Pith. sign in

REVIEW 3 major objections 6 minor 32 references

Influences of Uncertainties in Thermodynamic Models on Pareto-optimized Dividing Wall Columns for Ideal Mixtures

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that in Pareto-optimized dividing wall columns, vapor-liquid equilibrium model uncertainty — not caloric property uncertainty — is what destroys product purity, and that the losses grow as the column gains theoretical…

desk verdict Careful simulation study that fills a real gap; the central ranking holds within stated uncertainty ranges, but the combined screen should test intermediate perturbations before the numbers are used. read the letter →

arxiv 2505.15193 v1 pith:5DRXWFJV submitted 2025-05-21 physics.chem-ph physics.comp-ph

Lea Trescher , David Mogalle , Patrick Otto Ludl , Tobias Seidel , Michael Bortz , Thomas Gruetzner This is my paper · ORCID
classification physics.chem-phphysics.comp-ph
keywords DividingWallColumnuncertaintythermodynamicmodelssensitivityvapor-liquidequilibriumParetooptimizationVmindiagramdistillation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that when a dividing-wall column is Pareto-optimized for energy and stage count, the dominant operational risk from thermodynamic model error sits in the vapor-liquid equilibrium: activity coefficients and pure-component vapor pressures. Across three near-ideal ternary mixtures and four stage counts each, worst-case purity losses grew with total stage number and reached roughly 3 to 6 mol% under combined VLE uncertainties, while perturbations of vapor enthalpy and enthalpy of vaporization stayed below about 0.5 mol%. The authors identify the vapor pressure of the medium boiler as decisive independent of mixture or column size, and the products of the binary split with the highest minimum vapor demand as the most affected. The practical stakes are a design rule: direct data-quality and model-refinement efforts at the difficult binary split and at low mid-boiler concentrations, and recognize that adding stages can enlarge worst-case purity losses instead of buying safety.

What carries the argument

The argument is carried by fixed Pareto-optimal DWC designs from the authors' earlier NQ-curve optimization, simulated rigorously stage-to-stage under perturbed property models. The perturbation machinery is a Margules-type term added to NRTL activity coefficients, anchored to ±10% changes in binary infinite-dilution activity coefficients with thermodynamic consistency, plus multiplicative ±2% scaling of pure-component vapor pressures and 1–2% scaling of enthalpy terms. The organizing identity is the Vmin diagram — a shortcut map of the minimum boil-up required for each sharp binary split — because the split with the highest Vmin peak sets the column's vapor demand, and its products are the ones whose operating lines sit closest to the VLE. Losses arise when a perturbed VLE shifts the equilibrium line toward or across the operating line, and McCabe-Thiele diagrams are used to show why one product can remain protected when its split is much easier than the difficult split.

What would settle it

Re-run the same combined 512-scenario screening on a ternary mixture whose experimentally calibrated uncertainty ranges differ from Table 3, for example with caloric errors near 5% or activity-coefficient errors below 5%, and check whether the ranking still holds: VLE over caloric, medium-boiler vapor pressure decisive, and higher-stage columns losing more purity than lower-stage columns. A single mixture where a light- or heavy-boiler vapor-pressure perturbation produces the largest loss, or where the 56-stage column is less sensitive than the 25-stage column, would bound the claim.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that for steady-state Pareto-optimized dividing wall columns separating close-to-ideal ternary mixtures, model uncertainty in the vapor-liquid equilibrium is the dominant threat to product purity while caloric-property uncertainty is negligible. Screening all combinations of ±10% infinite-dilution activity coefficients and ±2% pure vapor pressures across four stage counts per mixture, the authors find worst-case purity losses that grow with total stage number and reach roughly 3 to 6 mol% when both VLE uncertainties act together; enthalpy of vaporization and vapor enthalpy perturbed by 1–2% cause losses below about 0.5 mol%. They identify the vapor pressure of the medium boiler as decisive independent of mixture and stage count, and the products belonging to the binary split with the highest minimum vapor demand, marked by the highest peak in the Vmin diagram, as the most affected. The side product B is the most sensitive product overall, except in the methanol/ethanol/butanol system where the medium/heavy-boiler split is easy and that heavy product stays nearly pure.

