Modeling and Simulation of FBAs

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Pressure swing adsorption (PSA) is used to separate multi-component mixtures in various industries. Various challenges were faced in modeling and dynamic simulation of PSA process since it contains different cycles in operation. In recent research (Sankararao and Gupta, 2007) it was found that the computer time taken to solve the mathematical models of PSA using linear driving force (LDF) approximation was excessive mainly for the blow-down step. Making a simple model for the fixed bed adsorbers (FBAs) will be the main objective in this study. Objectives of this study include, understanding the conventional pressure swing adsorption models being used for simulation, reviewing the recent improved models, simulating the models using mathematical techniques, analyzing the results.

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Improvement in Modeling and Simulation of Fixed Bed Adsorbers (FBAs) Abubacker Siddieq M.Tech PDE 500015447 (R670211001) UPES, Dehradun Date:26/04/2013 Under the guidance of, Dr. S.K.Gupta Distinguished Professor Department of Chemical Engg . UPES, Dehradun

Improvement in Modeling and Simulation of Fixed Bed Adsorbers (FBAs):

Abstract Pressure swing adsorption (PSA) is used to separate multi-component mixtures in various industries. Various challenges were faced in modeling and dynamic simulation of PSA process since it contains different cycles in operation. In recent research (Sankararao and Gupta, 2007) it was found that the computer time taken to solve the mathematical models of PSA using linear driving force (LDF) approximation was excessive mainly for the blow-down step. Making a simple model for the fixed bed adsorbers (FBAs) will be the main objective in this study. Objectives of this study include, understanding the conventional pressure swing adsorption models being used for simulation, reviewing the recent improved models, simulating the models using mathematical techniques, analyzing the results.

Abstract :

*Johanna Schell, Nathalie Casas., Seminar Frontiers in Energy Research

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PSA - process description Source : Process Design Case Study from Dept. of Chemical Engineering, Carnegie Mellon University

PSA - process description:

Cycle steps in PSA [11] Bed 1 Bed 2 Product Product Blowdown Purge Repressurization Feed t ads t pur t b t pr

Cycle steps in PSA[11]:

PSA cycles [11] Skarstrom PSA cycle Modified Skarstrom PSA cycle including pressure equalization Two bed PSA cycle including dual ended pressure equalization and no purge

PSA cycles[11]:

Modeling of fixed bed Adsorber Differential control volume

Modeling of fixed bed Adsorber:

Model equations of Adsorption column Material balance equation: LDF model derived by Jee et al., (2004) Rigorous model derived by Sankararao and Gupta (2007)

Model equations of Adsorption column:

Model equations of Adsorption column control volume across the adsorbent pellet Macro-void balance: concentrations at point 1, 2, 3 are c i b , c i p , q i p respectively.

Model equations of Adsorption column:

Model equations of Adsorption column Energy balance equation: Energy balance in LDF model by Jee et al., (2004) Energy balance in Rigorous model by Sankararao and Gupta (2007)

Model equations of Adsorption column:

Model equations of Adsorption column Pressure drop equation: Pressure relation in Jee et al., (2004) Pressure relation in Rigorous model by Sankararao and Gupta (2007) overall mass balance: ( P/RT= C b t ) Ideal gas law: (Low Reynolds number Ergun Equation)

Model equations of Adsorption column:

Numerical method of lines (MOL) Basic steps of numerical method of lines: 1. Space differencing 2. ODE integration In method of lines, we retain the index i to account for variations of the dependent variable c with x, but we treat ‘ t’ as a continuous variable. Thus, we keep the derivative c t (with respect to t) term, and substitute the derivatives c x or c xx (with respect to x ) terms with a difference approximations; this will lead a system of ODEs in t . Each of the numerical methods differs in: Method of approximation of spatial derivatives Number of points/nodes Accuracy (including any tendency towards oscillatory behavior) Stability Simulation time required

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The ode integrator chosen in this study is ode15s of MATLAB ® . ‘ode15s’ is a variable-order solver for stiff problems. It is based on the numerical differentiation formulas (NDFs). The NDFs are generally more efficient than the closely related family of backward differentiation formulas (BDFs), also known as Gear's methods. The ode15s properties let you choose among these formulas, as well as specifying the maximum order for the formula used. About ode15s

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Typical breakthrough curve for adsorption and desorption steps and its significance ( Knaebel , 2002) Significance of breakthrough curves

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RESULTS AND DISCUSSION

RESULTS AND DISCUSSION:

Assumptions [6] Ideal gas behavior Axially dispersed plug flow The equilibrium of adsorption is described by Henry’s isotherm, Mass transfer across the boundary layer surrounding the solid particles is characterized by the external-film mass transfer coefficient, k f . Uniform cross-sectional void fraction Uniform adsorbent properties along the axial coordinate, Negligible pressure drop and Negligible radial gradients dz

Assumptions[6]:

Learnings Phase 1 Phase 2 Phase 3 Phase 4 Integration Tolerance 1.0e -06 1.0e -06 1.0e -06 1.0e -06 Finite difference Central difference Upwind difference Upwind difference Upwind difference Number of axial nodes 100 100 100 100 Total number of ode 100 400 679+1 679+1 Equilibrium Isotherm Linear (Henry’s) Lang-Freund combined Lang-Freund combined Lang-Freund combined Maximum time taken to solve 1.57 s 8.46 s 58.47 s 111.55 s Maximum no. of ode routine calls 853 885 13286 10056

Learnings :

