources when establishing the process model based on pilot plant data. It could be relatively misleading since mass dispersion and also mass transfer kinetics influence the formation of the mass transfer zone along the adsorber column. Hence, dispersion and/or mass transfer coefficients could be estimated erroneously, which would preclude the employment of the model for the design of industrial-scale units. Numerous studies, rules-of-thumb, and empirical correlations for the representation of mass dispersion in packed-beds are available and commonly acknowledged [16‐21]. A summary of critical design parameters is presented in Table 1 [22]. The mathematical model of the PSA process shall include all sources of dispersion that are relevant for actual flow and plant characteristics. Including insignificant dispersion relations in the model can result in substantially prolonged calculation time, making the design of industrial-scale units simply impractical. Particularly, the effect of radial dispersion can be omitted provided that the Reynolds number (Re = ρUd/μ) remains larger than 10 and/or the ratio of adsorber length to adsorbent diameter (L/d) remains larger than 150. In such a case, the axial mass spreading becomes more significant than the radial mass spreading [12, 23]. Likewise, it is suggested that gas channelling effects become insignificant if the adsorber-to-adsorbent diameter ratio (D/d) is larger than 20 [24]. Usually, PSA pilot plants are designed in order to apply those correlations. It is crucial, however, to confirm that the scaled-up system exhibit the closest resembling flow and plant characteristics as were considered during PSA process modelling based on pilot plant data. Particular attention shall be put on maintaining the analogous packed-bed porosity which depends not only on adsorbent size and shape but also on the applied adsorber packing strategy [25].

The second factor to be considered is the occurrence of multiple flow resistances caused by gas flowing through the adsorber and piping system. The pressure drop along the packed-bed results from the friction between gas and adsorbent pellets, in addition to the gravitational potential energy change due to the rising of the fluid [26]. The pressure drop magnifies as the adsorber length L is increased and/or the adsorbent-to-adsorber diameter ratio d/D is reduced [18]. For that reason, large-scale systems would exhibit abbreviated MTZ in comparison to pilot plants. Consequently, enhanced performance figures obtained from the operation of larger adsorbers are expected, as long as (1) the target operating pressure for the production and regeneration processes is yet attainable within the selected cycle time, and (2) the speed of pressurisation/depressurisation within the adsorber is not significantly inhibited. Otherwise, the elevated pressure drop along the packed-bed becomes a performance-limiting factor. The described fluid dynamic conditions are likewise dependent on the pressure drop across multiple plant mountings, i.e. pipes, fittings, control valves, bends, in-line filters, connectors, silencers, or adsorber column elements as perforated plates or sieves for the packed-bed support. For that reason, industrial-scale piping constituents characterised by flow coefficients Cv being in agreement with the pilot-plant equipment shall be selected, if possible. Moreover, significant discrepancies in the operation regimes of small-and large-scale shut-off vales ought to be foreseen. Solenoid valves, which are typically applied in small-scale PSA pilot plants, are able to perform the shut-off action within a range of milliseconds [27], minimising the flow resistance across the valve and allowing the execution of short steps within the PSA cycle. On the other hand, industrial-scale systems are usually equipped with pneumatically-operated rotary/butterfly valves [28]. Their response time corresponds to a few seconds, depending on the performance of the pneumatic actuator. Therefore, very often the PSA cycle organisation must be adapted for the design of large-scale units to meet those limitations. Since PSA performance strongly depends on flow resistances in the piping system, altered Cv coefficients could significantly contribute to inaccurate mathematical model predictions of the large-scale system performance [8].

The third factor causing dissimilar operation regimes between pilot- and industrial-scale plants is usually an elevated superficial gas velocity within the adsorber column observed in larger PSA systems due to an increased throughput. When designing PSA plants, it is commonly accepted to limit the allowable gas velocity to less than 0.8 of the minimum fluidisation velocity during the production step, and to less than 1.8 of the minimum fluidisation velocity during the regeneration step [16]. Those requirements must be satisfied particularly during the PSA steps involving the rapid pressure change at both adsorber ends. By means of this strategy, the adsorbent attrition is most likely prevented, prolonging the lifespan of the material. In practice, to encounter those limitations, the aspect ratio of industrial-scale adsorber columns is typically adjusted to smaller values in comparison to those provided in pilot-plants. However, the proper engineering of the feed gas distribution system placed at the bottom of the column becomes more challenging as the adsorber diameter increases, which typically affects the capital costs.

