References

References

How to cite

Anand, M. (2026). Dynamic Column Breakthrough Simulator (Version 2026.09v4) [Computer software]. https://github.com/Mk-learning-python07/dynamic-column-breakthrough

Please also cite the underlying sources for whichever preset and theory your result depends on — they are listed below, and the preset and model sources a run used are repeated in its exported report.

Sources

Every entry follows APA 7th edition. "Accessed" is the date the entry was last checked against the publisher.

Theory

Reference	Used for	Accessed
Ruthven, D. M. (1984). Principles of adsorption and adsorption processes. Wiley.	Column mass/energy/momentum balances; all 'Ruthven Eq.' numbers; default axial dispersion D_L = 0.7D_m + 0.5v_0d_p (Eq 7.6) and Eqs 7.8/7.10; Knudsen + Bosanquet; LDF validity 1>β>0.5	2026-09-22
Wilkins, N. S., Rajendran, A., & Farooq, S. (2021). Dynamic column breakthrough experiments for measurement of adsorption equilibrium and kinetics. Adsorption, 27(3), 397–422. https://doi.org/10.1007/s10450-020-00269-6	DCB framing; compilation of the thermal Reality Check correlations (Eqs 25–28)	2026-09-22
Wilkins, N. S., Sawada, J. A., & Rajendran, A. (2022). Quantitative microscale dynamic column breakthrough apparatus for measurement of unary and binary adsorption equilibria on milligram quantities of adsorbents. Industrial & Engineering Chemistry Research, 61(20), 7032–7051. https://doi.org/10.1021/acs.iecr.2c00115	Measured q* mass balance in Experimental validation	2026-09-22

Correlations and mixture equilibrium

Reference	Used for	Accessed
Myers, A. L., & Prausnitz, J. M. (1965). Thermodynamics of mixed-gas adsorption. AIChE Journal, 11(1), 121–127. https://doi.org/10.1002/aic.690110125	IAST mixture equilibrium	2026-09-22
Glueckauf, E., & Coates, J. I. (1947). Theory of chromatography. Part IV. The influence of incomplete equilibrium on the front boundary of chromatograms and on the effectiveness of separation. Journal of the Chemical Society, 1315–1321. https://doi.org/10.1039/jr9470001315	Linear driving force (LDF) rate law	2026-09-23
Glueckauf, E. (1955). Theory of chromatography. Part 10: Formulae for diffusion into spheres and their application to chromatography. Transactions of the Faraday Society, 51, 1540–1551. https://doi.org/10.1039/TF9555101540	LDF coefficient 15D/R² for spherical particles	2026-09-22
Wakao, N., & Funazkri, T. (1978). Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds: Correlation of Sherwood numbers. Chemical Engineering Science, 33(10), 1375–1384. https://doi.org/10.1016/0009-2509(78)85120-3	Film coefficient Sh = 2 + 1.1 Sc^1/3 Re^0.6; Wakao axial dispersion option γ1 = 20/ε (Ruthven Eq 7.11)	2026-09-22
Edwards, M. F., & Richardson, J. F. (1968). Gas dispersion in packed beds. Chemical Engineering Science, 23(2), 109–123. https://doi.org/10.1016/0009-2509(68)87056-3	Edwards–Richardson dispersion option (Ruthven Eq 7.9)	2026-09-22
Wicke, E. (1973). Bedeutung der molekularen Diffusion für chromatographische Verfahren [Significance of molecular diffusion for chromatographic processes]. Berichte der Bunsengesellschaft für physikalische Chemie, 77(3), 160–171. https://doi.org/10.1002/bbpc.19730770305	Wicke axial dispersion option, γ1 = 0.45 + 0.55ε (Ruthven Eq 7.8)	2026-09-23
Fuller, E. N., Schettler, P. D., & Giddings, J. C. (1966). A new method for prediction of binary gas-phase diffusion coefficients. Industrial & Engineering Chemistry, 58(5), 18–27. https://doi.org/10.1021/ie50677a007	Molecular diffusivity D_m	2026-09-22
Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.	Pressure drop (momentum balance)	2026-09-22
Wen, C. Y., & Yu, Y. H. (1966). A generalized method for predicting the minimum fluidization velocity. AIChE Journal, 12(3), 610–612. https://doi.org/10.1002/aic.690120343	u_mf and fluidization margin (Computed params)	2026-09-22
Leva, M., & Grummer, M. (1948). Heat transfer to gases through packed tubes: Effect of particle characteristics. Industrial & Engineering Chemistry, 40(3), 415–419.	h_in in thermal Reality Check (Eq 27)	—
Yagi, S., & Kunii, D. (1957). Studies on effective thermal conductivities in packed beds. AIChE Journal, 3(3), 373–381. https://doi.org/10.1002/aic.690030317	k_z in thermal Reality Check (Eq 28)	2026-09-22
Sieder, E. N., & Tate, G. E. (1936). Heat transfer and pressure drop of liquids in tubes. Industrial & Engineering Chemistry, 28(12), 1429–1435. https://doi.org/10.1021/ie50324a027	External wall coefficient h_out = 0.027 Re^0.8 Pr^1/3 in the thermal Reality Check (Eq 26)	2026-09-22

Physical property data

Reference	Used for	Accessed
Linstrom, P. J., & Mallard, W. G. (Eds.). (n.d.). NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology. Retrieved September 23, 2026, from https://doi.org/10.18434/T4D303	Shomate coefficients for the gas heat capacity C_p,gas (Check vs NIST)	2026-09-23

