An optimisation-based approach for process plant layout - Industrial

Jun 22, 2018 - The multi-floor process plant layout problem involves determining the most ... to achieve potential savings in the overall plant design...
1 downloads 0 Views 2MB Size
Subscriber access provided by Kaohsiung Medical University

Process Systems Engineering

An optimisation-based approach for process plant layout Jude Ejeh, Songsong Liu, Mazaher Molaei Chalchooghi, and Lazaros G Papageorgiou Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00260 • Publication Date (Web): 22 Jun 2018 Downloaded from http://pubs.acs.org on June 24, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

❆◆ ❖P❚■▼■❙❆❚■❖◆✲❇❆❙❊❉ ❆PP❘❖❆❈❍ ❋❖❘ P❘❖❈❊❙❙ P▲❆◆❚ ▲❆❨❖❯❚ ❏✉❞❡ ❖✳ ❊❥❡❤✱





❙♦♥❣s♦♥❣ ▲✐✉✱



▼❛③❛❤❡r ▼✳ ❈❤❛❧❝❤♦♦❣❤✐✱

❛♥❞ ▲❛③❛r♦s ●✳

∗✱†

P❛♣❛❣❡♦r❣✐♦✉

†❈❡♥tr❡

❢♦r Pr♦❝❡ss ❙②st❡♠s ❊♥❣✐♥❡❡r✐♥❣✱ ❉❡♣❛rt♠❡♥t ♦❢ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣✱ ❯♥✐✈❡rs✐t② ❈♦❧❧❡❣❡ ▲♦♥❞♦♥✱ ▲♦♥❞♦♥ ❲❈✶❊ ✼❏❊✱ ❯❑❀



❙❝❤♦♦❧ ♦❢ ▼❛♥❛❣❡♠❡♥t✱ ❙✇❛♥s❡❛ ❯♥✐✈❡rs✐t②✱ ❇❛② ❈❛♠♣✉s✱ ❋❛❜✐❛♥ ❲❛②✱ ❙✇❛♥s❡❛ ❙❆✶ ✽❊◆✱ ❯♥✐t❡❞ ❑✐♥❣❞♦♠❀ ❊✲♠❛✐❧✿ ❧✳♣❛♣❛❣❡♦r❣✐♦✉❅✉❝❧✳❛❝✳✉❦