The fourth factor affecting differences between pilot- and large-scale PSA plants is related to dissimilar heat exchange conditions in the column. As the diameter of column D increases, the dissipation of heat generated due to adsorption and compression is delayed. Consequently, the PSA performance of industrial-scale PSA units is reduced in relation to the pilot plant, due to diminished adsorption capacity at elevated operating temperatures. Consideration of this effect is indispensable when designing processes characterised by short PSA cycles and large values of adsorption enthalpy, which typically occurs in cases of gas separation on zeolites [29]. Therefore, large adsorbers would tend to operate under adiabatic conditions [30]. In order to ensure correctness of the mathematical model prediction, the heat transfer between pilot-scale adsorbers and environment shall be reduced by insulating columns prior to experimental research.

The employment of the developed mathematical model based on a pilot-plant outcome for the design of industrial-scale units can be assessed by consideration of process performance data at different cycle conditions. In this case, the half-cycle time is considered. The success of a quantitative prediction of the PSA performance lies in the accurate prediction of the breakthrough curve of the adsorber. An agreement of empirical and numerical results indicates the reliable estimation of both mass transfer kinetics as well as mass dispersion in the studied system since both factors primarily influence the shape of the breakthrough curve. Moreover, the consideration of different half-cycle times allows insight into the PSA operation at various bed utilisations which would correspond to the operation of units at different magnitudes. By means of this strategy, the development of MTZ along the adsorber column can be simulated and the formation of the concentration front can be examined, because a relatively good agreement among experimental and simulated temperature profiles is achieved, as shown in Fig. 2.

Empirical and numerical performance indicators of high-purity N₂-PSA at different half-cycle times are presented in Fig. 3. Independent from the purity level, the dynamic simulation predicts qualitatively well productivity and air demand. A slight imprecision in quantitative estimation of performance data occurs only on the highest investigated purity level of 10 ppm O₂, which could most likely be caused by inaccuracy in the estimation of adsorption isotherms at very low oxygen partial pressure [33] and/or measurement uncertainty at very low oxygen concentration [31]. The effect of the PSA half-cycle time on the nitrogen productivity greatly depends on the required product purity. On one hand, shorter cycles enlarge productivity at low purity levels (> 100 ppm O₂ in product stream) by preventing premature column breakthrough due to enhanced channelling effects promoted by relatively large gas superficial velocity. On the other hand, longer cycles allow extended gas residence time in the adsorber column which improves the gas separation efficiency at high purity levels (< 10 ppm O₂ in product stream). Since the variation of the half-cycle time changes the time span proportion of pressurisation and production steps, the air demand increases as the half-cycle time is reduced at every investigated product purity level due to a smaller amount of compressed air utilised for the production purpose [8].

Numerical breakthrough curves at different half-cycle times are presented in Fig. 4. Given that the final product purity corresponds to the integral average value of the oxygen concentration within the PSA cycle, the maximum allowable product contamination level detected at the end of the production step depends on the selected half-cycle time. Since the dynamic simulation corresponds to the operation of practical PSA systems, it can be seen that at every investigated product purity level the breakthrough curve does not begin at the zero-level of oxygen concentration. Therefore, the MTZ propagates through the entire adsorber length, which is shown in Fig. 5.

An extended MTZ along the adsorber occurs at low purity levels, indicating an enhanced mass dispersion caused by the elevated gas superficial velocity. In contrast, at high nitrogen purity levels, the MTZ is situated mostly at the bottom part of the bed; therefore, the top part is occupied almost exclusively by purified nitrogen. As a result of the type-I isotherm describing the equilibrium in the studied system [33], at all investigated process conditions, the oxygen concentration front is self-sharpening in the initial phase of the production step and approaches a constant pattern behaviour as the half-cycle time is increased. Whereas at thermodynamic equilibrium both components are adsorbed by the CMS in a similar quantity, a roll-up effect occurs which indicates a dominant adsorption of nitrogen over oxygen due to its higher concentration in the feed stream. Therefore, both factors, the shape of concentration front propagation and the magnitude of the roll-up effect, would eventually have an impact on the bed utilisation. The velocity of selected oxygen concentration levels U_y of 0.15 and 0.05 kmol/kmol at different adsorption duration t and the extend of the roll-up effect χ, indicated by a grey area in Fig. 5, are presented in Table 3. The bed utilisation φ is calculated by a numerical integration according to Eq. 1, where: y—oxygen mole fraction [kmol/kmol], y_in—oxygen mole fraction in inlet stream which equals 0.209 kmol/kmol, L—packed-bed length [mm], L_max—total packed-bed length which equals 581 mm. The extend of the roll-up effect χ is calculated by a numerical integration according to Eq. 2, where L_yin—packed-bed length at which oxygen mole fraction refers to the inlet stream.

