Introduction

The increasing global focus on carbon emissions has led to growing interest in the application of hydrogen. Hydrogen is typically purified prior to further processing, particularly in fuel cells1. Pressure swing adsorption (PSA) technology, as one of the most important techniques for gas separation and purification, is widely used in both industrial and lab-scale. The traditional PSA process mostly uses conventional adsorbents, such as activated carbon and zeolite, for the purification of gas mixtures containing high concentrations hydrogen, including CO2/H22, H2/CO and H2/CH43, H2, CO, CH4, and CO24, H2/N2/CH4/Ar5. To investigate the adsorption dynamics and thermal effects of adsorption, Ahn et al. conducted a comparing activated carbon and zeolite 5A. They observed a significant roll-up effect of CH4 on the CO breakthrough curve in the activated carbon adsorption bed, whereas only a minor roll-up was noted for CH4 in the zeolite adsorption bed. Increasing the adsorption pressure and decreasing the feed flow rate both contribute to extending the breakthrough time6. Baamran et al. compared the H2 purification performances of three commercially activated carbons (AC-3, AC-6, and AC-9) through mixture gas adsorption isotherms and dynamic experiments. The adsorbates exhibited varying affinities towards the activated carbons, with CO2 being the most adsorbed gas followed by CH4 and CO, while H2 showed much lower affinity7. Based on the principle of PSA technology, Papadias et al. developed a novel technique to track impurities in hydrogen. Impurities are adsorbed at high pressure, while hydrogen is exhausted, then desorbed at a low pressure with a high concentration of hydrogen8. Mondal et al. evaluated the capacity of adsorption bed with different adsorbents (Maxsorb-III and A-20) at different temperatures and pressures by PSA unit. Evaluations were also conducted on the total power consumption and heat rejection of the PSA system. The findings indicated that the Maxsorb-III is significantly more cost-effective than A-20 for removing CO29.

During the research process, layered beds for multi-component separation in PSA processes were investigated. The results demonstrate that layered beds can optimize performance by minimizing bed size while maximizing sorbent utilization. Jang et al. performed breakthrough experiments to compare the performance of single adsorbent beds with that of layered beds. The results revealed distinct selectivity differences among the adsorbents: activated carbon exhibited strong adsorption for CH4, while zeolite 5 A demonstrated strong adsorption for CO10. Park et al. studied hydrogen separation using cracked gas containing H2/CO2/CH4/CO in a layered bed with activated carbon followed by zeolite 5 A. The characteristics of the adsorption dynamics were predicted. An optimum ratio between the length of the activated carbon layer and the total bed length was identified to enhance the bed utilization11. Ribeiro et al. introduced a zeolite layer following the activated carbon layer in both single and four-bed PSA systems. They then explored the purification performance and found that addition of the zeolite layer enhanced both hydrogen purity and recovery during the PSA process12. To ensure high hydrogen purity and recovery, Leila et al. designed a three-layered bed consisting of a silica gel layer, followed by a primary activated carbon layer, and an exit layer of zeolite LiLSX for the mixture of hydrogen and natural gas. This demonstrates the potential of PSA technology as a technically feasible approach for obtaining exceptionally high-purity hydrogen13. Comparing the purification performances in previous researches, it was revealed that the layered bed shows superior performance compared to the single bed.

The PSA technology for hydrogen purification has been well-established through extensive research and application in current industrial processes. Porous materials, such as the traditional adsorbents activated carbon and zeolite, are widely used in PSA processes. Material-organic frameworks (MOFs) have ultrahigh surface areas that contain absorptive sites for gases, which are considered as one of the most potential materials in the areas of adsorption, hydrogen purification, storage and fuel cell technology14,15,16. Mao et al. discovered a more efficient method for hydrogen purification using MOFs. They subsequently summarized and compared the performance of this method in separating hydrogen from mixture gas (CO2, N2, CH4, CO)17. Gérard et al. found that MOFs exhibit superior selectivity for carbons and offer a more cost-effective regeneration process when compared to zeolites18. CuBTC, a well-known MOF, was developed for hydrogen adsorption studies. Silva et al. performed a PSA model using CuBTC as the adsorbent for a mixture gas (CO2, CH4, CO and N2), revealing its high adsorption capacity19. Building on the foundation laid by Silva’s work, Xiao et al. made further efforts to study the effects of operating parameters, including feeding time, adsorption pressure, and feed flow rate, on the performance of CuBTC for hydrogen purification20. Esfandiari et al. studied the effect of incorporating activated carbon as a void space filling agent within the CuBTC for hydrogen separation. The results showed that the addition of low-cost activated carbon significantly enhanced the adsorptive properties of CuBTC for this application21. Kloutse et al. presented adsorption data for two ternary mixtures on CuBTC and MOF-5, respectively. The findings revealed significant differences in H2/N2 selectivity among the various adsorbents22. Rostami et al. investigated the effects of MOF structure on hydrogen adsorption. The results indicated that increased porosity leads to a larger internal surface area, providing more active sites for adsorbate interaction23. Xiang et al. synthesized a highly porous MOF, UTSA-16, which effectively adsorbs CO2. UTSA-16 also exhibited consistent and reversible performance in its results for CO2 sorption. Notably, UTSA-16 offers a cost-effective solution for CO2 capture and separation, as its raw material expenses are lower compared to other alternatives, making it an advantageous option for these applications24. Agueda et al. evaluated a PSA process using UTSA-16 for hydrogen recovery and purification, measuring the adsorption isotherms with the Dual Langmuir isotherm. The simulated PSA cycle achieved exceptional levels of hydrogen purity, recovery, and productivity, demonstrating the process’s efficiency25. Most researchers have focused on studying the PSA process using layered bed with two kinds of adsorbents. Sadegh et al. discovered a novel approach by combining three different adsorbents: CuBTC, activated carbon, and zeolite 5 A. The unique combination achieved an exceptionally high hydrogen purity level, exceeding 99.99%, demonstrating the potential of using multiple adsorbents in PSA processes for enhanced purification efficiency26. An important characteristic of UTSA-16 found in positive initial evaluation is the high volumetric density and efficient H2 PSA desorption capability. The effect of different adsorbents on the performance of PSA units has been investigated by many authors. Activated carbon and zeolite are commonly used as adsorbents in hydrogen purification PSA units. As UTSA-16 is a cost-effective MOF material for the PSA process, this research is an investigation of the performance of UTSA-16 as a new adsorbent in hydrogen purification PSA units. The study also compares the performance of UTSA-16 with the conventional adsorbents of activated carbon and zeolite 5 A.

