혼합좌표계를 이용하는 Finite Element Method에 대한 충진층의 유체-고체계 해석-I. 충진층 흡착관의 수치모사

박판욱; 김인실; 조태제; 정용옥

HWAHAK KONGHAK, Vol.30, No.5, 594-604, October, 1992

Analysis of Fluid-Solid System in a Fixed-Bed by Finite Element Method Using Mixed Coordinate-I. Numerical Simulation of a Fixed-Bed adsorption Column

박판욱, 김인실, 조태제, 정용옥

초록

원통좌표와 구좌표로 구성된 혼합 좌표계를 이용하여 흡착제 충진층 흡착관의 수치해를 구하고자 finite ele- ment method(FEM)를 흡착관의 모델식에 적용하였다. 이 혼합 좌표계는 두 좌표계를 연결하는 flux term을 쉽게 처리할 수 있었다. 세 가지 Peclet 수에 대한 breakthrough 곡선은 수학적인 해석해와 잘 일치하였으며, 관의 입구에서 Dirichlet 경계조건은 근사해와 해석해의 편차를 일으켰다. Danckwerts경계조건은 계가 획산 율속이더라도 경계에서 확산속을 억제함을 알 수 있었으며, Peclet수가 적을 경우의 해의 큰 편차는 관의 입구에서 확산속 때문이다. 본 simulation 결과는 Danckwerts 경계조건의 세 가지 Peclet수에 해석해와 잘 일치하였다.

The Finite Element Method(FEM) was formulated for numerical solution of a fixed-bed adsorp-tion column using mixed coordinate system which consists of a cylindrical and spherical coordinates. The mixed coordinate system is implemented by connecting of interfacial resistances between two coordinates. The breakthrough curves for three Peclet numbers are simulated and then compared with an exact analytic solution. The finite element solution obtained by adopting the Dirichlet boundary conditions as the inlet gives larger disagreements with an exact analytic solution. The merit of the Danckwerts boundary condition is that it prohibits the diffusion flux at the boundary even though the system is diffusion dominated. The larger disagreements in solutions especially when the Peclet number is small might be caused by the diffusion flux at the inlet. The simulation results agree good with analytical solutions for three defferent Peclet numbers.

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Carey GF, Finlayson BA, Chem. Eng. Sci., 30, 587 (1975)
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Park YO, Ph.D. Thesis, University of Houston (1989)

[Referenced By]

[1] Meyer OA, Weber TW, AIChE J., 13, 457 (1967)

[2] Lee RG, Weber TW, Can. J. Chem. Eng., 47, 54 (1969)

[3] Deans HA, Lapidus L, AIChE J., 6, 656 (1960)

[4] McGurie ML, Lapidus L, AIChE J., 11, 85 (1965)

[5] Froment GF, Chem. Eng. Sci., 7, 29 (1961)

[6] Froment GF, Ind. Eng. Chem., 59, 18 (1967)

[7] Lerou JJ, Froment GF, Chem. Eng. Sci., 32, 853 (1977)

[8] Kheshgi HS, Hagan PS, Reyes SC, Pirkle JC, AIChE J., 34, 1373 (1988)

[9] McGreavy C, Cresswell DL, Can. J. Chem. Eng., 47, 583 (1969)

[10] Feick J, Ouon D, Can. J. Chem. Eng., 48, 205 (1970)

[11] Villadsen JV, Stewart WE, Chem. Eng. Sci., 22, 1483 (1967)

[12] Stewart WE, Villadsen JV, AIChE J., 15, 28 (1969)

[13] Finlayson BA, Chem. Eng. Sci., 26, 1081 (1971)

[14] Hansen KW, Chem. Eng. Sci., 26, 1555 (1971)

[15] Young LC, Finlayson BA, Ind. Eng. Chem. Fundam., 12, 413 (1973)

[16] Karanth NG, Hughes R, Chem. Eng. Sci., 29, 197 (1974)

[17] Ferguson NB, Finlayson BN, AIChE J., 20, 540 (1974)

[18] Sharma CS, Hughes R, Chem. Eng. Sci., 34, 613 (1979)

[19] Gros JB, Bugarel R, Chem. Eng. J., 13, 165 (1977)

[20] Villadson J, Michelsen ML, "Solution of Differencial Equation Models by Polynomial Approximation," Prentice-Hall Inc., Englewood Cliffs, New Jersey (1978)

[21] Jensen KF, Ray WH, Chem. Eng. Sci., 37, 199 (1982)

[22] Raghavan NS, Duncan TW, Ruthven DM, Chem. Eng. J., 26, 223 (1983)

[23] Liapis AI, Rippin DWT, Chem. Eng. Sci., 33, 593 (1978)

[24] Liapis AI, Litchfield RJ, Chem. Eng. Sci., 35, 2366 (1980)

[25] Marcussen L, Chem. Eng. Sci., 37, 299 (1982)

[26] Raghavan NS, Ruthven DM, AIChE J., 29, 923 (1983)

[27] Raghavan NS, Ruthvan DM, Chem. Eng. Sci., 39, 1201 (1984)

[28] Giudice SD, Tratta A, Chem. Eng. Sci., 33, 697 (1978)

[29] Mills PL, Lai S, Dudukovic MP, Ramachandran PA, Ind. Eng. Chem. Res., 27, 191 (1988)

[30] Mills PL, Lai S, Dudukovic MP, Ramachandran PA, Comput. Chem. Eng., 12, 37 (1988)

[31] Gardini L, Servida A, Morbidelli M, Carra S, Comput. Chem. Eng., 9, 1 (1985)

[32] Carey GF, Finlayson BA, Chem. Eng. Sci., 30, 587 (1975)

[33] Finlayson BA, "Nonlinear Analysis in Chemical Engng," McGraw-Hill, New York (1980)

[34] Khanna R, Seinfield JH, Adv. Chem. Eng., 13, 113 (1987)

[35] Garga-Garza O, Dudukovic MP, Comput. Chem. Eng., 6, 131 (1982)

[36] Hlavacek V, Rompay PV, Chem. Eng. Sci., 36, 1587 (1981)

[37] Tezduyar TE, Deans HA, Park YO, Park PW, World Congress III of Chem. Eng., 247, 913-257 in Reactor Design. Sept. 21-23, Tokyo, Japan (1986)

[38] Tezduyar TE, Park YO, Comput. Meth. Mech. Engng., 59, 307 (1986)

[39] Tezduyar TE, Park YO, Deans HA, Int. J. Numer. Methods Fluids, 7, 1013 (1986)

[40] Park YO, Dean HA, Tezduyar TE, Int. J. Numer. Methods Fluids, 11, 769 (1990)

[41] Park PW, Park YO, Fourth World Congress of Chem. Eng., 6. 1-8, June 16-21, Karlsruhe, Germany (1991)

[42] Rasmuson A, Neretnieks I, AIChE J., 26, 686 (1980)

[43] Raghavan NS, Ruthven DM, AIChE J., 29, 922 (1983)

[44] Deisler PF, Wilhelm RH, Ind. Eng. Chem., 45, 1219 (1953)

[45] Bubcock RE, Green DW, Perry RH, AIChE J., 12, 922 (1966)

[46] Rosen JB, J. Chem. Phys., 20, 387 (1952)

[47] Park YO, Ph.D. Thesis, University of Houston (1989)