Load-bearing premise

The assumed uncertainty ranges in Table 3 — ±10% for infinite-dilution activity coefficients, ±2% for pure vapor pressures, ±1% for enthalpy of vaporization, and ±2% for vapor enthalpy — are treated as representative for all three mixtures even though they were estimated mainly from one mixture, and the authors explicitly disclaim general validity.

Editorial extensions

If this is right

  • Design-stage thermodynamic data efforts should concentrate on VLE quantities, especially the medium boiler's vapor pressure and the infinite-dilution activity coefficients of the highest-Vmin binary split, rather than on caloric property models.
  • A Pareto-optimal DWC with more total stages is not automatically safer: if the VLE model is wrong, purity losses grow with stage number, so an extra-stages safety margin can widen worst-case product giveaway.
  • Combined VLE uncertainties act approximately additively in this setting, so screening the individual vapor-pressure and activity-coefficient corner cases separately and summing the worst cases gives a practical bound without running a full 512-scenario sweep.
  • Mixtures with one clearly easy binary split can shield the corresponding product from thermodynamic uncertainty, as seen for the heavy product in the methanol/ethanol/butanol system.
  • The same stage-dependent logic applies to any uncertainty that shifts the equilibrium line relative to the operating line, so process-variable and VLE uncertainties can be expected to compound in the same parts of the column.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the stage-dependence generalizes, common oversizing practice for DWCs should be reconsidered: adding stages to buy margin may increase worst-case sensitivity, and a natural extension is to optimize stage allocation against worst-case VLE rather than nominal VLE.
  • Because the Table 3 uncertainty ranges were calibrated mainly against one mixture, applying the ranking to a new system requires re-estimating those ranges; a system with larger caloric uncertainty could overturn the conclusion that caloric properties are insignificant.
  • The Vmin-peak rule suggests a cheap screening test for any candidate ternary system: compute the Vmin diagram, identify which binary split has the highest minimum boil-up, and concentrate VLE measurement on that binary's low-concentration range; this prediction can be tested on non-ideal mixtures.
  • In dynamic operation the vapor split is fixed by construction and cannot be re-tuned, so the same VLE perturbation could produce larger transient purity excursions than the steady-state losses reported here.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper investigates how uncertainties in thermodynamic models (activity coefficients, pure vapor pressures, and vapor/evaporation enthalpies) affect product purities in Pareto-optimized dividing wall columns (DWCs) for three near-ideal ternary mixtures at four different total stage counts. Using a stage-to-stage MESH simulation with the nominal optimized column specifications fixed, the authors screen individual and combined perturbations and report worst-case purity losses. They find that VLE-related uncertainties dominate over caloric ones, that losses increase with total stage number when the VLE or internal vapor/liquid ratio is perturbed, and that the medium-boiler vapor pressure is the most influential property. The results are interpreted using Vmin diagrams, and the joint effects of simultaneous uncertainties are presented as approximately additive superpositions.

Significance. The paper addresses a practically important gap: thermodynamic model uncertainty is rarely considered in DWC design optimization. The systematic screening across mixtures and stage numbers, and the connection to Vmin-diagram features, provides a useful framework for identifying critical properties and for understanding why extra stages can increase operational risk. The simulation setup is described in enough detail to re-implement, and the results are internally consistent. However, the headline conclusions are conditional on the assumed uncertainty ranges, which are mainly validated for one mixture and applied uniformly; this limits the generality of the "decisive" rankings. If the requested sensitivity checks are provided, the framework would be considerably more robust.