The constant pattern behaviour does not occur in the studied system even at prolonged adsorption duration since higher concentration levels propagate faster in relation to lower concentration levels at all investigated process conditions. Therefore, the self-sharpening MTZ results in a larger bed utilisation at longer cycle times despite an intensified nitrogen adsorption associated with the roll-up effect. Moreover, it can be noticed that a faster propagation of concentration profiles results in an increased nitrogen productivity at both studied levels of product purity, which indicates an enhanced kinetic selectivity of the CMS in respect to the air components.

Considering that (1) the mathematical model accurately predicts the PSA performance at various half-cycle times and thus proving the correct estimation of both axial mass dispersion and mass transfer kinetics at various product purity levels, and (2) a further propagation of MTZ along the adsorber leads to an improved bed utilisation, the dynamic simulation of units in industrial dimensions can be performed as long as the process conditions are corresponding.

The scheme of the PSA system implemented in the process simulator is presented in Fig. 6. The numerical investigation of the performance at different scale-up factors α was executed by a proportional increase of (1) volume of packed-beds V_A1 and V_A2, (2) volume of nitrogen receiver V_R, (3) volume of top and bottom adsorbers voids V_T and V_B, (4) Cv coefficients of selected valves V, and (5) purge stream flow rate F_purge. Applied values are given in Tables 4 and 5. By means of this strategy, the adsorber column geometry as well as flow resistances are corresponding to the pilot-plant, enabling a systematic study of the system behaviour. Here, the HCT equals 60 s at all investigated process conditions. Operating temperature, adsorption pressure, and the equalisation method refer to the data presented in Table 2. The sensitivity study exhibited no substantial variation in dynamic simulation results at increased number of calculations nodes. Therefore, the number of calculation nodes is not altered and equals 70 at all investigated process conditions to avoid an extended computation time.

The PSA performance results at different scale-up factors are displayed in Fig. 7.

The effect of the plant scale-up factor α on PSA performance indicators strongly depends on the required product purity. When generating the product at low purity levels (≥ 1000 ppm O₂), both productivity and air demand values remain rather insensitive to the PSA system enlargement. It is observed that the nitrogen productivity increases by scaling-up the system up to an α-value of about 100, which indicates reduced mass axial dispersion effects as the adsorbent-to-adsorber diameter ratio d/D is reduced. At α = 100, the productivity is enlarged by about 2% in relation to the pilot-plant operation. At larger values of scale-up factor (α > 100), the effect of axial mass dispersion becomes irrelevant; however, the productivity decreases due to an extended pressure drop along the packed-bed, which disables the proper adsorbent regeneration, as shown in Fig. 8. The minimum value of the air demand is observed at α = 500, indicating the highest bed utilisation.

When generating the product at high purity levels (≤ 100 ppm O₂), the productivity increases and the air demand decreases as the system approaches the industrial-scale. Especially at the highest investigated nitrogen purity level (10 ppm O₂), the enlargement of the PSA system by the factor of 2000 results in a productivity increase of about 36%, and the air demand reduction of about 27% in relation to the pilot-plant operation. In this case, the elevated flow resistance during the counter-current depressurisation proves to not be a limiting factor, as the relatively condensed oxygen mass transfer zone is situated mostly in the bottom part of the bed. Therefore, an increased pressure drop along the packed-bed inhibits the evacuation of the purified nitrogen accumulated in the top part of the column. Hence, it is strongly recommended to utilise larger PSA pilot plants for investigating high-purity nitrogen production in order to gain more reliable design data.