Various methodologies has been employed to optimize PSA processes. In the early stage, Tagliabue et al. built a cryogenic exchange system, which increased the unit’s total load by 25% and enhance H2 recovery to 2.5%27. Babatabar et al. developed a comprehensive model using ASPEN Plus software to predict and optimize hydrogen production. Sensitivity analysis was also conducted to assess the model’s robustness. Subsequently, the effect of main parameters was analyzed to identify the optimal conditions for hydrogen production, highlighting the model’s capability in enhancing process efficiency28. Wang et al. optimized purification purity and recovery simultaneously using a graphical method, achieving high accuracy29. Knaebel et al. employed the PSA process to efficiently separate hydrogen from a hydrogen-methane mixture. Subsequently, an optimization strategy was developed to assess the optimal operating conditions, aiming to maximize hydrogen recovery while satisfying the requirements for hydrogen purity and cyclic steady state30.

Currently, various methodologies are employed for optimization and prediction. Numerous studies have shown that neural network models possess distinct advantages over traditional mechanical models. Specially, neural network exhibit superior nonlinear processing capabilities, self-learning abilities, generalization skills, flexibility, and robustness. With the widespread application of ANN in the establishment, prediction, and optimization of data models, numerous scholars have successfully employed ANN for PSA optimization, achieved remarkable results across various fields31,32,33,34. This highlights the significant advantage and application value of ANN in enhancing PSA optimization processes. Ye et al. applied ANN to optimize both the breakthrough curves and cycles of PSA. The results demonstrated the feasibility of using an ANN model to predict the optimal operating conditions for PSA breakthrough curves and cycles35,36. ANN as a predictive tool for arbitrary functions with desired accuracy has been well-established. However, it also has been proved that the limitations of gradient search techniques can lead to inconsistent and unpredictable performance37. Therefore, Sexton et al. conducted a comparative study of two typical global search techniques: simulated annealing (SA) and genetic algorithms (GA), to evaluate their performance. Additionally, the optimization of ANN by SA and GA was also investigated and compared. The results revealed that GA consistently outperformed SA in obtaining superior solutions38. Yu et al. established an optimization strategy using Latin hypercube sampling (LHS) in conjunction with ANN. Then, the dual-objective and tri-objective optimization based this strategy were studied. The results showed that the ANN trained using the LHS strategy not only achieve high accuracy in optimizing the PSA process but also successfully identified optimal operating conditions39. ANN can model the complex relationships between inputs and outputs40. Back propagation neural network (BPNN) is one of the most mature and widely used. Zamaniyan et al. developed a BPNN model to gain a better knowledge and optimize hydrogen production for industrial application41. However, the network structure, initial weights, and bias values significantly influence network training, yet these parameters are difficult to determine accurately. In this work, we propose using a genetic algorithm to optimize the network structure of BPNN. Subsequently, we apply this optimized model to predict PSA performance.

In this work, there are mainly focused on two parts of research contents. Firstly, the hydrogen purification performances of a three-layered bed packed with novel adsorbent UTSA-16, activated carbon and zeolite 5 A were investigated for multi-component SMR off-gas (H2/CH4/CO/CO2 = 76/3/4/17 mol%) using the Aspen Adsorption platform. Secondly, optimization of a specific combination is explored using BP neural network-genetic algorithm (BPNN-GA). The optimization performance of conventional BPNN and BPNN-GA is compared, demonstrating that BPNN-GA is significantly reduces the error compared to conventional BPNN. This research clearly demonstrates the feasibility of using the BPNN-GA model to .identify optimal operating condition for the PSA cycle.

There are six sections in this work. Section “Introduction” introduces the PSA technique and the application of ANN. Section “Model description” presents the mathematical models used in the adsorption process, including the mass balance equation, energy balance equation, adsorption isotherms and kinetic model, and equations of state. Section “PSA model parameters and validation” describes the establishment and validation of the PSA model, including the model parameters and validation through PSA breakthrough curves. Section “ PSA cycle model” presents the PSA cycle model, a three-layered bed PSA cycle model is built, and the performance of PSA cycle is studied. Section “Optimization by machine learning model” introduces the optimization of the PSA process using machine learning model, specifically comparing bi-objective and multi-objective optimization approaches using BPNN and BPNN-GA models. Finally, section “Conclusion” provides the conclusion.