Materials and isotherms

Reference	Used for	Accessed
Haghpanah, R., Majumder, A., Nilam, R., Rajendran, A., Farooq, S., Karimi, I. A., & Amanullah, M. (2013). Multiobjective optimization of a four-step adsorption process for postcombustion CO₂ capture via finite volume simulation. Industrial & Engineering Chemistry Research, 52(11), 4249–4265. https://doi.org/10.1021/ie302658y	Zeolite 13X preset: bed/particle properties (Table 3)	2026-09-22
Wilkins, N. S., & Rajendran, A. (2019). Measurement of competitive CO₂ and N₂ adsorption on Zeolite 13X for post-combustion CO₂ capture. Adsorption, 25(2), 115–133. https://doi.org/10.1007/s10450-018-00004-2	Zeolite 13X preset: CO₂/N₂ DSL isotherms	2026-09-22
Wilkins, N. S., McKinnon, D. M., Nguyen, T. T. T., Pai, K. N., Chachra, G., Song, P., Lotfollahzade Moghaddam, A., Toy, R., & Rezaei, S. (2025). An explicit dual-site BET isotherm model for the prediction of nonideal competitive and cooperative adsorption equilibrium. Industrial & Engineering Chemistry Research, 64(51), 24808–[end page]. https://doi.org/10.1021/acs.iecr.5c02627	DSBET isotherm model	2026-09-22
Dantas, T. L. P., Luna, F. M. T., Silva, I. J., Jr., Torres, A. E. B., de Azevedo, D. C. S., Rodrigues, A. E., & Moreira, R. F. P. M. (2011). Carbon dioxide–nitrogen separation through adsorption on activated carbon in a fixed bed. Chemical Engineering Journal, 169(1–3), 11–19. https://doi.org/10.1016/j.cej.2010.08.026	Activated Carbon preset: Toth isotherms + bed properties (Tables 1, 8)	2026-09-22
Rajagopalan, A. K., Avila, A. M., & Rajendran, A. (2016). Do adsorbent screening metrics predict process performance? A process optimisation based study for post-combustion capture of CO₂. International Journal of Greenhouse Gas Control, 46, 76–85. https://doi.org/10.1016/j.ijggc.2015.12.033	Mg-MOF-74 and UTSA-16 presets: isotherm parameters only	2026-09-22
Nguyen, T. T. T., Lin, J.-B., Shimizu, G. K. H., & Rajendran, A. (2022). Separation of CO₂ and N₂ on a hydrophobic metal organic framework CALF-20. Chemical Engineering Journal, 442(Part 1), Article 136263. https://doi.org/10.1016/j.cej.2022.136263	CALF-20 (pellet) preset: isotherms and properties (Table 2)	2026-09-22

Numerics

Reference	Used for	Accessed
Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., & Woodward, C. S. (2005). SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3), 363–396. https://doi.org/10.1145/1089014.1089020	SUNDIALS CVODE (primary integrator)	2026-09-22
Gardner, D. J., Reynolds, D. R., Woodward, C. S., & Balos, C. J. (2022). Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 48(3), Article 31. https://doi.org/10.1145/3539801	SUNDIALS CVODE (current release)	2026-09-22
Demmel, J. W., Gilbert, J. R., & Li, X. S. (1999). An asynchronous parallel supernodal algorithm for sparse Gaussian elimination. SIAM Journal on Matrix Analysis and Applications, 20(4), 915–952. https://doi.org/10.1137/S0895479897317685	SuperLU_MT sparse linear solver inside CVODE	2026-09-22
Randall, C. R. (2024). scikit-SUNDAE: Python bindings to SUNDIALS differential algebraic equation solvers [Computer software] (SWR-24-137). https://github.com/NatLabRockies/scikit-sundae https://pypi.org/project/scikit-sundae/	Python bindings to CVODE	2026-09-22
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., . . . van Mulbregt, P. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 17(3), 261–272. https://doi.org/10.1038/s41592-019-0686-2	Fallback integrators (solve_ivp LSODA/BDF), root finding	2026-09-22
Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., Fernández del Río, J., Wiebe, M., Peterson, P., . . . Oliphant, T. E. (2020). Array programming with NumPy. Nature, 585(7825), 357–362. https://doi.org/10.1038/s41586-020-2649-2	Array computation throughout the engine	2026-09-22

Fallback integrators

Reference	Used for	Accessed
Petzold, L. (1983). Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM Journal on Scientific and Statistical Computing, 4(1), 136–148. https://doi.org/10.1137/0904010	Adams/BDF switching in LSODA	2026-09-22
Hindmarsh, A. C. (1983). ODEPACK, a systematized collection of ODE solvers. In R. S. Stepleman et al. (Eds.), Scientific computing (IMACS Transactions on Scientific Computation, Vol. 1, pp. 55–64). North-Holland.	ODEPACK, source of LSODA	2026-09-22
Byrne, G. D., & Hindmarsh, A. C. (1975). A polyalgorithm for the numerical solution of ordinary differential equations. ACM Transactions on Mathematical Software, 1(1), 71–96. https://doi.org/10.1145/355626.355636	Variable-order multistep basis of LSODA; cited for BDF fallback	2026-09-22
Shampine, L. F., & Reichelt, M. W. (1997). The MATLAB ODE suite. SIAM Journal on Scientific Computing, 18(1), 1–22. https://doi.org/10.1137/S1064827594276424	Variable-order BDF formulation of SciPy BDF	2026-09-22

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Developed by Muthukrishnan Anand, with the assistance of Claude (Anthropic).

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