major comments (3)
  1. [Section 2.5, Table 3] The uncertainty magnitudes (γ∞ ±10%, p° ±2%, Δhv ±1%, hv ±2%) are derived from comparisons that are shown mainly for System 1 (Fig. 5), then applied uniformly to all three mixtures without equivalent data for Systems 2 and 3. Because the conclusions are comparative ("VLE decisive", "pB° decisive"), the relative sizes of these ranges are load-bearing. If, for example, the real pure-component vapor-pressure error were significantly smaller than 2% for System 2, the pB°-dominance claim could fail. The caveat in Section 3.1 ("no claim of general validity") mitigates this, but the abstract and highlights present the conclusions unconditionally. Please either provide uncertainty estimates for all mixtures or perform a sensitivity analysis of the key results to the assumed ranges (e.g., ±5% γ, ±1% p°) to demonstrate robustness.
  2. [Section 3.2, Fig. 10] The combined scenarios use only the extreme perturbation levels (±10% γ, ±2% p°) and omit the nominal and any intermediate values. This screening design cannot detect non-monotonic responses in product purity, and it limits the support for the "addition of individual influences" statement in Section 3.2 (Fig. 8); the superposition claim is verified only for the extremes. Please test at least one intermediate perturbation level for the most critical combinations (e.g., the pB° + ABC worst cases), or provide a justification for why the extrema bound the losses, particularly given that the individual-scenario screening (Section 3.1) did include the nominal value.
  3. [Section 3.1, Table 4] The comparison between VLE and caloric properties is not on an equal footing: the assumed uncertainty for activity coefficients (±10%) is an order of magnitude larger than that for Δhv (±1%) and hv (±2%). The highlight "Caloric properties are unsignificant" is therefore a statement about these specific ranges, not about the models in general. Please either perform a symmetric comparison at equal perturbation levels (e.g., ±10% for all properties) or explicitly state in the abstract and conclusions that the ranking is conditional on the ranges identified as realistic. This is related to the first major comment but applies specifically to the VLE-versus-caloric claim.
minor comments (6)
  1. [Section 2.2, Table 1] The text states that the mixtures have "close-to-ideal behavior (i.e., activity coefficients γi ≈ γj ≈ 1)", but Table 1 lists infinite-dilution activity coefficients up to 1.229 for System 2 (methanol–butanol). Please clarify the criterion used, or state that the activity coefficients are close to unity in the concentration ranges of interest.
  2. [Section 2.5, Eq. (3)] The typeset equation for the Margules perturbation appears garbled (missing summation limits and unreadable bracket structure). Please provide a cleanly typeset version with correct indices and parentheses.
  3. [Section 3.1, Table 4] The definition Δxi = 0.95 − xi should specify that losses are measured relative to the 95 mol% product specification, not necessarily to the actual nominal purity, which may be slightly above 0.95.
  4. [Section 3.2, Figs. 10–11] The Self-Organizing Patch Plots lack axis or colorbar labels. Adding a legend explaining the binary encoding (0 = negative deviation, 1 = positive deviation) and the color scale for purity loss would make the figures interpretable without referencing the text in detail.
  5. [Abstract] The novelty claim "For the first time" is not substantiated relative to prior work. Please cite the closest works (e.g., [18] on simple columns) and specify what is new for DWCs, so the claim is verifiable.
  6. [Highlights] The highlight "Vapor pressure of medium boiler is decisive independent of mixture or stages" should be qualified with "within the investigated uncertainty ranges" to avoid overgeneralization, consistent with the caveat in Section 3.1.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the purity-loss results are simulation outputs from independently calibrated thermodynamic-model perturbations, not re-fitted quantities.

full rationale

The paper's central results are worst-case product-purity losses obtained by applying fixed perturbation ranges (Table 3) to thermodynamic models and simulating the resulting steady-state DWCs. The uncertainty magnitudes are calibrated in Section 2.5 against independent DDB/NIST experimental data and literature ranges, not against the target purity losses. The simulated losses are therefore outputs, not re-fitted inputs. The optimized column designs are taken from the authors' previous work [9], but this is a legitimate input to the present study rather than a circular definition of the present conclusions. The perturbation scheme is attributed to Burger et al. [18], which includes a co-author of this paper, but that citation supplies an externally published method, not the load-bearing conclusion; the ranking of VLE versus caloric properties emerges from the simulations and is not imposed by the method. The statement in Section 3.1 that 'no claim of general validity is made here' is an honest limitation about the chosen uncertainty ranges, not a circular step. The fact that the conclusions would change under different assumed uncertainty magnitudes is a standard assumption-sensitivity concern, not a circularity. No equation in the paper reduces a predicted effect to its calibrated input by construction, and no fitted parameter is renamed as a prediction. The paper is self-contained as a parametric uncertainty study, so the appropriate circularity finding is none.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a stack of modeling assumptions: the equilibrium stage model, the nominal NRTL/Antoine property models, the Burger/Mathias perturbation scheme, the specific uncertainty magnitudes in Tab. 3, the Vmin shortcut framework, and steady-state simulation. None of these are derived in this paper; they are pulled from the prior literature or chosen by the authors. The free parameters are the four uncertainty magnitudes, which are estimated from experimental data and applied uniformly across mixtures.