Learnings Time (s) Numerical diffusion in Phase-1:

Learnings :

Learnings Rectification of numerical diffusion with upwind difference in subsequent phases: PHASE-3 PHASE-2

Learnings :

( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 4 LSTP/min Simulation of O2-N2-Zeolite 5A system O 2 saturated bed, Air Feed

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Simulation of O2-N2-Zeolite 5A system ( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 2 LSTP/min O 2 saturated bed, Air Feed

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( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 6 LSTP/min Simulation of O2-N2-Zeolite 5A system O 2 saturated bed, Air Feed

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( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 4 LSTP/min for different feed and initial condition Simulation of O2-N2-Zeolite 5A system N 2 saturated bed, pure O 2 Feed

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( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 6 LSTP/min for different feed and initial condition Simulation of O2-N2-Zeolite 5A system N 2 saturated bed, pure O 2 Feed

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( ___ ) Model predicted breakthrough curve for O 2 -N 2 -Zeolite 5A system (in phase 2) and (□) experimental data for feed at 2 LSTP/min for different feed and initial condition Simulation of O2-N2-Zeolite 5A system N 2 saturated bed, pure O 2 Feed

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simulated profile of concentration of oxygen in the bed for O2-N2-Zeolite 5A system Simulation of O2-N2-Zeolite 5A system

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simulated profile of concentration of nitrogen in the bed for O2-N2-Zeolite 5A system Simulation of O2-N2-Zeolite 5A system

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simulated profile of temperature in the bed for O 2 -N 2 -Zeolite 5A system Simulation of O2-N2-Zeolite 5A system

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simulated profile of pressure in the bed for O2-N2-Zeolite 5A system (in phase 4) Simulation of O2-N2-Zeolite 5A system

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Simulation of O2-N2-Zeolite 5A system

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Simulation of O2-N2-Zeolite 5A system

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Conclusions A code has been written to solve the coupled partial differential equations (i.e., the multicomponent LDF fixed bed adsorber) using numerical method of lines in MATLAB ® effectively. Simulation studies were performed and presented in four different phases. During these studies, we found that, T he numerical method chosen is taking important part in CPU time for solving. It was necessary to increase the number of axial nodes (finite difference discretization points) to reach the required accuracy and reduce the false (numerical) diffusion, oscillations in calculation, But at the same time, computer time and number of iterations are also keep increasing. H igher order upwind difference were the optimal choice between accuracy and oscillation while central difference suffers numerical diffusion and serious oscillation. The code written to simulate in this (phase 4) study was found to be performing better than the earlier studies because, it elapsed 112 s for the simulation of O 2 –N 2 on Zeolite 5A (for a process time of 500 s and 100 number of nodes) but it was 280 s (for LDF model) in the study of Sankararao and Gupta (2007). These results give a confidence to work ahead in improving the blowdown step simulation.

Conclusions :

Future work This study was performed with an objective of reducing the simulation time taking for PSA cycle especially for blowdown step. It was found that method of lines is giving better performance. We could have a strong feel about achieving faster simulation by using higher order discretization formulae. In this study we used first and second order finite difference approximations. From some experiences, it was found that the programs compiled in C (compiled language) runs seven times faster than the MATLAB ® codes. Some free tools are available to convert the MATLAB codes to FORTRAN. They can be used to analyze the performance using compiled languages like C, C++, and FORTRAN to extend this study. And In this study only LDF model was solved and analyzed. These problems can be also formulated and analyzed for the rigorous model developed by Sankararao and Gupta (2007).

Future work :

[1] B.Sankararao, & S.K.Gupta. (2007). Modeling and simulation of fixed bed adsorbers (FBAs) for multi-component gaseous separations. Computers and Chemical Engineering , 31:1282-1295. [2] B.Sankararao, & S.K.Gupta. (2007). Multi-objective optimization of pressure swing adsorbers for air separation. Ind. Eng. Chem , 46:3751-3765. [3] Basmadjian, D. (1999). The Art of Modeling in Science and Engineering. Washington, D.C. [4] Bird, R.B., Stewart, W.E., & Lightfoot, E.N. (2002). Transport phenomena. New york: Wiley. [5] Davis, M. E. (n.d.). Numerical methods and Modeling Chemical Engineers. John Wiley & Sons. [6] Froment, G. F., & Bischoff, K. B. (1979). Chemical reactor analysis and design. Wiley. [7] Henley, E. J., & Seader, J. D. (2006). Separation Process Principles. John Wiley & Sons. [8] Inglezakis, V. J., & Poulopoulos, S. G. (2006). Adsorption, Ion Exchange and Catalysis. Elsevier Science & Technology Books. [9] Karimi, A., Vafajoo, L., Safecordi, A. A., & Kazemeini, M. (n.d.). Scientific Research and Essays, 5(17) , 2391-2399. [10] Knaebel, K.S. (2002). A “How To” Guide for Adsorber Design. Ohio: Adsorption Research. [ 11] Knaebel, K.S., Ruthven, D.M., & Farooq, S. (1994). Pressure Swing Adsorption. New York: VCH Publishers. [ 12] Schiesser. (1991). The Numerical Method of Lines: Integration of Partial Differential Equations. San Diego: Academic Press. [ 13] Suzuki, M. (1990). Adsorption Engineering. Amsterdam: Tokyo and Elsevier Science Publishers. [14] Aspen ADSIM Adsorption Reference Guide. (2001). Aspen Technology. Bibliography

Bibliography:

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