P❤♦♥❡✿ ✰✹✹ ✭✵✮✷✵ ✼✻✼✾ ✷✺✻✸

❆❜str❛❝t ❚❤✐s ♣❛♣❡r ♣r❡s❡♥ts ❛♥ ♦♣t✐♠✐s❛t✐♦♥✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ❢♦r t❤❡ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠✳ ❚❤❡ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠ ✐♥✈♦❧✈❡s ❞❡t❡r♠✐♥✐♥❣ t❤❡ ♠♦st ❡✣❝✐❡♥t ✲ ❜❛s❡❞ ♦♥ ♣r❡❞❡✜♥❡❞ ❝r✐t❡r✐❛ ✲ s♣❛t✐❛❧ ❛rr❛♥❣❡♠❡♥t ♦❢ ❛ s❡t ♦❢ ♣r♦✲ ❝❡ss ♣❧❛♥t ❡q✉✐♣♠❡♥t ✇✐t❤ ❛ss♦❝✐❛t❡❞ ❝♦♥♥❡❝t✐✈✐t②✳ ❆ ♥✉♠❜❡r ♦❢ ❝♦st ❛♥❞ ♠❛♥❛❣❡✲ ♠❡♥t✴❡♥❣✐♥❡❡r✐♥❣ ❞r✐✈❡rs ✭❡✳❣✳ ❝♦♥♥❡❝t✐✈✐t②✱ ♦♣❡r❛t✐♦♥s✱ ❧❛♥❞ ❛r❡❛✱ s❛❢❡t②✱ ❝♦♥str✉❝t✐♦♥✱ r❡tr♦✜t✱ ♠❛✐♥t❡♥❛♥❝❡✱ ♣r♦❞✉❝t✐♦♥ ♦r❣❛♥✐s❛t✐♦♥✮ ❤❛✈❡ ❜❡❡♥ ❝♦♥s✐❞❡r❡❞ ♦✈❡r t❤❡ ❧❛st t✇♦ ❞❡❝❛❞❡s ✐♥ ♦r❞❡r t♦ ❛❝❤✐❡✈❡ ♣♦t❡♥t✐❛❧ s❛✈✐♥❣s ✐♥ t❤❡ ♦✈❡r❛❧❧ ♣❧❛♥t ❞❡s✐❣♥ ♣r♦❝❡ss✳ ❚❤✐s ✇♦r❦ ❝♦♥st✐t✉t❡s ❛♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ♣r❡✈✐♦✉s ✇♦r❦ ❜② P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r✲ ❣✐♦✉ ✶ t♦ ❛❞❞r❡ss t❤❡ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠✳ ◆❡✇ ❢❡❛t✉r❡s ✐♥tr♦❞✉❝❡❞ ♠♦❞❡❧❧❡❞ t❛❧❧ ❡q✉✐♣♠❡♥t ✇✐t❤ ❤❡✐❣❤ts ❣r❡❛t❡r t❤❛♥ t❤❡ t②♣✐❝❛❧ ✢♦♦r ❤❡✐❣❤t ✐♥ ❝❤❡♠✐❝❛❧ ♣r♦❝❡ss ♣❧❛♥ts✱ ✇✐t❤ ❝♦♥♥❡❝t✐♦♥ ♣♦✐♥t ❛t ❛ ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❤❡✐❣❤t ❢♦r ❡❛❝❤ ❡q✉✐♣♠❡♥t✳ ✶