free parameters (4)
  • Activity coefficient perturbation magnitude at infinite dilution (γij∞) = ±10%
    Chosen as representative uncertainty from comparing nominal NRTL predictions to DDB/NIST experimental VLE data (Fig. 5). Applied uniformly to all binary pairs and mixtures.
  • Pure vapor pressure uncertainty (pi°) = ±2%
    Derived from model-data scatter in vapor pressure; applied as multiplicative factor 0.98-1.02 to each component.
  • Enthalpy of vaporization uncertainty (Δhv) = ±1%
    Chosen as realistic variation from data; found to have small but stage-dependent effect.
  • Vapor enthalpy uncertainty (hv) = ±2%
    Chosen as realistic variation; effects negligible in all tested cases.
assumptions (7)
  • domain assumption Equilibrium stage model with MESH equations accurately represents DWC separation performance
    Used in Section 2.4 for all simulations; standard for distillation design but an idealization.
  • domain assumption NRTL model with Aspen databank parameters is the correct nominal thermodynamic model
    Section 2.1: nominal VLE is calculated with NRTL and extended Antoine; all perturbations are relative to this model.
  • domain assumption The Margules-based perturbation term (Eq. 3) produces thermodynamically consistent and realistic VLE uncertainty
    Adopted from Burger et al. [18]; the paper does not independently validate this perturbation scheme for the studied mixtures beyond T-x-y diagrams.
  • ad hoc to paper The chosen uncertainty magnitudes are representative of real model errors for all three mixtures
    Section 2.5: same uncertainties applied to each mixture based on one example (System 1) and literature; this is a load-bearing choice for the quantitative conclusions.
  • domain assumption Vmin diagrams (infinite stages, pure products, constant relative volatilities) provide meaningful indicators for finite-stage DWC behavior
    Used in Section 3 to interpret which binary split limits performance; inherited from shortcut methods.
  • domain assumption Steady-state simulation is sufficient to assess design sensitivity
    Explicitly stated in Section 1 and 4; dynamic verification is ongoing work.
  • domain assumption The three near-ideal mixtures are representative of mixtures for which NRTL activity coefficients are approximately 1
    Section 2.2; real non-ideal mixtures are deferred to future work.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Influences of Uncertainties in Thermodynamic Models on Pareto-optimized Dividing Wall Columns for Ideal Mixtures." pith.science (2026). https://pith.science/paper/5DRXWFJV

@misc{pith2026250515193,
  author       = {Pith},
  title        = {Pith review of: Influences of Uncertainties in Thermodynamic Models on Pareto-optimized Dividing Wall Columns for Ideal Mixtures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DRXWFJV}},
  note         = {Machine review of arXiv:2505.15193}
}
read the original abstract

This article examines the effect of individual and combined uncertainties in thermodynamic models on the performance of simulated, steady-state Pareto-optimized Dividing Wall Columns. It is a follow-up of the previous work analogously treating deviations in process variables. Such deviations and uncertainties that may even be unknown during the design process can significantly influence the separation result. However, other than process variables, uncertainties in thermodynamics are usually not systematically considered during design. For the first time, the effects of uncertain thermodynamic properties on Pareto-optimized DWCs with different numbers of stages and for different mixtures are presented and compared qualitatively and quantitatively. Depending on the number of stages and mixture characteristics, particularly critical properties are identified. On the one hand, this provides information on aspects requiring special attention prior to design, and on the other hand, it also indicates in which section of the DWC a stage supplement might be most beneficial.

Figures

Figures reproduced from arXiv: 2505.15193 by the authors.

