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Hatta number

Dimensionless comparison of liquid-phase reaction with liquid-side transport in a specified reactive gas–liquid absorption model.

Version
v1 · 2026-10-17 · History
Domain-specific #
14179
Domain group
Applied Sciences & Engineering
Origin domain
Engineering & Design (beyond software)
Subdomain
Gas Liquid Reactive Absorption → Engineering & Design (beyond software)
Aliases
Hatta number, Ha

Core Idea

The Hatta number (\(\mathrm{Ha}\)) compares reaction of an absorbed gas in a liquid with its liquid-side transport under a declared model. Its ordered reaction-to-transport quotient is an internal part of the calculation; the reacting system, kinetic law, and transfer reference make it a specific gas–liquid index.[ref-dac51c504c59][ref-db4d17aa8b70] In a first-order film model, \(\mathrm{Ha}=\sqrt{k_1D_A}/k_L^0\): reaction constant \(k_1\) and liquid diffusivity \(D_A\) appear above the physical liquid-side transfer coefficient \(k_L^0\). This formula is conditional.[^ref-db4d17aa8b70]

Scope of Application

The number travels literally between reactive gas–liquid systems when each states its kinetic law and liquid-side transport reference.

  • First-order film: use the stated \(k_1\), \(D_A\), and \(k_L^0\) form.[^ref-db4d17aa8b70]
  • Pseudo-first-order film: replace \(k_1\) with \(k_2B^0\) only under the handbook's specified treatment.[^ref-db4d17aa8b70]
  • Packed CO2–MEA: use Ha to assess liquid-film discretisation; the accessible abstract does not give its exact formula.[^ref-80319a410778]
  • CO2–DEA membrane contactor: calculate Ha and enhancement \(E\) separately under its reaction and film model.[^ref-2127f7659384]
  • O2–S(IV) bubbling system: use its own kinetic/diffusive quotient and liquid transfer coefficient, not the CO2 formulas.[^ref-5d86dbfbe107]

Clarity

Ha answers how reaction compares with liquid-side transport within the chosen model. It is neither observed gas uptake nor the enhancement factor \(E\).[^ref-db4d17aa8b70] In the CO2–DEA study, \(E\) approaches Ha only where Ha exceeds one and the limiting enhancement \(E_\infty\) greatly exceeds Ha; they cannot be treated as equal along the entire modeled path.[^ref-2127f7659384] Ask which reaction law, transport coefficient, and availability limit a reported number assumes before treating it as a regime judgment.

Manages Complexity

Ha compresses reaction and transport inputs into one dimensionless comparison. That can guide whether a liquid film needs detailed modeling, as in the reported packed CO2–MEA use.[^ref-80319a410778] The compression does not erase chemistry: changing reaction order, contact model, or available liquid reactant can change the calculation or its interpretation. A large Ha alone does not establish an instantaneous reaction or predict the observed flux.[ref-db4d17aa8b70][ref-2127f7659384]

Abstract Reasoning

Identify the absorbing gas and reactive liquid, then fix the transport model and physical transfer reference. Choose the kinetic law and only its required concentration inputs; calculate Ha and check the model's interpretation limits.[^ref-db4d17aa8b70] For the first-order film formula, increasing \(k_1\) with other inputs fixed raises Ha, while increasing \(k_L^0\) lowers it. Neither change alone proves a particular measured uptake.[^ref-db4d17aa8b70]

Knowledge Transfer

The same comparison works across unlike gas–liquid contacts when each supplies its own inputs. Chen and colleagues' O2–S(IV) bubbling model defines Ha through a positive-root kinetic/diffusive term divided by liquid transfer coefficient; their estimated value near 1.4 checks a proposed rapid-reaction regime only for those conditions.[^ref-5d86dbfbe107] The packed CO2–MEA use asks a different modeling question.[^ref-80319a410778] Ratio is the internal ordered quotient; it does not itself supply the chemistry. Beyond reactive gas–liquid absorption, a similar comparison needs its own defined metric and scales.

Relationships to Other Abstractions

Local relationship map for Hatta numberParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Hatta numberDOMAINPrime abstraction: Ratio — is part ofRatioPRIME

Current abstraction Hatta number Domain-specific

Parents (1) — more general patterns this builds on

  • Hatta number is part of Ratio Prime

    An ordered reaction-to-transport ratio is an internal constituent of the model-defined Hatta calculation.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Hatta number sits in a sparse region of the domain-specific corpus (94th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2721 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-17

References

[^ref-dac51c504c59]: Alexei A. Lapkin and Pawel K. Plucinski, “Engineering Factors for Efficient Flow Processes in Chemical Industries,” in Chemical Reactions and Processes under Flow Conditions (Royal Society of Chemistry, 2009), §1.2.2, doi:10.1039/9781847559739-00001. https://books.rsc.org/books/edited-volume/165/chapter/88117/Engineering-Factors-for-Efficient-Flow-Processes . Engineering chapter, full HTML inspected; its displayed Table 1.1 has inconsistent low-Ha rows, so no table threshold is used here.

[^ref-db4d17aa8b70]: James R. Fair et al., “Gas Absorption and Gas–Liquid System Design,” §14 in Perry's Chemical Engineers' Handbook, 7th ed. (McGraw-Hill, 1997), printed pp.14-18, 14-21–14-22, Eqs. (14-65), (14-79), (14-83), Fig. 14-14. https://schneider.cheme.cmu.edu/Files/Perry%27s%20Chemical%20Engineers%27%20Handbook%207th%20Edition/14.%20Gas%20Absorption%20and%20Gas-Liquid%20System%20Design.pdf . Authoritative full chapter inspected; Eq. (14-79) gives an enhanced transfer coefficient, while (14-65) and (14-83) give conditional Ha forms.

[^ref-2127f7659384]: Grigorios Pantoleontos et al., “Modeling, Simulation, and Membrane Wetting Estimation in Gas–Liquid Contacting Processes Including Shell-Side Reaction: Biogas Upgrading Using DEA Solution,” Industrial & Engineering Chemistry Research 63 (2024): 9185–9202, doi:10.1021/acs.iecr.4c00525. https://pmc.ncbi.nlm.nih.gov/articles/PMC11190974/ . Original full HTML inspected, especially §3.3, Fig. 2 and results around Fig. 11; equations are image-rendered.

[^ref-5d86dbfbe107]: M. Chen, X. H. Deng, and F. Q. He, “Study on the Kinetics of S(IV) Oxidation in the Basic Aluminum Sulfate Wet Flue Gas Desulfurization Process,” RSC Advances 7 (2017): 39341–39348, doi:10.1039/C7RA07518A. https://pubs.rsc.org/en/content/articlepdf/2017/ra/c7ra07518a . Original full paper inspected, especially §4.1–4.3, Eqs. (6)–(13), and the conclusion. Its Eq. (9) is used only for the paper's stated liquid-side model, not as a universal Hatta formula.

[^ref-80319a410778]: Chinmay Kale et al., “Modelling of the Reactive Absorption of CO2 Using Mono-Ethanolamine,” International Journal of Greenhouse Gas Control 17 (2013): 294–308, doi:10.1016/j.ijggc.2013.05.019. https://www.sciencedirect.com/science/article/pii/S1750583613002351 . Original publisher abstract and highlights inspected; full methods and numerical Ha values not verified.