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

❚❤❡ ♥✉♠❜❡r ♦❢ ✢♦♦rs✱ ❧❛♥❞ ❛r❡❛✱ ❛❧❧♦❝❛t✐♦♥ ♦❢ ❡❛❝❤ ❡q✉✐♣♠❡♥t t♦ ❛ ✢♦♦r ❛♥❞ t❤❡ ♦✈❡r✲ ❛❧❧ ❧❛②♦✉t ♦❢ ❡❛❝❤ ✢♦♦r ✇❡r❡ ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ ♦♣t✐♠✐s❛t✐♦♥ ♠♦❞❡❧ ✇❤✐❧st ♣r❡✈❡♥t✐♥❣ ♦✈❡r❧❛♣ ♦❢ ❡q✉✐♣♠❡♥t✳ ❚❤❡ ❝♦♥♥❡❝t✐♦♥ ❝♦sts✱ ❤♦r✐③♦♥t❛❧ ❛♥❞ ✈❡rt✐❝❛❧✱ ❛s ✇❡❧❧ t❤❡ ❝♦♥✲ str✉❝t✐♦♥ ❝♦sts ✇❡r❡ ❛❝❝♦✉♥t❡❞ ❢♦r ✇✐t❤ ❛♥ ♦✈❡r❛❧❧ ♦❜❥❡❝t✐✈❡ t♦ ♠✐♥✐♠✐③❡ t❤❡ t♦t❛❧ ❝♦st✳ ❚❤❡ ♦✈❡r❛❧❧ ♣r♦❜❧❡♠ ✇❛s ❢♦r♠✉❧❛t❡❞ ❛s ❛ ♠✐①❡❞✲✐♥t❡❣❡r ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣ ✭▼■▲P✮ ♠♦❞❡❧ ❜❛s❡❞ ♦♥ ❛ ❝♦♥t✐♥✉♦✉s ❞♦♠❛✐♥ r❡♣r❡s❡♥t❛t✐♦♥ ❛♥❞ ✐ts ❛♣♣❧✐❝❛❜✐❧✐t② ❞❡♠♦♥str❛t❡❞ ❜② ❛ ♥✉♠❜❡r ♦❢ ✐❧❧✉str❛t✐✈❡ ❡①❛♠♣❧❡s✳ ❘❡s✉❧ts s❤♦✇❡❞ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♥✉♠❜❡r ♦❢ ❡q✉✐♣♠❡♥t ❤❛♥❞❧❡❞ ❜② t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧s ✐♥ ♠♦❞❡st ❝♦♠♣✉t❛t✐♦♥❛❧ t✐♠❡s✳ ❋✐♥❛❧❧②✱ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ✇❡r❡ ✐♥❝❧✉❞❡❞ t♦ ✐♥❝r❡❛s❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡✣❝✐❡♥❝②✱ ❛♥❞ t❤❡✐r ♣❡r❢♦r♠❛♥❝❡ t❡st❡❞ ✇✐t❤ t❤❡ ❧❛st ❡①❛♠♣❧❡✳