Model description

Mass balance equation

The gas phase in this study behaved as an ideal gas mixture. For each component, mass balance equation can be formulated as follows:

$$- {D_L}\frac{{{\partial ^2}{y_i}}}{{\partial {z^2}}}+{u_z}\frac{{\partial {y_i}}}{{\partial z}}+\frac{{\partial {y_i}}}{{\partial t}}+\frac{{RT}}{p}\frac{{1 - {\varepsilon _b}}}{{{\varepsilon _b}}}{\rho _p}\left( {\frac{{\partial \overline {{{q_i}}} }}{{\partial t}} - y\sum\limits_{{j=1}}^{n} {\frac{{\partial \overline {{{q_j}}} }}{{\partial t}}} } \right)=0,\quad i=1, \ldots ,N.$$
(1)

The overall mass balance equation as follows:

$$- {D_L}\frac{{{\partial ^2}p}}{{\partial {z^2}}}+p\frac{{\partial u}}{{\partial z}}+\frac{{\partial p}}{{\partial t}}+{u_z}\frac{{\partial p}}{{\partial z}} - \frac{p}{T}\left( { - {D_L}\frac{{{\partial ^2}T}}{{\partial t}}+\frac{{\partial T}}{{\partial t}}+{u_z}\frac{{\partial T}}{{\partial z}}} \right)+\frac{{1 - {\varepsilon _b}}}{{{\varepsilon _b}}}{\rho _p}RT\sum\limits_{{j=1}}^{N} {\frac{{\partial {q_j}}}{{\partial t}}} =0,$$
(2)

where \({D_L}\) represents the dispersion coefficient in axial direction, \({u_z}\) represents the physical velocity in axial direction, \({y_i}\) represents the molar fraction of species i, \({q_i}\) represents the concentration of species i in the adsorbed phase, \({\varepsilon _b}\) represents the void fraction of interparticle, \({\rho _p}\) represents the density of pellets in the adsorbent, R represents the universal gas constant, T and p respectively represents the temperature and the pressure in the adsorption bed, t represents the adsorption time, and z represents the axial position in the bed.

Energy balance equation

The energy balance consists of two components: the gas and solid phase within the adsorption bed, and the wall of the adsorption bed.

The energy balance equation can be formulated for both the gas and solid phases of the adsorption bed as follows:

$$- {K_L}\frac{{{\partial ^2}T}}{{\partial {z^2}}}+\left( {{\varepsilon _t}{\rho _g}{C_{pg}}+{\rho _b}{C_{ps}}} \right)\frac{{\partial T}}{{\partial t}}+{\rho _g}{C_{pg}}{\varepsilon _b}{u_z}\frac{{\partial T}}{{\partial z}} - {\rho _b}\sum\limits_{i}^{N} {{Q_i}} \frac{{\partial {q_i}}}{{\partial t}}+\frac{{2{h_i}}}{{{R_{bi}}}}\left( {T - {T_w}} \right)=0.$$
(3)

For the wall of the adsorption bed, the energy balance is constructed as:

$${\rho _w}{C_{pw}}{A_w}\frac{{\partial {T_w}}}{{\partial t}}=2\pi {R_{bi}}{h_i}\left( {T - {T_w}} \right) - 2\pi {R_{bo}}{h_o}\left( {{T_w} - {T_{atm}}} \right),$$
(4)

where \({A_w}=\pi (R_{{bo}}^{2} - R_{{bi}}^{2})\), \({K_L}\) represents the thermal dispersion coefficient in axial direction, \({C_{pg}}\) represents the heat capacity for the gas phase of mixture gas, \({C_{ps}}\) represents the specific heat capacity for the solid phase of the adsorbent, \({\varepsilon _t}\) represents the overall void fraction of the adsorption bed, \({Q_i}\) represents the adsorption heat of species i, \({T_w}\) and respectively represents the temperature of the wall and the atmospheric.

Adsorption isotherms and kinetic model

The dual-site Langmuir (DSL) model is employed to describe the equilibrium isotherms of activated carbon and zeolite 5 A6:

$$q_{i}^{ * }=\frac{{{q_{{m_i}1}}{B_{i1}}{p_i}}}{{1+\sum\nolimits_{n} {\left( {{B_{n1}}{p_j}} \right)} }}+\frac{{{q_{{m_i}2}}{B_{i2}}{p_i}}}{{1+\sum\nolimits_{n} {\left( {{B_{n2}}{p_j}} \right)} }},$$
(5)

with, \({q_{m1}}={k_1}\), \({B_1}={k_2}{\operatorname{e} ^{\left( {{{{k_3}} \mathord{\left/ {\vphantom {{{k_3}} T}} \right. \kern-0pt} T}} \right)}}\), \({q_{m2}}={k_4}\), \({B_2}={k_5}{\operatorname{e} ^{\left( {{{{k_6}} \mathord{\left/ {\vphantom {{{k_6}} T}} \right. \kern-0pt} T}} \right)}}\).

where \(q_{i}^{ * }\) represents equilibrium adsorption amount of species i, \({q_{{m_i}}}\) and \({B_i}\) are the DSL isotherm parameters.

For UTSA-16, the experimental adsorption isotherms is consistent with the DSL model in Agueda’s work25, the DSL model can also be written as follows:

$$q_{i}^{ * }=\frac{{{q_{{m_i}1}}{B_{i1}}p}}{{1+{B_{i1}}p}}+\frac{{{q_{{m_i}2}}{B_{i2}}p}}{{1+{B_{i2}}p}},$$
(6)

with, \({B_{i1}}={B_{01}}{\operatorname{e} ^{\left( { - \frac{{{Q_{i1}}}}{{RT}}} \right)}}\), \({B_{i2}}={B_{02}}{\operatorname{e} ^{\left( { - \frac{{{Q_{i2}}}}{{RT}}} \right)}}\).