In the industrial practice, the particular scale-up factor of top and bottom adsorber voids does not necessarily grow closely with the general scale-up factor α. In this case, it is expected that a provision of smaller void volumes would result in reduced air demand figures without a significant impact on the productivity [8, 37]; provided that wall effects and gas channeling are insignificant for the considered adsorber geometry, i.e. L/D > 5 and D/d > 20. Otherwise, a notable effect of void volumes on PSA performance would be expected, especially as the required product purity level increases, regardless of the plant size.

Furthermore, it is clear that the allowable gas velocity during the regeneration step becomes a limiting factor during the design of industrial-scale PSA systems. To assess whether the simulated processes could be applied in practice, an analysis of the gas velocity during the PSA cycle is be performed. The development of the gas velocity formed during the operation of the PSA pilot plant (α = 1) at different column heights is presented in Fig. 9. The highest amplitudes of the gas velocity are detected at the bottom of the adsorber during the pressure equalisation step, as well as at the beginning of production and regeneration steps. Those extremum values of the gas velocity shall be compared to the minimum fluidisation velocity determined at the same time in order to verify the hydrodynamic constraints of the system. The determination of the minimum fluidisation velocity U_f is based on the Ergun pressure drop equation. No significant difference in the minimum fluidisation velocity at different column heights was detected. The ratio of the actual gas velocity to the minimum fluidisation velocity at different scale-up factors α during the nitrogen production at 1000 ppm O₂ purity level is presented in Table 6. An additional sensitivity study exhibited no substantial variation in values of the gas velocities along the column at different product purity levels; however, the production of low-purity nitrogen is associated with fairly higher values of the gas velocity in relation to the high-purity nitrogen generation.

Taking into consideration the hydrodynamic limitations of the system during the counter-current regeneration step (U/U_f ≤ 1.8), it is proved that the employed scale-up strategy is valid up to the scale-up factor α equal to about 7.5. A further increase of the adsorber volume is not recommended. Thus, as long as the design of larger PSA units is considered, other scale-up approaches shall be examined and verified.

Provided that the gas velocity shall be reduced in order to encounter the hydrodynamic limitations of the system, a very common practice is the adjustment of the adsorber aspect ratio to lower values. Moreover, the size of industrial PSA systems is commonly restricted by the available space indoors or outdoors. Hence, very often the L/D ratio of adsorbers is adjusted to meet those requirements. For that reason, a systematic study of the effect of the L/D ratio on the PSA performance was conducted. Dynamic simulations were executed at the PSA scale-up factor equal to 500; therefore, in this case, the volume of a single packed-bed equals about 993 L. Other operating conditions of the process refer to those applied in the previous section. The results are presented in Fig. 10.

The nitrogen productivity remains rather insensitive to the variation of the L/D ratio, especially at low product purity levels (≥ 100 ppm O₂). Nonetheless, at all investigated process conditions, the increased L/D ratio results in lower air demand values, as the impact of mass axial dispersion along the adsorber length is diminished. However, the effect proves to be rather insignificant as the required product purity level decreases. Therefore, utilisation of adsorber columns with large L/D ratios is recommended exclusively when high purity nitrogen (≤ 10 ppm O₂) is required, mostly due to the substantial air demand reduction.

The considerable effect of the adsorber aspect ratio on the gas velocity is presented in Table 7. As expected, the gas velocity is significantly reduced at a lower L/D value. It is proved that the presented industrial-scale PSA process could be implemented in practice at the L/D ratio equal to 1, as long as the process conditions are corresponding. In this case, the hydrodynamic limitations of the system are not compromised.

Differences among process performance figures obtained during the operation of PSA plants at different magnitudes could as well arise from the execution of dissimilar adsorber packing strategies, which results in the variation of the packed-bed density ρ_bed and packed-bed porosity ε_bed characteristics. Whereas the packed-bed density of small-scale columns can be somehow elevated by the employment of alternative packing methods and their combinations, i.a. tapping, vibrating, snowstorm filling; the industrial-scale adsorbers are filled almost exclusively (1) by the snowstorm filling method if adsorbers are equipped with top flanges, or (2) by the standard flow-pack method if adsorbers are equipped only with an inlet nozzle. All efforts invested to increase the packed-bed density lead to an elevated adsorption capacity of the system, as well as to lower porosity of the packed-bed and a reduction of mass dispersion effects. The results of sensitivity studies concerning the effect of packed-bed density ρ_bed on PSA performance at different plant scale-up factors and adsorber aspect ratios are presented in Fig. 11. The selected range of the packed-bed density corresponds to the information provided in the adsorbent data sheet. The packed-bed porosity ε_bed was calculated according to Eq. 3, based on the experimentally determined value of adsorbent apparent density ρ_app, which equals 1193.12 kg/m³.