❑❡②✇♦r❞s ▼✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t❀ ▼✐①❡❞ ✐♥t❡❣❡r ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣✭▼■▲P✮❀ ❖♣t✐♠✐s❛t✐♦♥

ACS Paragon Plus Environment

Page 2 of 33

Page 3 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✶ ■◆❚❘❖❉❯❈❚■❖◆



✶ ■♥tr♦❞✉❝t✐♦♥ ❖✈❡r t❤❡ ♣❛st t✇♦ ❞❡❝❛❞❡s✱ t❤❡ ❧❛②♦✉t ♦❢ ❡q✉✐♣♠❡♥t ✐♥ ♣r♦❝❡ss ♣❧❛♥ts ❤❛✈❡ ❣❛✐♥❡❞ ✐♥❝r❡❛s✐♥❣ r❡❧❡✈❛♥❝❡✱ ❢r♦♠ ❛♥ ❡❝♦♥♦♠✐❝✱ s❛❢❡t②✱ ♦♣❡r❛t✐♦♥❛❧ ❛♥❞ ♠❛✐♥t❡♥❛♥❝❡✲r❡❧❛t❡❞ ♣♦✐♥t ♦❢ ✈✐❡✇✳ ✷✱✸ ▲❛②♦✉t ❞❡s✐❣♥ ❣❡♥❡r❛❧❧② ✐♥✈♦❧✈❡s ♦❜t❛✐♥✐♥❣ ❛ s✉✐t❛❜❧❡ ❛rr❛♥❣❡♠❡♥t ♦❢ ✐t❡♠s ❛♥❞ t❤❡✐r ❝♦♥♥❡❝✲ t✐♦♥s ✇✐t❤✐♥ ❛ ♣r❡❞❡✜♥❡❞ ❛r❡❛ ❜❛s❡❞ ♦♥ ♣r❡✲s♣❡❝✐✜❡❞ ❝r✐t❡r✐❛✳ ❚❤❡s❡ ✐t❡♠s ♠❛② ❜❡ ♣r♦❝❡ss ✈❡ss❡❧s ❛♥❞ ❡q✉✐♣♠❡♥t✱ ✇♦r❦ ❝❡♥tr❡s ♦r ❞❡♣❛rt♠❡♥ts ✇✐t❤✐♥ ❛♥ ♦r❣❛♥✐s❛t✐♦♥❀ ✇✐t❤ ❝♦♥♥❡❝t✐♦♥s ❜② ♣✐♣❡s✱ ❝♦♥✈❡②♦rs✱ ✈❡❤✐❝✉❧❛r tr❛♥s♣♦rt ♦r ❛♥② s✉✐t❛❜❧❡ ♠❛t❡r✐❛❧ ❤❛♥❞❧✐♥❣ ❡q✉✐♣♠❡♥t✳ ✸✱✹ ▲❛②♦✉t ❞❡s✐❣♥s ❤❛✈❡ ❜❡❡♥ ❢♦✉♥❞ t♦ ❤❛✈❡ ❛ tr❡♠❡♥❞♦✉s ✐♠♣❛❝t ♦♥ t❤❡ ❝♦sts ❛♥❞ ♣r♦❞✉❝t✐✈✐t② ♦❢ ❛♥② s②st❡♠ ✐♥✈♦❧✈❡❞ ✷ ✱ ❛s s✉❝❤ r❡s❡❛r❝❤❡rs ❤❛✈❡ ❝♦♥st❛♥t❧② s♦✉❣❤t ♦✉t ♠❡t❤♦❞s t♦ ✜♥❞ t❤❡ ❜❡st s♦❧✉t✐♦♥ t♦ s✉❝❤ ❞❡s✐❣♥ ♣r♦❜❧❡♠s ✲ ❣❡♥❡r❛❧❧② r❡❢❡rr❡❞ t♦ ❛s t❤❡ ❧❛②♦✉t ♣r♦❜❧❡♠✳ ❲❤❡♥ ❝♦♥❝❡r♥❡❞ ✇✐t❤ ✐t❡♠s t❤❛t ❛r❡ ♥❡❡❞❡❞ ❢♦r t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❣♦♦❞s ♦r ❞❡❧✐✈❡r② ♦❢ s❡r✈✐❝❡s✱ ✐t ❤❛s ❜❡❡♥ r❡❢❡rr❡❞ t♦ ❛s t❤❡ ❢❛❝✐❧✐t② ❧❛②♦✉t ♣r♦❜❧❡♠✳ ✹ ❆♠✐❞st t❤❡ ❝❧❛ss❡s ♦❢ t❤❡ ❢❛❝✐❧✐t② ❧❛②♦✉t ♣r♦❜❧❡♠ ✭s❡❡ ❉r✐r❛ ❡t ❛❧✳ ❢♦r ❛ ❞❡t❛✐❧❡❞ r❡✈✐❡✇✮ ✐s t❤❡ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠✱ ♦♥ ✇❤✐❝❤ t❤✐s ✇♦r❦ ♣r✐♠❛r✐❧② ❢♦❝✉s❡s✳ Pr♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠ ❛❞❞r❡ss❡s t❤❡ ❧❛②♦✉t ♣r♦❜❧❡♠ ❢♦r ✐t❡♠s ✐♥ ❛ t②♣✐❝❛❧ ❝❤❡♠✐❝❛❧ ♣r♦❝❡ss ♣❧❛♥t✳ ✺ Pr❡✈✐♦✉s ❛♣♣r♦❛❝❤❡s t♦ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ❞❡s✐❣♥ ✇❡r❡ ❢r♦♠ ❛ ♣r❛❝t✐❝❛❧ ♣♦✐♥t ♦❢ ✈✐❡✇✱ ✇❤❡r❡ ❞❡❝✐s✐♦♥s ✇❡r❡ ♠❛❞❡ ❜❛s❡❞ ♦♥ ❡♥❣✐♥❡❡r✐♥❣ ❥✉❞❣❡♠❡♥t ✻ ✱ ❜✉t ❡s♣❡❝✐❛❧❧② ❢r♦♠ t❤❡ ❧❛t❡ ✾✵s✱ ♠♦r❡ s❝✐❡♥t✐✜❝ ❛♣♣r♦❛❝❤❡s ✐♥ t❡r♠s ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧❧✐♥❣ ❤❛✈❡ ❜❡❡♥ ❛❞♦♣t❡❞ t♦ s♦❧✈❡ t❤❡ ♣r♦❜❧❡♠ ✶✱✼✕✶✷ ✳ ▼♦st ♦❢ t❤❡ ♣r❡✈✐♦✉s r❡s❡❛r❝❤ ❤❛✈❡ ❢♦❝✉s❡❞ ♦♥ ❛ ❝♦st✲r❡❞✉❝✐♥❣ ♦❜❥❡❝t✐✈❡✱ ✇✐t❤ ❛ ✈❛r②✐♥❣ ♥✉♠❜❡r ♦❢ s❝❡♥❛r✐♦s✳ ●❡♦r❣✐❛❞✐s ❛♥❞ ▼❛❝❝❤✐❡tt♦ ✾ ♣r♦♣♦s❡❞ ❛ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦❣r❛♠♠✐♥❣ ❛♣♣r♦❛❝❤ ✇✐t❤ ❛♥ ♦❜❥❡❝t✐✈❡ t♦ ♠✐♥✐♠✐③❡ ❝♦st ✲ ♣✉♠♣✐♥❣✱ ♣✐♣❡ ❝♦♥♥❡❝t✐♦♥ ❛♥❞ ✢♦♦r ❝♦♥str✉❝t✐♦♥ ✲ ❛♥❞ ✇❛s ❢♦r♠✉❧❛t❡❞ ❛s ❛ ♠✐①❡❞ ✐♥t❡❣❡r ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣ ✭▼■▲P✮ ♣r♦❜✲ ❧❡♠✳ ❘❡s✉❧ts s❤♦✇❡❞ t❤❡ ♠♦❞❡❧ ✇❛s ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡✣❝✐❡♥t ❢♦r ❛ s♠❛❧❧ ♥✉♠❜❡r ♦❢ ✉♥✐ts✳ P❛♣❛❣❡♦r❣✐♦✉ ❛♥❞ ❘♦tst❡✐♥ ✶✷ ❢✉rt❤❡r s♦❧✈❡❞ t❤❡ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠ ♦✈❡r ❛ ❝♦♥t✐♥✉✲ ♦✉s s♣❛t✐❛❧ ❞♦♠❛✐♥ ✇❤✐❧st ✐♥tr♦❞✉❝✐♥❣ ♠♦r❡ r❡❛❧✐st✐❝ ❝♦♥str❛✐♥ts ❢♦r s✐♥❣❧❡✲✢♦♦r ❝❛s❡ st✉❞✐❡s✳ ❇❛r❜♦s❛✲P♦✈♦❛ ❡t ❛❧✳ ✼✱✽ ❛❝❝♦✉♥t❡❞ ❢♦r ❞✐✛❡r❡♥t ✐♥♣✉ts ❛♥❞ ♦✉t♣✉ts ❢♦r ❡❛❝❤ ❡q✉✐♣♠❡♥t✱ ✐rr❡❣✲ ✉❧❛r s❤❛♣❡s✱ ❛ ✸✲❞✐♠❡♥s✐♦♥❛❧ r❡♣r❡s❡♥t❛t✐♦♥✱ ❛❧❧♦✇❡❞ ❢♦r ❞✐✛❡r❡♥t ♣r♦❞✉❝t✐♦♥ s❡❝t✐♦♥s✱ ❛♥❞ ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✶ ■◆❚❘❖❉❯❈❚■❖◆