The momentum balance in an adsorption bed can be described by the Ergun’s equation:

$$- \frac{{dp}}{{dz}}=a\mu {v_z}+b\rho {v_z}\left| {\overrightarrow v } \right|,$$
(7)

the coefficients can be written as:

\(a=\frac{{150}}{{4R_{p}^{2}}}\frac{{{{\left( {1 - {\varepsilon _b}} \right)}^2}}}{{\varepsilon _{b}^{3}}},\quad b=1.75\frac{{\left( {1 - {\varepsilon _b}} \right)}}{{2{R_p}\varepsilon _{b}^{3}}},\)

with \({v_z}\) represents Darcy’s velocity, \(\mu\) represents dynamic viscosity, and \({R_p}\) represents the particle radius.

The linear driving force (LDF) model can be used to describe the sorption rate into an adsorbent pellet, with \({\omega _i}\) as the single lumped mass-transfer parameter42

$$\frac{{\partial {q_i}}}{{\partial t}}={\omega _i}\left( {q_{i}^{ * } - {q_i}} \right),\quad i=1, \ldots ,N,$$
(8)

where \({\omega _i}\) represents the mass transfer parameters of species i, \(q_{i}^{ * }\) and \({q_i}\) respectively represents the equilibrium adsorption amount and dynamic adsorption amount of species i.

Equation of state

Based on the ideal gas law, \(pV=nRT\), the molar fraction of the mixture gas can be expressed as \(c=pV=nRT\). The molar fraction of species i can be represented as:

$${y_i}=\frac{{{n_i}}}{n}=\frac{{{{{n_i}} \mathord{\left/ {\vphantom {{{n_i}} V}} \right. \kern-0pt} V}}}{{{n \mathord{\left/ {\vphantom {n V}} \right. \kern-0pt} V}}}=\frac{{{c_i}}}{c}=\frac{{{c_i}RT}}{p},\quad i=1, \ldots ,N.$$
(9)

The specific heat capacity of a gas mixture can be determined by calculating the weighted average of molar fractions as:

$${C_{pg}}=\sum\limits_{{i=1}}^{N} {{y_i}{C_{pi}}} .$$
(10)

The density of the gas mixture can be expressed as:

$$\rho =cM=c\sum\limits_{{i=1}}^{N} {{y_i}{M_i}} ,$$
(11)

where \({M_i}\) represents the molar weight of species i.

PSA model parameters and validation

The model describing the adsorption process is primarily based on mass and energy balance equations. Additionally, a suitable adsorption isotherm can accurately predict the breakthrough curves in the PSA process. To simulate a PSA process, the following assumptions are made:

  1. (1)

    The gas flow model in the adsorption bed follows an axial dispersed flow model;

  2. (2)

    Thermal equilibrium exists between fluid and particles;

  3. (3)

    The mass transfer coefficient is expressed by the linear driving force (LDF) equation;

  4. (4)

    The gas phase in the adsorption bed can be considered as the ideal gas state;

  5. (5)

    The gradients of the radial concentration and temperature can be ignored in the adsorption bed.

PSA model parameters

In this work, the purification performance of a three-layered bed is investigated using three types of adsorbents: activated carbon, zeolite 5 A, and UTSA-16. The adsorption isotherms for SMR off-gas on each of these adsorbents are studied and validated. The simulation results are then compared with experimental data, demonstrating good accuracy11,25. Table 1 shows the characteristics of the adsorbents and the adsorption bed of the physical properties. Tables 2 and 3 respectively present the DSL parameters and heat of adsorption values for activated carbon, zeolite 5 A, and UTSA-16.

Table 1 Physical properties of adsorbents and adsorption bed.
Full size table
Table 2 DSL parameters and heat of adsorption for activated carbon and zeolite 5 A11.
Full size table
Table 3 DSL parameters and heat of adsorption for UTSA-1625.
Full size table

In Table 3, \({Q_{i1}}\) \({Q_{i2}}\) are parameters in DSL model.

As we can see from Fig. 1, the adsorption equilibrium for the SMR off-gas on activated carbon (a) and zeolite 5 A (b) is parameterized in Ref11. at 293.15 K, while UTSA-16 (c) is parameterized in Ref25. at 298 K. Comparing the experimental results, the simulated results show good agreement, which indicated that the DSL model can effectively predict the breakthrough curves in this work as the adsorption isotherm model.

Fig. 1
figure 1

Adsorption isotherms of SMR off-gas on (a) activated carbon, (b) zeolite 5 A at 293.15 K and (c) UTSA-16 at 298 K (Symbol: experimental data from Refs11,25. ; lines: simulation).

Full size image

Model validation by PSA breakthrough curves

After validated the adsorption isotherm models, the PSA breakthrough curves and cycle models are conducted in Aspen Adsorption platform. Figure 2 presents a schematic diagram of the PSA cycle for a three-layered bed in Aspen Adsorption.

Fig. 2
figure 2

The PSA cycle schematic for three-layered bed system in Aspen Adsorption simulations.