Figure 2
Figure 2. Pareto-curves for the separations of Systems 1 - 3 in products with 95 mol% purity in DWCs. Dashed rectangle: Pareto-optimal columns used in the following. In order to understand the designations used in this work, [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Scheme of DWC with binary splits assigned to the different sections [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Nominal composition profiles. Solid lines: main column. [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figures from the paper (2 more)
Figure 7
Figure 7. Figure 7: Maximum losses in product purities in case of individual uncertainties in thermodynamics with [PITH_FULL_IMAGE:figures/full_fig_p024_7.png]
Figure 9
Figure 9. Figure 9: VLE of BC separation and operation lines in lower main column sections of System 1 and 2. Shown are [PITH_FULL_IMAGE:figures/full_fig_p030_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    M., & Grützner, T

    Waibel, Y., Trescher, L., Ränger, L. M., & Grützner, T. (2023). First multiple dividing wall column: Design and operation. Chemical Engineering Research and Design, 193, 132-144

    work page 2023

  2. [2]

    Kaibel, G. (1987). Distillation columns with vertical partitions. Chemical engineering & technology, 10(1), 92-98

    work page 1987

  3. [3]

    J., & Skogestad, S

    Halvorsen, I. J., & Skogestad, S. (2011). Energy efficient distillation. Journal of Natural Gas Science and Engineering, 3(4), 571-580

    work page 2011

  4. [4]

    Kiss, A. A. (2013). Advanced distillation technologies: design, control and applications. John Wiley & Sons

    work page 2013

  5. [5]

    C., Skogestad, S., & Lien, K

    Christiansen, A. C., Skogestad, S., & Lien, K. (1997). Complex distillation arrangements: extending the Petlyuk ideas. Computers & chemical engineering , 21, S237-S242

    work page 1997

  6. [6]

    Asprion, N., & Kaibel, G. (2010). Dividing wall columns: fundamentals and recent advances. Chemical Engineering and Processing: Process Intensification , 49(2), 139- 146

    work page 2010

  7. [7]

    Dejanović, I., Matijašević, L., & Olujić, Ž. (2010). Dividing wall colu mn—A breakthrough towards sustainable distilling. Chemical Engineering and Processing: Process Intensification, 49(6), 559-580

    work page 2010

  8. [8]

    M., Preißinger, U., & Grützner, T

    Ränger, L. M., Preißinger, U., & Grützner, T. (2019). Multiple Dividing‐Wall Columns–Current Status and Future Prospects. Chemie Ingenieur Technik, 91(4), 420- 428. Page 39 of 40

    work page 2019

Show all 32 references
  1. [9]

    relevant

    and in this present work, are limited to steady-state simulations. Verifications using dynamic models are part of ongoing work. In this subsequent work, the effects of uncertainties in thermodynamic models from the nominal case on the same steady -state, Pareto -optimal column...

  2. [10]

    M., Mogalle, D., Seidel, T., Bortz, M., & Grützner, T

    Trescher, L., Ränger, L. M., Mogalle, D., Seidel, T., Bortz, M., & Grützner, T. (2025). Pareto-optimal Dividing Wall Columns for Ideal Mixtures and Influences of Deviations in Process Variables. Computers & Chemical Engineering, 109045

    2025

  3. [11]

    J., & Skogestad, S

    Halvorsen, I. J., & Skogestad, S. (2000). Distillation theory. Encyclopedia of separation science, 1117-1134

    2000

  4. [12]

    Górak, A., & Sorensen, E. (Eds.). (2014). Distillation: fundamentals and principles. Academic Press

    2014

  5. [13]

    Sattler, K. (2012). Thermische Trennverfahren: Grundlagen, Auslegung, Apparate. John Wiley & Sons

    2012

  6. [14]

    D., Henley, E

    Seader, J. D., Henley, E. J., & Roper, D. K. (2006). Separation process principles

    2006

  7. [15]

    Larsen, A. H. (1986). Data quality for process design. Fluid Phase Equilibria, 29, 47-58

    1986

  8. [16]

    Mathias, P. M. (2014). Sensitivity of Process Design to Phase Equilibrium. A New Perturbation Method Based Upon the Margules Equation. Journal of Chemical & Engineering Data, 59(4), 1006-1015

    2014

  9. [17]