Page 4 of 33



s❛❢❡t② ❛♥❞ ♦♣❡r❛❜✐❧✐t② ❢❛❝t♦rs✳ ❚❤❡s❡ ♣r♦❜❧❡♠s ✇❡r❡ ❛❧❧ ❢♦r♠✉❧❛t❡❞ ❛s ❛♥ ▼■▲P ❣✐✈✐♥❣ ❝♦♠✲ ♣✉t❛t✐♦♥❛❧❧② ❡✣❝✐❡♥t s♦❧✉t✐♦♥s ❢♦r ❛ s♠❛❧❧ ♥✉♠❜❡r ♦❢ ✉♥✐ts✳ ❋♦r♠✉❧❛t✐♦♥s t♦ ❛❞❞r❡ss s❝❡♥❛r✐♦s ✇✐t❤ ♠✉❧t✐♣❧❡ ✢♦♦rs ❤❛✈❡ ❛❧s♦ ❜❡❡♥ ❝♦♥s✐❞❡r❡❞✳ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶✵ ❞❡✈❡❧♦♣❡❞ ❛♥ ▼■▲P ❢♦r♠✉❧❛t✐♦♥ t♦ ❛❧❧♦✇ ❢♦r ❛ ♠✉❧t✐✲✢♦♦r ❧❛②♦✉t ✇✐t❤ ✢♦♦r ❝♦♥str✉❝t✐♦♥ ❝♦sts ✭✜①❡❞ ❛♥❞ ❛r❡❛✲❞❡♣❡♥❞❡♥t✮ ❛♥❞ ✈❡rt✐❝❛❧ ♣✉♠♣✐♥❣ ❝♦sts✳ ❚❤❡ ♠♦❞❡❧ s✉❝❝❡ss❢✉❧❧② ❤❛♥❞❧❡❞ ✉♣ t♦ ✶✶ ✉♥✐ts ✇✐t❤✐♥ ❛ ♠♦❞❡st ❈P❯ t✐♠❡✳ ❋♦r ❧❛r❣❡r ♥✉♠❜❡r ♦❢ ✉♥✐ts✱ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ♣r♦♣♦s❡❞ ❛ r✐❣♦r♦✉s ❞❡❝♦♠♣♦s✐t✐♦♥ ❛♣♣r♦❛❝❤ ❛♥❞ ❛♥ ✐t❡r❛t✐✈❡ s♦❧✉t✐♦♥ s❝❤❡♠❡✱ ✇✐t❤ t❤❡ ❧❛t❡r ♣r♦❞✉❝✐♥❣ ❛ s♦❧✉t✐♦♥ ✇✐t❤ ❛ ❤✐❣❤❡r ❞❡❣r❡❡ ♦❢ ♦♣t✐♠❛❧✐t②✳ ❆♥ ✐♠♣r♦✈❡♠❡♥t✲t②♣❡ ❛❧❣♦r✐t❤♠ ✇❛s ♣r♦♣♦s❡❞ ❜② ❳✉ ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶✸ ❛♣♣❧✐❝❛❜❧❡ t♦ ❛ s✐♥❣❧❡ ✢♦♦r✳ ❆♣❛rt ❢r♦♠ ❛ ❝♦st ♠✐♥✐♠✐s❛t✐♦♥ ♦❜❥❡❝t✐✈❡✱ ♦t❤❡r ❛✉t❤♦rs ❤❛✈❡ ✐♥tr♦❞✉❝❡❞ ♦t❤❡r ❝r✐t❡r✐❛ t♦ t❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥✳ P❡♥t❡❛❞♦ ❛♥❞ ❈✐r✐❝ ✺ ♣r❡s❡♥t❡❞ ❛ ♠✐①❡❞ ✐♥t❡❣❡r ♥♦♥✲❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣ ✭▼■◆▲P✮ ♣r♦❜❧❡♠ ♥♦t ♦♥❧② t♦ ♠✐♥✐♠✐③❡ ♣✐♣✐♥❣ ❝♦st✱ ❧❛♥❞ ❛❧❧♦❝❛t✐♦♥ ❝♦st✱ ❜✉t ❛❧s♦ ✜♥❛♥❝✐❛❧ r✐s❦ ❛♥❞ s❛❢❡t② ❝♦sts✳ ❖t❤❡r ❢❛❝t♦rs ❤❛✈❡ ❜❡❡♥ t❤❡ r♦✉t✐♥❣ ❛♥❞ ❧❛②♦✉t ♦❢ ♣✐♣❡s ✻ ✱ s❛❢❡t② ❛♥❞ r✐s❦ ❛ss❡ss♠❡♥t ✶✶✱✶✹✕✶✼ ✱ ❧♦♥❣✲❧❡♥❣t❤ ❡q✉✐♣♠❡♥t ✶✼✕✶✾ ✱ ❛r❡❛ ♠✐♥✐♠✐s❛t✐♦♥ ✷✵ ❀ ✇✐t❤ ✈❛r②✐♥❣ s♦❧✉✲ t✐♦♥ t❡❝❤♥✐q✉❡s ✶✼✱✷✶✕✷✺ ✳ ❚❤✐s ♣❛♣❡r ♣r♦♣♦s❡s ❛ ❣❡♥❡r✐❝ ♠♦❞❡❧ t♦ t❤❡ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠✱ ✐♥✐t✐❛❧❧② ♣r♦♣♦s❡❞ ❜② P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✭❛♥ ✐♠♣r♦✈❡♠❡♥t ♦♥ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r✲ ❣✐♦✉ ✶✵ ✮ ❜✉t ❡①t❡♥❞❡❞ t♦ ❛❝❝♦✉♥t ❢♦r ❧♦♥❣✲❧❡♥❣t❤ ❡q✉✐♣♠❡♥t✱ ✐✳❡✳ ❡q✉✐♣♠❡♥t t②♣✐❝❛❧❧② s♣❛♥✲ ♥✐♥❣ ♠✉❧t✐♣❧❡ ✢♦♦rs✱ ✇✐t❤ ❝♦♥♥❡❝t✐♦♥ ♣♦✐♥ts ❛t ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❤❡✐❣❤ts ❢♦r ❡❛❝❤ ❡q✉✐♣♠❡♥t✳ ❑✉ ❡t ❛❧✳ ✶✽ ♣r❡s❡♥t❡❞ ❛ ▼■◆▲P ♠♦❞❡❧ ❛♥❞ ❛❝❝♦✉♥t❡❞ ❢♦r t❛❧❧ ❡q✉✐♣♠❡♥t✱ ♠✐♥✐♠✐③✐♥❣ t♦t❛❧ ❧❛②♦✉t ❛r❡❛ ✇✐t❤ ❛ ❤②❜r✐❞ ♦♣t✐♠✐s❛t✐♦♥ ♠❡t❤♦❞✳ ❚❤✐s ✇♦r❦ s❡❡❦s t♦ ♣r♦♣♦s❡ ❛ ♠♦r❡ ❡✣❝✐❡♥t ▼■▲P ♠♦❞❡❧ t♦ ❤❛♥❞❧❡ ❛ ❧❛r❣❡r ♥✉♠❜❡r ♦❢ ✉♥✐ts t❤❛♥ ♣r❡✈✐♦✉s❧② r❡❝♦r❞❡❞✳ ❙②♠♠❡tr② ❜r❡❛❦✲ ✐♥❣ ❝♦♥str❛✐♥ts ❛r❡ ❛❧s♦ ✐♥tr♦❞✉❝❡❞ t♦ r❡❞✉❝❡ s♦❧✉t✐♦♥ s❡❛r❝❤ ♦✈❡r ♠✉❧t✐♣❧❡ ♦♣t✐♠❛❧ s♦❧✉t✐♦♥s✳ ❚❤❡ r❡st ♦❢ t❤✐s ♣❛♣❡r ✐s str✉❝t✉r❡❞ ❛s ❢♦❧❧♦✇s✿ t❤❡ ♣r♦❜❧❡♠ ✐s ❞❡s❝r✐❜❡❞ ✐♥ s❡❝t✐♦♥ ✷ ✇✐t❤ ✉♥❞❡r❧②✐♥❣ ❛ss✉♠♣t✐♦♥s❀ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s ❛r❡ t❤❡♥ ♣r♦♣♦s❡❞ ✐♥ s❡❝t✐♦♥ ✸ t♦ ❛❞❞r❡ss t❤❡ ♣r♦❜❧❡♠❀ ❝❛s❡ st✉❞✐❡s t♦ s❤♦✇ ♠♦❞❡❧ ♣❡r❢♦r♠❛♥❝❡ ❛♥❞ ❛♣♣❧✐❝❛❜✐❧✐t② ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ s❡❝t✐♦♥