Full size image

For the breakthrough experiment, the inlet stream referred to as “feed”, adsorption bed as “Bed1”, and outlet stream as “product” are used. Table 4 shows the cycle sequence of a three-layered bed PSA process. Figure 3 shows the pressures swing of the adsorption bed during the PSA cycles. The SMR off-gas is fed through the “feed” into “Bed1”, where the mixture gas adsorbed by the adsorbent. During the adsorption (AD) step, high purity hydrogen product can be obtained at the outlet “product”, the adsorption bed pressure remains near 12 bar. During both the depressurization pressure equalization (DPE) and pressurization pressure equalization (PPE) steps, the “valve VI” remains open to maintain the pressure equilibrium between “Bed1” and “Bed2”. Due to the change of pressure, the adsorbates expect H2 flow out of the adsorption bed through “waste” in the blowdown (BD) step. In the purge (PG) step, product hydrogen of high purity from “Bed2” is used to purge “Bed1” through “valve VI” to purify the adsorbent deeply, the adsorption bed pressure drops to 1 atm (atmospheric pressure). Finally, in the pressurization (PR) step, the mixture gas is fed through the inlet “feed”, the pressure in adsorption bed is gradually increased to the adsorption pressure 12 bar, and the PSA cycle is repeated subsequently.

Fig. 3
figure 3

Pressure swing of the adsorption bed PSA cycles.

Full size image
Table 4 Cycle sequence of three-layered bed PSA process.
Full size table

The purification performance is also investigated by constructing a three-layered bed PSA cycle model using the Aspen Adsorption platform. The breakthrough curves between the simulated results and the experimental data are compared in Fig. 4. The experimental data for the layered bed packed with activated carbon and zeolite 5 A is obtained from Jang’s research10, while the data for UTSA-16 is obtained from Grande’s work43. The simulated breakthrough experiments on activated carbon, zeolite 5 A and layered bed packed with activated carbon and zeolite 5 A are respectively conducted under the same operating conditions. The feed flow rate is set at 1.24 × 10−5 kmol/s, and the adsorption pressure is 8 atm. In Fig. 4a, CO is the first breakthrough component in activated carbon due to its higher adsorption affinity for CH4 compared to CO. Approximately 800 s later, CH4 breakthrough occurs as a result of competitive adsorption with CO2, leading to the roll-up phenomenon. There is a deviation between the simulated results and experimental data, which can be attributed to the utilization of the average heat of gas adsorption during the simulation step, while the experimental adsorption process involves heat exchange with the ambient environment. The adsorption affinity of zeolite 5 A is as follows: CO2 > CO > CH4 > H2. Therefore, in Fig. 4b, CH4 is the first component to breakthrough in zeolite 5 A. After, the CO also shows the roll-up phenomenon, which is due to competitive adsorption with the more strongly adsorbed component, CO2. The simulated breakthrough curves of a layered bed packed with activated carbon and zeolite 5 A are also compared to the experimental data in Fig. 4c, with an activated carbon height ratio of 0.7. It can be observed that the breakthrough curves of CH4 and CO occur almost simultaneously. The breakthrough time for CH4 in the layered bed is earlier than that in activated carbon or zeolite 5 A due to the larger adsorption capacity of activated carbon for CH4 compared to zeolite 5 A. The simulated results are in good agreement with the experimental data.This indicates that in the layered bed, the gas propagation rate is slower, which facilitates the absorption of the impurity gas. Figure 4d shows the new type adsorbent of MOF—UTSA-16, which was named by Xiang’s work24. The first breakthrough component occurs at approximately 180 s for CO, which is significantly shorter compared to activated carbon and zeolite 5 A. Longer breakthrough time caused because of the frequency of regeneration is reduced. According to the Fig. 4d, the adsorption affinity of UTSA-16 is as follows: CO2 > CH4 > CO > H2. The adsorption capacity of UTSA-16 towards CO is higher compared to activated carbon and zeolite 5 A, indicated that the UTSA-16 can be used for hydrogen purification effectively.

Fig. 4
figure 4

Simulated (line) and experimental (symbol) breakthrough curves of (a) activated carbon, (b) zeolite 5 A, (c) layered bed packed with activated carbon and zeolite 5 A, and (d) UTSA-16.

Full size image

PSA cycle model

Three-layered bed PSA cycle model

After validated the breakthrough curves for the three types of adsorbents, a six-step three-layered two-bed PSA cycle simulation model is constructed. The operating conditions for the PSA cycle simulation included a feed flow rate of 1.24 × 10−5 kmol/s, an adsorption pressure of 12 bar, a purge-to-feed (P/F) ratio of 0.11, and an adsorption temperature of 298 K. The height ratio for each adsorbent in the adsorption bed is as follows: activated carbon: zeolite 5 A: UTSA-16 = 1:1:1.

Fig. 5
figure 5

The combinations of activated carbon (AC), zeolite 5 A (Z5A), and UTSA-16.

