강흡착 성분을 위한 PSA 모델링 및 전산모사

민준호, 문기호, 장대준

현대중공업(주) 산업기술연구소 에너지□환경연구실

Modeling and Robust Simulation of Strong-Adsorbate PSA

J. Min, K. Moon, and D. Chang

Energy□Environment Research Department, Industrial Research Institute,

Hyundai Heavy Industries CO., LTD.

1 Introduction

The concern of conventional PSA systems has chiefly concentrated on purification of weakly adsorbate components and subsequently high pressure operation. For hydrogen purification, operating pressure of tens of atmosphere are not uncommon. In modeling the processes the gas-phase accumulation or time derivative of gas-phase concentration is considered one of leading contributions.

Recently, PSA process for strong adsorbates attracts research attention especially for VOC removal and CO2 recovery. If the simulation algorithms for weak-adsorbate PSA are directly extended to strong-adsorbate one, it cannot guarantee robustness of rapid convergence and small numerical errors. The main reason is that gas-phase accumulation is negligibly small compared with convection and adsorption. Those intricacies are more complicated owing to difference of the characteristic time scale of bed dynamics from that of particle adsorption.

This study presents a proper dimensionless formulation and a robust numerical algorithm. There are rigorous consideration on numerical errors and calculation time, followed by simulation result of pilot CO2 PSA of Hyundai Heavy Industries.

2 Modeling

The mass conservation equations are as follow, with axial pressure gradient ignored.

[eqn: {partial c_b,i } over partialt + partial over partialz (u_b c_b,i ) - D_b {partial^2 c_b,i } over {partialz^2 } + {1-epsilon_t } over epsilon_t partialq_i over partialt =0]                    (1)

[eqn: partialq_i over partialt = h_i (q_i^ast - q_i ) = h_i (K_i c_b,i -q_i )]                         (2)

Here, the isotherm for each component in a mixture is generalized by [eqn: q_i^ast `=` K_i ({bold c}, T) cdot c_i`(P, T)], where K depends on mixture composition as well as temperature.

The main difference in modeling of strong-adsorbate PSA from that of weak-adsorbate one originates from the magnitude of K; it is in the range of hundreds for the former, but close to unity for the latter. In other words, K for strong adsorbate is in the range of hundreds, and the mass in adsorbents is hundreds times as large as that in gas phase.

Most of traditional approaches to nondimensionalization are based implicitly or explicitly on the consideration that the first term or gas-phase accumulation of Eq. (1) should balance convection. If the strategy is extended straight to strong-adsorbate system with low pressure, the formulated equation becomes stiff, and necessarily requires extremely many integration, leading to global error accumulated. In consequence, it cannot confirm robust algorithm.

In strong-adsorbate PSA the formulation should be so carried out that the convection balances the adsorption. In order to deduce proper equations and algorithm, the magnitude of contribution terms must be compared in dimensionless sense, and the matrices for calculation made diagonally dominant. Appropriately formulated governing equations can be easily solved by FDM, FEM, and orthogonal collocation method. Based on the discussion, suitable dimensionless equations are as follow:

1) Component mass conservation;

[eqn: 1 over {P K_c } {partial P y_i} over {partial tau} + {partial (U_b y_i ) } over {partial zeta} - 1 over Pe_mb {partial^2 y_i } over {partial zeta}^2 + N_i left(Pi_i y_i - Q_i /P right) = 0]                (3)

2) Overall mass conservation:

[eqn: 1 over {PK_c} {partial P} over {partial tau} + {partial U_b } over {partial zeta} +sum_j N_j left(Pi_j y_j - Q_j /P right) = 0]                           (4)

3) Mass transfer equation:

[eqn: {partial Q_i } over partialtau = t_c h_i P left(Pi_i y_i - Q_i over P right) = k P left(Pi_i y_i - Q_i over P right)]                            (5)

The dynamics of the governing equations are dependent on the magnitude of K and [eqn: k]. When the magnitude of K is equal to order one, the gas-phase accumulation term is comparable to convection and adsorption. In case of strong-adsorbate PSA, the magnitude of K is extremely large, the gas-phase accumulation term is negligible.

The parameter [eqn: k] manifests the relative rate of adsorption compared to bed dynamics. When [eqn: k] is large, Eq. (5) becomes stiff, and local equilibrium assumption is more plausible. In another extreme of small [eqn: k], the adsorption is sluggish, and numerical integration of Eq. (5) is simple. In commercial PSA, the processes are so designed that the convection balances the adsorption, and consequently that [eqn: k] is of order one. In other words, if the convection is larger in magnitude than adsorption([eqn: k<<1]), the adsorption is not sufficient. If convection is smaller([eqn: k>>1]), the process performance should be improved by reducing the cycle time. In consequence, two effects are same in magnitude ([eqn: k = O(1)]).

The governing equations Eqs. (3) to (5) are for isothermal cases. The axiom of balance of convection and adsorption also holds for nonisothermal cases, where governing equations contains much more terms. The results shown in next section corresponds to nonisothermal cases, though not explicitly stated.

3 Results and Discussion

The pilot CO2 PSA of Hyundai Heavy Industries is taken as a simulated system. The isotherms of pure components are found to obey Langmuir model, and the isotherms in a mixture are supposed to be of coupled Langmuir model. The cycle consists of pressurization, adsorption, rinse, and desorption. The cycle time tc is about 660sec, and the bed length L and diameter are 1.8 and 0.3m, respectively. The feed is assumed to be a mixture of CO2 and N2 with the former mole fraction equal to 0.7. The governing equations are solved by finite difference method.

Figure 1 presents the axial distribution of gas-phase concentration and adsorbed amount of CO2 for [eqn: Delta t /t_c]=0.001, 0.01, 0.1, and [eqn: Delta z/L]=0.001 in the adsorption step. The results with time difference smaller than 0.01 are practically indistinguishable from the numerically exact solution. Figure 2 shows more rigorous analysis of truncation error. For the spatial difference, it is found that the simulation is convergent within tolerance of 0.001 if the step size is less than 0.01.

The result of good convergence with relatively large time and spatial differences guarantees robust simulation of the process. It takes two minutes or less to simulate one cycle by ordinary personal computers. It is found that starting from a clean bed the system needs 10 cycles to reach a steady state in terms of concentration and temperature. Consequently, a half an hour is sufficient to get a periodically steady state.

Figure 3 presents numerically exact solutions and results with gas-phase accumulation neglected. Apparently, the neglect does not cause any significant deviation. Consequently, in the strong-adsorbate PSA system gas-phase accumulation term is not important.

Figure 4 shows axial distribution of adsorbed amount at the end of each step in the periodically steady state. The gas-phase concentration is not important as described, and the distribution of adsorbed amount dominantly determines the performance of the process.

4 Conclusion

In strong-adsorbate PSA the gas-phase accumulation is not one of the leading contributions, and the adsorption balances the convection. In addition, the adsorption rate into particles is in the same magnitude of concentration propagation velocity. Based on these consideration, the formulated equation results in diagonally dominant matrices and subsequently robust convergence, even for relatively large time and spatial differences. For the nonisothermal simulation of HHI pilot CO2 PSA, it is found that it takes about ten cycles for a initially clean bed to reach a periodically steady state.

Reference

1. D. M. Ruthven, Principles of Adsorption and Adsorption Processes, John Wiley & Sons, 1984, New York.

2. R. T. Yang, Gas Separation by Adsorption Processes, Butterworths, 1987, Boston.

3. D. M. Ruthven, S. Farooq, and K. S. Knaebel, Pressure Swing Adsorption, VCH, 1994, New York.