이산화탄소 PSA 모델링 및 전산모사

장대준, 민준호, 문기호

현대중공업(주) 산업기술연구소 환경연구실

Modeling and Simulation of CO2 PSA

Daejun Chang, Joonho Min, and Kiho Moon

Environment Research Department, Hyundai Industrial Research Institute,

Hyundai Heavy Industries CO., LTD.

1 Introduction

Separation of carbon dioxide from combustion flue streams is highly encouraged due to its role in greenhouse effect as well as its use as chemical substance. While several processes including liquefaction, membrane, PSA, and hybrids of them have been suggested to serve the task, PSA and its hybrid with membrane process are considered to be the most promising.

Numerous investigations in the field of PSA have been dedicated to analysis of recovery of weak adsorbates, especially hydrogen. In spite of process analogy to weak-adsorbate PSA, the strong-adsorbate carbon dioxide PSA is distinguished from the former, in view of significant adsorptive amount and relatively low-pressure operation with vacuum recovery. These distinctions prevent naive extensions of weak-adsorbate PSA to strong-adsorbate ones.

This study presents a non-isothermal LDF model with a proper dimensionless formulation and a robust numerical algorithm. Two isotherm models based on coupled Langmuir and ideal adsorbed solution(IAS) theory are also taken into consideration. The results of simulation are compared with experimental ones in view of productivity, purity, and recovery ratio.

2 Modeling

Based on LDF assumption, the mass conservation equations are expressed by the equations.

[eqn: {partial c_i } over partialt + partial over partialz (u c_i ) - D_b {partial^2 c_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_i -q_i )]                         (2)

Assuming the adsorbent and gas phases are not in thermal equilibrium, the energy conservation equations are generally expressed by the equations.

[eqn: {partial {sum c_i H_i^g }} over {partial t} + {partial {u sum c_i H_i^g } } over {partial z} -D_b {partial^2 {sum c_i H_i^g }} over {partial z^2} + 1-epsilon_t over epsilon_t sum_j { dot q_j H_j^g*} +{A h_T} over {epsilon_t } (T_b -T_s ) =0]    (3)

[eqn: {partial sum q_i H_i^s (T_s )} over {partial t} + {partial c_p H^p } over {partial t} - sum_j dot q_j H_j^g* + {A h_T} over {1-epsilon_t } (T_s -T_b ) = 0]              (4)

Introduction of characteristic scales and straightforward nondimensionalization lead to the following dimensionless expressions.

[eqn: 1 over K partial over { partial tau} left({Py_i over Theta_b}right) &+& {partial } over {partial zeta} left(U_b {{P y_i} over Theta_b} right) &-&1 over Pe_mb {partial^2 } over {partial zeta^2} left(Py_i over Theta_b right) &+&N_i left(Pi_i Py_i over Theta_b -Q_i right)=0]      (5)

[eqn: {partial Q_i} over {partial tau} = t_c h_i P left(Pi_i y_i over Theta_b - Q_i over P right)]                           (6)

[eqn: sum left(Py_i over Theta_b right) Lambda_i^g left[ 1over K {partial Theta_b } over{partial tau}+ U {partial Theta_b}over{partial zeta} - 1 over Pe_mb {partial^2 Theta_b}over{partial zeta^2} right] +(Theta_b -Theta_s ) left[M_b - sum_j Lambda_j^g k_j dot{Q_j} right] =0]      (7)

[eqn: left{ sum_i k_i Q_i Lambda_i^s + eta_T right} {partial Theta_s} over {partial tau} + 1over delta^g sum_j k_j dot{Q_j} [Delta h_j + (Theta_s - Theta_b ) delta_j^s ]~ + (Theta_b - Theta_s ) left[ M_s +sum_k k_k dot{Q_k} Lambda_k^g right] =0]   (8)

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 partition function K is a constant for isothermal linear isotherm and a nonlinear coefficient for coupled Langmuir model. For IAS theory, it is commonly estimated by iterative method.

It is K that clearly distinguishes the behavior of strong-adsorbate PSA from that of weak-adsorbate ones. Its magnitude is in the range of O(1) for hydrogen PSA while O(100) for carbon dioxide PSA. The statement means that under same operating condition the response of the former is hundred times as fast as that of the latter. Consequently, for the latter the leading contribution comes from convective mass transfer and adsorption rate, not from the gas phase accumulation.

The characteristics of multiple time scales should be also addressed. The characteristic time scale in dimensionless form is O(1) for Eq. (5) and [eqn: O(t_c h_i )] for Eq. (6). If the latter is not O(1), Eqs. (5) and (6) are not in the same mode, and numerical integration can give rise to some significant problem. For example, if the latter is far greater than O(1), the adsorption rate is considerably faster than the bed dynamics, and equilibrium model is more plausible.

When two-phase model is assumed, the adsorption contribution to energy balance should be taken into careful consideration. As for the gas phase, the leaving or adsorbing flow has no effect on gas-phase temperature. The same argument holds for the adsorbent phase. Two phases interact with each other only through the heat transfer and the enthalpy difference of transferred mass.

3 Results and Discussion

The pilot CO2 PSA of Hyundai Heavy Industries is taken as a simulated system. It consists of subsidiary two PSA units. The first PSA serves concentration of feed stream, of which carbon dioxide fraction is usually less than 0.15. The second PSA carries out the main purification. In order to enhance recovery and process performance, a residual stream from the second PSA is returned to the first PSA. The adsorbent is zeolite. The cycle time is about 660sec, and the bed length L and diameter are 1.8 and 0.2m, respectively.

The isotherm model was found important to predict process performance, especially for recovery and product purity. While the isotherms of pure components are found to obey Langmuir model, the expression of mixture isotherm based on coupled Langmuir model is subject to considerable discrepancy from experimental data, mainly due to the strong interaction between adsorbing species. Introduction of IAS theory mitigated the discrepancy.

Figure 1 shows the measured and simulated temperature changes on the axial position of 1/8, 3/8, 5/8, and 7/8 of bed length. Results based on coupled Langmuir model usually predicts small temperature change  in adsorption step since the model underestimates the carbon dioxide adsorption in the pressure range from 0.2 to 0.8 atm. Relatively precise approximation by IAS theory leads to more quantitatively plausible results.

Figure 2 presents the process performance of recovery and purity with respect to productivity. Coupled Langmuir model considerably underestimates the recovery and purity while IAS theory does well. The product purity for coupled Langmuir model could not be improved above 0.96, even by total rinse. These arguments state that IAS model is highly recommended for modelling of carbon dioxide PSA.

4 Conclusion

A nonisothermal linear-driving-force model was proposed for CO2 PSA. Nondimensionalization indicated that the leading contributions come from the convective mass transfer and adsorption rate. Formulation based on the indication results in a rapid and precise numerical simulation of CO2 PSA. In simulating Hyundai Heavy Industries' pilot CO2 PSA, it was found that isotherm model has a predominant effect on the process performance as well as on the dynamic behavior. Strong interaction between the adsorbed species was not precisely reflected by coupled Langmuir model, but by IAS (Ideal Adsorbed Solution) theory. The productivity, recovery ratio, and purity was quantitatively predicted by the latter.

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.

4. J. Min, K. Moon, and D. Chang, "Modelling and Robust Simulation of Strong-Adsorbate PSA," 1998 Fall Conference of KIChE, Kwangju.

5. Y. Kim et al., HWAHAK KONGHAK, 36(4), pp. 562 (1998).

Figure 1. Temperature profiles at 1/8, 3/8, 5/8, and 7/8 of bed length.

Figure 2. Effect of rinse flow rate on recovery, productivity, and purity.