Full size image

The combinations of three adsorbents have been investigated to optimize the purification performance. Typically, the first layer adsorbs a strongly adsorptive component, and the other layers remove light components. Studies have shown that in two-component layers it is better to use activated carbon as the first layer at the beginning of the bed and then zeolite. Yavary et al. found that the adsorption capacity of CO2 on zeolite 5 A increases rapidly and is difficult to desorb, which is not conducive to the purification of the adsorbent. Therefore, CO2 in the mixed gas should be avoided from entering the zeolite 5 A adsorbent layer as much as possible44. In this work, three combinations of the adsorbents are illustrated in Fig. 5. The length of each layer remains constant. Accordingly, in this work, attempts were made to find the optimal position of UTSA-16 in a three-layered bed containing activated carbon and zeolite 5 A in sequence. The PSA unit was simulated using the same configuration as mentioned previously. The purification performance is compared by simulating the PSA cycle for each combination. To evaluate the purification performance, the purity, recovery, and productivity of hydrogen production can be calculated by:

$${\text{H2 purity (\%)}}=\frac{{\int_{{t=0}}^{{{t_{AD}}}} {{{\left. {{{\dot {n}}_{{H_2}}}} \right|}_{product}}dt} }}{{\sum\nolimits_{{i=0}}^{n} {\int_{{t=0}}^{{{t_{AD}}}} {{{\left. {{{\dot {n}}_i}} \right|}_{product}}dt} } }} \times 100\%$$
(12)
$${\text{H2 recovery (\%)}}=\frac{{\int_{{t=0}}^{{{t_{AD}}}} {{{\left. {{{\dot {n}}_{{H_2}}}} \right|}_{product}}dt - \int_{{t=0}}^{{{t_{PG}}}} {{{\left. {{{\dot {n}}_{{H_2}}}} \right|}_{VI}}dt} } }}{{\sum\nolimits_{{i=0}}^{n} {\int_{{t=0}}^{{{t_{AD}}}} {{{\left. {{{\dot {n}}_i}} \right|}_{feed}}dt+\int_{{t=0}}^{{{t_{PR}}}} {{{\left. {{{\dot {n}}_{{H_2}}}} \right|}_{feed}}dt} } } }} \times 100\%$$
(13)

,

$${\text{H2 productivity }}\;\left( {\frac{{mol}}{{kg \cdot h}}} \right){\text{=}}\frac{{\int_{{t=0}}^{{{t_{AD}}}} {{{\left. {{{\dot {n}}_{{H_2}}}} \right|}_{product}}dt} }}{{{{{t_{cycle}}{m_{adsorbent}}} \mathord{\left/ {\vphantom {{{t_{cycle}}{m_{adsorbent}}} {3600}}} \right. \kern-0pt} {3600}}}}$$
(14)

.

The purification performances of three different combinations have been calculated and are presented in Table 5. Combination (a), with UTSA-16 is the first layer near the inlet, exhibits lower purity compared to combinations (b) and (c). However, when UTSA-16 is positioned further from the inlet as in combination (c), it achieve significantly higher purity while maintaining similar recovery and productivity as combination (b). Considering that the fuel cell vehicles require a purity greater than 99.99% during operation to prevent degradation of the fuel cell system45, hydrogen purity holds paramount importance. While the hydrogen purity of combination (a) is only 99.7244%. Therefore, this work focuses on discussing and optimizing combination (c) in the subsequent section.

Table 5 The purification performance of combinations.
Full size table

Performance evaluation of PSA cycle

The effects of adsorption time, P/F ratio, and adsorption pressure on PSA cycle of the three-layered bed are investigated, and the results are presented in Table 6. It is evident from the table that the three-layered bed model can obtain a high hydrogen purity of over 99.99% while maintaining high recovery and productivity simultaneously.

In Fig. 6a, as the adsorption time increases, the longer time the adsorbate stays on the adsorbent, the more SMR off-gas except H2 in the outlet, leads to the purity of hydrogen decreases. However, the recovery and productivity of hydrogen production increase significantly. The P/F ratio is defined in Ref42. , represents the ratio of the amount of hydrogen introduced during the purge step to the amount of hydrogen entering the adsorption bed during the adsorption step. As the P/F ratio increases, the purity of the hydrogen increases, while the recovery and productivity of the process decrease.

Table 6 Parametric study of hydrogen purification performance for three-layered bed model.
Full size table

As shown in Fig. 6b, the hydrogen purity increases dramatically as the P/F ratio ranges from 0.11 to 0.17. However, the growth rate slows down when the ratio reaches from 0.17 to 0.25, indicating that an excessively high P/F ratio may lead to wastage. Meanwhile, Fig. 6c illustrates the effect of adsorption pressure on hydrogen purity, recovery, and productivity for the three-layered bed model. Adsorption pressure plays a crucial role in the mass transfer rate by enhancing molecular adsorption at higher pressures. However, it also results in reduced utilization of the adsorbent. As the results show, as adsorption pressure increases, both the purity and productivity of the process increase, whereas the recovery decreases.

Fig. 6
figure 6figure 6

The effects of (a) adsorption time, (b) P/F ratio, and (c) adsorption pressure on hydrogen purity, recovery, and productivity for three-layered bed model.

Full size image

Optimization by machine learning model

Definition of BP neural network model

Artificial neural networks (ANNs) as one of the most popular machine learning methods, findings widespread application in solving complex problems in engineering applications and scientific fields. ANNs are employed to estimate or approximate functions that rely on a multitude of inputs and are often unknown. Back propagation neural network (BPNN) is one of the common methods for training artificial neural networks. The BPNN architecture typically consists of three layers of neurons: an input layer, a hidden layer, and an output layer. In the hidden layer, a tangent sigmoid transfer function (tansig) is used, while a log-sigmoid transfer function (logsig) is used at the output layer. To train these designed networks, the Levenberg–Marquardt backpropagation (trainlm) with 1000 iterations is selected. Figure 7 shows the structure of the BPNN for the three-layered bed model of the PSA process.

Fig. 7
figure 7

The structure diagram of back propagation neural network.