At all investigated process conditions, the elevated packed-bed density results in a linear increase in productivity figures. The increment of the adsorber packed-bed density by about 8% causes an enlargement of the nitrogen productivity of about 12%, 20%, and 49% at product purity levels of 1000 ppm O₂, 100 ppm O₂, and 10 ppm O₂, respectively, regardless the adsorber volume or aspect ratio. Furthermore, the air demand decreases predominantly linearly with the elevation of packed-bed density at all investigated process conditions. This effect becomes more significant as the product purity increases. The enlargement of the adsorber packed-bed density by about 8% causes the air demand reduction of about 5%, 11%, and 27% at product purity levels of 1000 ppm O₂, 100 ppm O₂, and 10 ppm O₂, respectively.

In order to confirm that the mathematical model can be utilised for the design of large-scale PSA systems, the experimental performance results obtained during the operation of an industrial twin-bed N₂-PSA plant equipped with the same adsorbent are compared to the outcome of dynamic simulations at the corresponding process conditions. The properties of the industrial-scale PSA system are presented in Table 8. The experimental data were provided by SysAdvance©, Portugal.

Taking into consideration the volume of the large-scale adsorber, it can be deduced that a pilot-plant scale-up factor α = 1052 would apply in this case. However, the dynamic simulation was adapted to correctly simulate the functioning of industrial-scale shut-off valves installed in the system. Therefore, Cv coefficients were arbitrarily adjusted, predominantly to smaller values in relation to those implemented for the simulation of pilot-plant behaviour, multiplied by a factor of 1052. Moreover, in certain cases, a linear increase of Cv values was implemented, in order to account for a prolonged response time of industrial-scale shut-off valves, which tend to operate analogously to actuators. The comparative valve coefficients Cv are shown in Table 9. By means of this strategy, the pressure swing is not achieved as rapidly as when utilising pilot-scale units, as presented in Fig. 12, which resembles a realistic operation regime of large-scale PSA plants. If possible, the validation of generated pressure curves presented in Fig. 12b with experimental data is strongly recommended to verify whether Cv values are adjusted correctly.

Simulation results of the industrial-scale PSA are shown in Table 10. The presented outcome clearly demonstrates the significance of the proper estimation of flow resistances along the piping system for accurate prediction of the unit performance. When implemented values of Cv coefficients simply scaled-up by the factor α, the mathematical model underestimates the productivity by nearly 38%. In this case, very rapid pressurisation and depressurisation at the beginning of the PSA cycle, as shown in Fig. 12a, give rise to an excessive gas velocity along the adsorber, which surpasses the hydrodynamic limitations of the system. Moreover, the production pressure does not correspond to the experimental value, as reported in Table 8.

On the other hand, when the implemented Cv coefficients are adapted to simulate pragmatic pressure profiles, observed during the operation of large-scale systems, as shown in Fig. 12b, the mathematical model predicts the PSA productivity with inaccuracy smaller than 1%. Furthermore, as reported in Table 10, the ratio of the gas velocity to the minimum fluidisation velocity falls within the recommended range for the operation of packed-bed reactors. In this case, reduced pressurisation and depressurisation rates result in significantly smaller oxygen concentration amplitudes, observable on the oxygen breakthrough curve during the pressure equalisation step, as well as at the beginning of production and regeneration steps, as presented in Fig. 13. Thus, increased flow resistances along the piping system reduce the driving force for the desorption process at the time of the adsorber depressurisation, which results in the minor transfer of the highly oxygen-enriched gas into the neighbour column. For that reason, the adsorption capacity in the subsequent production step is larger for the process with adapted Cv coefficients in relation to the process with straightforwardly scaled-up Cv values. Thereby, an increased nitrogen productivity is obtained. Moreover, a slightly lower air demand was identified when adapted Cv coefficients are implemented in the process simulator, pointing out the improved bed utilisation at the same product purity level.