    Mathias, P. M. (2016). Effect of VLE uncertainties on the design of separ ation sequences by distillation –Study of the benzene –chloroform–acetone system. Fluid Phase Equilibria, 408, 265-272

    2016

  10. [18]

    Mathias, P. M. (2017). Guidelines for the analysis of vapor –liquid equilibrium data. Journal of Chemical & Engineering Data, 62(8), 2231-2233

    2017

  11. [19]

    Burger, J., Asprion, N., Blagov, S., & Bortz, M. (2017). Simple perturbation scheme to consider uncertainty in equations of state for the use in process simulation. Journal of Chemical & Engineering Data, 62(1), 268-274

    2017

  12. [20]

    J., & Skogestad, S

    Halvorsen, I. J., & Skogestad, S. (1999). Optimal operation of Petlyuk distillation: steady-state behavior. Journal of Process Control, 9(5), 407-424

    1999

  13. [21]

    M., Trescher, L., von Kurnatowski, M., Bortz, M., & Grützner, T

    Ränger, L. M., Trescher, L., von Kurnatowski, M., Bortz, M., & Grützner, T. (2021). Vapor and liquid split flexibility in dividing wall columns in relation to the theoretical stage allocation. Chemical Engineering and Processing-Process Intensification, 163, 108365

    2021

  14. [22]

    Ge, X., Ao, C., Yuan, X., & Luo, Y. (2014). Investigation of the effect of the vapor split ratio decision in design on operability for DWC by numerical simulation. Industrial & Engineering Chemistry Research, 53(34), 13383-13390

    2014

  15. [23]

    J., & Skogestad, S

    Halvorsen, I. J., & Skogestad, S. (2003). Minimum energy consumption in multicomponent distillation. 1. V min diagram for a two-product column. Industrial & Engineering Chemistry Research, 42(3), 596-604

    2003

  16. [24]

    M., Preißinger, U., & Grützner, T

    Ränger, L. M., Preißinger, U., & Grützner, T. (2018). Robust initialization of rigorous process simulations of multiple dividing wall columns via Vmin diagrams. ChemEngineering, 2(2), 25

    2018

  17. [25]

    M., Grützner, T., & Bortz, M

    Seidel, T., Ränger, L. M., Grützner, T., & Bortz, M. (2022). Simultaneous simulation and optimization of multiple dividing wall columns. Computers & Chemical Engineering, 157, 107607

    2022

  18. [26]

    Heertjes, P. M. (1960). Determination of Vapour-Liquid Equilibria of Binary Mixtures. Chemical and Process Engineering, 41, 385-386

    1960

  19. [27]

    Page 40 of 40

    Jin Z., Hu A., Liu K., Chinese Journal of Chemical Engineering, 1(1), 47-51, 1993. Page 40 of 40

    1993

  20. [28]

    D., Hollenbach, G

    Kesselman, W. D., Hollenbach, G. E., Myers, A. L., & Humphrey, A. E. (1968). Vapor-liquid equilibrium data for benzene-alkyl-benzene systems. Journal of Chemical & Engineering Data, 13(1), 34-36

    1968

  21. [29]

    Saito, S. (1969). Separation of Hydrocarbons. 2. Vapor− Liquid Equilibriums of Normal Paraffin− Aromatic Systems. Asahi Garasu Kogyo Gijutsu Shoreikai Kenkyu Hokoku, 15, 397-407

    1969

  22. [30]

    EFCE Working Party on Distillation, Absorption, and Extraction. (1969). Recommended test mixtures for distillation columns. Institution of Chemical Engineers (Groot-Brittanje)

    1969

  23. [31]

    H., & Hasse, H

    Stöbener, K., Klein, P., Horsch, M., Küfer, K. H., & Hasse, H. (2016). Parametrization of two-center Lennard-Jones plus point-quadrupole force field models by multicriteria optimization. Fluid Phase Equilibria, 411, 33-42

    2016

  24. [32]

    M., von Kurnatowski, M., Bortz, M., & Grützner, T

    Ränger, L. M., von Kurnatowski, M., Bortz, M., & Grützner, T. (2020). Multi- objective optimization of dividing wall columns and visualization of the high - dimensional results. Computers & Chemical Engineering, 142, 107059

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.