Full size image

The adsorption time, P/F ratio, and adsorption pressure as three inputs of the BPNN, with the hydrogen purity, recovery, and productivity as three outputs. Table 7 shows the boundary conditions for these three inputs. Using Eqs. (12) to (14) from section “Three-layered bed PSA cycle model”, a total of 117 data sets are generated from the simulated PSA cycle model. Figure 6 illustrates the flow chart of BPNN, providing a straightforward explanation of the optimization algorithm process. To enhance the optimization solution, this work introduces a heuristic algorithm, namely genetic algorithm (GA), to optimize the structure of BPNN.

Table 7 Lower and upper boundaries of inputs.
Full size table

Implementation of genetic algorithm

The GA is a heuristic approach that solves search and optimization problems by drawing inspiration from natural evolution. It mimics the fundamental principles of natural genetics. The working procedure of GA in solving problems can be described as follows:

(1) Chromosome coding

GA manipulates the population of chromosomes, which represent solutions to specific problems in string format. Each position on a chromosome can be considered as a gene. Any representation used for a problem is termed the GA encoding of that problem46.

(2) Initial population

The initial population can be randomly generated, taking into consideration the complexity and size of the problem.

(3) Fitness function

The fitness function is a calculation method used to evaluate the quality of a chromosome. Generally, the objective function is employed to formulate the equation for the fitness function.

(4) Selection

A GA uses selection operations to determine the fitness of the chromosomes in a population. The higher the fitness of chromosomes, the higher the probability of being inherited to the next generation, while chromosomes with lower fitness have a lower probability of being inherited to the next generation or even directly eliminated. The selection strategies in genetic algorithm include roulette wheel selection, random traversal sampling, tournament selection and some other methods.

(5) Crossover

Appropriate crossover can be selected by considering the problem and chromosome representation. The crossover operation strategies include single-point crossover and multi-point crossover.

(6) Mutation

The mutated genes are generated with a certain mutation probability through the random method. The purpose of the mutation operation is to prevent over maturation and avoid omitting important genetic information.

BP neural network optimized by genetic algorithm

In a three-layer neural network, the number of neurons in the input layer is determined by n1, while the number of neurons in the hidden layer is set as n2. The number of hidden layer neurons has a significant impact on the performance of neural networks. Too many neurons can lead to overfitting, while too few may result in underfitting. To address this, the article initially employs an empirical formula to determine the optimal number of hidden layer neurons. The relationship can be expressed as n2 = n1 × 2 + 147,48,49. Consider a PSA cycle with 3 input parameters and 3 output parameters, structured as a neural network with 3 nodes in the input layer, 7 nodes in the hidden layer, and 3 nodes in the output layer. Therefore, the total weight is \(3 \times 7+7 \times 3=42\), and \(7+3=10\) bias values. The total number of optimization parameters of genetic algorithm is \(42+10=52\). The BPNN optimized by genetic algorithm (BPNN-GA) are: initial population; fitness calculation; and selection of genetic operators (selection, crossover, and mutation). Table 8 shows the parameters values used for GA in this work.

Table 8 The parameters values of GA.
Full size table

Figure 8 presents a flow chart illustrating the BPNN-GA procedure, with the black frame on the right representing the flow chart of BPNN. The BPNN-GA process can be divided into three parts. Firstly, the BPNN structure is determined by the inputs and outputs, and the weights and bias values of neural network are obtained. Subsequently, a GA is used to optimize the values of weights and bias for BPNN, yielding the optimal initial values. Finally, training and prediction using existing database are conducted for BPNN-GA. The BPNN-GA process mainly involves initializing the population, calculating the fitness function, and executing genetic operators. The objective of BPNN-GA is to improve the values of initial weights and bias.

The 117 data samples from the Aspen Adsorption platform are divided into three parts: training set, validation set, and test set. The proportion of the three parts usually divided into 70%, 15%, and 15%. The training set helps the neural network learn and fit the model. The validation set is used to stop training early if the network’s performance fails to improve or remains stagnant for several epochs. Meanwhile, the test set is employed to evaluate the generalization performance of the network, without influencing the training process. The test error serves as a metric to evaluate the fit of BPNN.

Fig. 8
figure 8

Flow chart of back propagation neural network optimized by genetic algorithm.

Full size image

Comparison between the BPNN and BPNN-GA models

The correlation coefficient (R) is used to measure the accuracy and performance of both BPNN and BPNN-GA models. The closer that R is to 1, the more accuracy the neural network is. Figures 9 and 10 respectively illustrate the R values between the target output of the Aspen model and the predicted output of BPNN and BPNN-GA models. As we can see, the R values of the targets of Aspen model and the BPNN prediction outputs based on the training set, validation set, test set and whole data set are respectively 09877, 0.9891, 0.9245, and 0.9780. Notably, all R values for the BPNN-GA model are significantly closer to 1 compared to the BPNN model. This indicates that the BPNN-GA model is highly suitable for analyzing and predicting PSA cycle performance. Additionally, the predicted outputs of hydrogen production were compared using both BPNN and BPNN-GA models to evaluate the predictive capabilities. The results, shown in Fig. 11, reveal that the test error for BPNN is 0.0513, which is larger than that the 0.0173 error for BPNN-GA. This further confirms that BPNN-GA provides more effective predictions.

Fig. 9
figure 9

Correlation coefficients (R) of the targets of Aspen model and the BPNN prediction outputs based on (a) training set, (b) validation set, (c) test set and (d) whole data set.

Full size image
Fig. 10
figure 10

Correlation coefficients (R) of the targets of Aspen model and the BPNN-GA prediction outputs based on (a) training set, (b) validation set, (c) test set and (d) whole data set.

Full size image
Fig. 11
figure 11

Evolution process of test sets.

Full size image

Bi-objective optimization by BPNN-GA

After comparing the performances of BPNN and BPNN-GA, the multi-objective optimization is studied. According to the parametric study, it is observed that there is a contradiction between the hydrogen purity and recovery. To achieve both high purity and recovery rate in purification performance, in this section, hydrogen purity in the three-layered bed PSA model is quite high, which is not considered in this optimization. The recovery and productivity are mainly studied in next step. The optimization problem is expressed as follows:

$${\text{Min:}}\;\; - \left( {\alpha {\text{Re}}{{\text{c}}_{{H_2}}}+\left( {1 - \alpha } \right){\text{Pr}}{{\text{o}}_{{H_2}}}} \right)\quad \alpha \in \left[ {0,1} \right]$$
(15)
$${\text{s}}{\text{.t}}{\text{.:}}\;\;{\text{Re}}{{\text{c}}_{{H_2}}}>0.35,\;\;{\text{Pr}}{{\text{o}}_{{H_2}}}>4.0,$$
(16)
$$lb<{x_i}<ub,$$
(17)

where \(\alpha\) represents the weight of hydrogen recovery, \(lb\) and \(ub\) are the boundary conditions of input variables.

Table 8 shows the bi-objective optimal results using the BPNN-GA model, and the practical results obtained from the Aspen model. As the parametric study shows, the weight of α is shown in Table 9. The results show that there are some differences between BPNN-GA model and Aspen model, which are due to different calculation methods of two kinds models. The errors observed are within an acceptable range, which indicated that the BPNN-GA model constitutes a valid optimization algorithm.

Table 9 Comparison results of bi-objective optimal based on BPNN-GA model and practical by Aspen model.
Full size table

Multi-objective optimization by BPNN-GA

A BPNN-GA model is established to achieve multi-objective optimization of hydrogen purity, recovery, and productivity. The multi-objective optimization problem is expressed as follows31,35:

$${\text{Min:}}\;\; - \left( {a{\text{Pu}}{{\text{r}}_{{H_2}}}+b{\text{Re}}{{\text{c}}_{{H_2}}}+c{\text{Pr}}{{\text{o}}_{{H_2}}}} \right)\quad a,b,c \in \left[ {0,1} \right],\;\;a+b+c \in \left[ {0,1} \right]$$
(18)
$${\text{s}}{\text{.t}}{\text{.:}}\;\;{\text{Pu}}{{\text{r}}_{{H_2}}}>v1,\;\;{\text{Re}}{{\text{c}}_{{H_2}}}>v2,\;\;{\text{Pr}}{{\text{o}}_{{H_2}}}>v3,$$
(19)
$$lb<{x_i}<ub,$$
(20)

where a, b, and c are respectively represents the weights of hydrogen purity, recovery, and productivity. \(v1\), \(v2\), and \(v3\) are respectively the lower bound values of hydrogen purity, recovery, and productivity. \(lb\) and \(ub\) are the boundary conditions of input variables. The weights are determined by the actual production cost, and different weights can affect the performance of purification. In this work, the multi-objective optimization goal is to design operating conditions that enable to reach a high value simultaneously of the hydrogen purity, recovery and productivity. With a set as 0.5, b set as 0.25, c set as 0.25. \(v1\) set as 0.99 of lower bound for purity, \(v2\) set as 0.35 of lower bound for recovery, and \(v3\) set as 4.0 mol/kg/h of lower bound for productivity. As the results showed in Table 10, the optimization result satisfied the set optimization conditions.

Table 10 Comparison results of multi-objective optimal based on BPNN-GA model and practical by Aspen model.
Full size table

Conclusion

The hydrogen purification performances of a three-layered bed packed with novel adsorbent UTSA-16, activated carbon and zeolite 5 A were investigated for multi-component SMR off-gas (H2/CH4/CO/CO2 = 76/3/4/17 mol%) using the Aspen Adsorption platform. Firstly, the simulated adsorption isotherms and breakthrough curves were validated against experimental results for each type of adsorbent. Then, a PSA cycle was developed for the three-layered bed to compare the hydrogen purification performance of various adsorbents combinations. The results demonstrated that positioning UTSA-16 far from the inlet significantly boosts hydrogen purity, although at the cost of reduced recovery and productivity. Moreover, this work introduced and investigated a novel optimization method for the PSA cycle using the BPNN-GA model. By considering adsorption time, P/F ration, and adsorption pressure as inputs, and hydrogen purity, recovery, and productivity as outputs. A comparison was then made between the predicted hydrogen production outputs obtained using the BPNN and BPNN-GA models. The test error for BPNN was 0.0513, significantly higher than the 0.0173 error for BPNN-GA, indicating the effectiveness of GA in optimizing the BPNN structure. Moreover, multi-objective optimal results were obtained using the BPNN-GA model. The results showed that introducing the GA model to optimize the BPNN structure allows for more precise determination of hydrogen purification performance under different weights, which is consistent with our expectation. This research clearly demonstrates the feasibility of identifying the optimal operating conditions for the PSA cycle using the BPNN-GA model. In this work, two machine learning algorithms of BPNN and BPNN-GA were used and compared to predict and optimize hydrogen purification performance. For further work, other algorithms like support vector machine can be used for comparison to find the most suitable optimization algorithm for hydrogen purification.