ACS Paragon Plus Environment

Page 5 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✷ P❘❖❇▲❊▼ ❉❊❙❈❘■P❚■❖◆



✹✱ ✇❤❡r❡ ❛❞❞✐t✐♦♥❛❧ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ❛r❡ ❛❧s♦ ✐♥tr♦❞✉❝❡❞ ❛♥❞ t❡st❡❞✳ ❋✐♥❛❧❧②✱ ❝♦♥❝❧✉❞✐♥❣ r❡♠❛r❦s ❛r❡ ❣✐✈❡♥ ✐♥ s❡❝t✐♦♥ ✺✳

✷ Pr♦❜❧❡♠ ❉❡s❝r✐♣t✐♦♥ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❛ss✉♠♣t✐♦♥s ❛r❡ ♠❛❞❡ ✐♥ t❤❡ ♠♦❞❡❧ ❢♦r♠✉❧❛t✐♦♥✳ ❊q✉✐♣♠❡♥t ✐t❡♠s ❛r❡ ❞❡✲ s❝r✐❜❡❞ ❜② r❡❝t❛♥❣✉❧❛r s❤❛♣❡s✳ ■♥ ❛❧❧ ❝❛s❡s✱ r❡❝t✐❧✐♥❡❛r ❞✐st❛♥❝❡s ❛r❡ ❛ss✉♠❡❞✱ ✇✐t❤ ❝♦♥♥❡❝✲ t✐♦♥s ❜❡t✇❡❡♥ ❡q✉✐♣♠❡♥t t❛❦❡♥ ❢r♦♠ t❤❡✐r r❡s♣❡❝t✐✈❡ ❣❡♦♠❡tr✐❝❛❧ ❝❡♥tr❡s ✐♥ t❤❡ ①✲② ♣❧❛♥❡✳ ❱❡rt✐❝❛❧ ❞✐st❛♥❝❡s ❛r❡ ♠❡❛s✉r❡❞ ❢r♦♠ ❛ ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❤❡✐❣❤t ♦❢ ❡❛❝❤ ❡q✉✐♣♠❡♥t✳ ❊❛❝❤ ❡q✉✐♣♠❡♥t ✐s ❛❧❧♦✇❡❞ t♦ r♦t❛t❡ ✐♥ ✾✵♦ ❛♥❣❧❡s ✐♥ t❤❡ ①✲② ♣❧❛♥❡✱ ❛♥❞ ♠✉st st❛rt ❢r♦♠ t❤❡ ❜❛s❡ ♦❢ ❡❛❝❤ ❛✈❛✐❧❛❜❧❡ ✢♦♦r✳ ❚❤❡ ✢♦♦r ❤❡✐❣❤t ✐s ✜①❡❞ ❛❝r♦ss ❛❧❧ ✢♦♦rs ❛♥❞ ✐❢ ❛♥ ❡q✉✐♣♠❡♥t ❡①❝❡❡❞s s✉❝❤ ❤❡✐❣❤t✱ ✐t ✐s ❛❧❧♦✇❡❞ t♦ ❡①t❡♥❞ t❤r♦✉❣❤ ❛✈❛✐❧❛❜❧❡ ✢♦♦rs✳ ❚❤❡ ♣r♦❜❧❡♠ ❞❡s❝r✐♣t✐♦♥ ❢♦r t❤❡ ♣r♦❝❡ss ❧❛②♦✉t ♣r♦❜❧❡♠ ✐s ❛s ❢♦❧❧♦✇s✳

●✐✈❡♥ ✿ • ❛ s❡t ♦❢ ◆ ❡q✉✐♣♠❡♥t ✐t❡♠s ❛♥❞ t❤❡✐r ❞✐♠❡♥s✐♦♥s ✭❧❡♥❣t❤✱ ❜r❡❛❞t❤ ❛♥❞ ❤❡✐❣❤t✮❀ • ❛ s❡t ♦❢ ❑ ♣♦t❡♥t✐❛❧ ✢♦♦rs ❢♦r ❧❛②♦✉t❀ • ❝♦♥♥❡❝t✐✈✐t② ♥❡t✇♦r❦ ❛♠♦♥❣st ❡q✉✐♣♠❡♥t❀ • ❝♦st ❞❛t❛ ✭❝♦♥♥❡❝t✐♦♥✱ ♣✉♠♣✐♥❣✱ ❧❛♥❞✱ ❛♥❞ ❝♦♥str✉❝t✐♦♥✮❀ • ✢♦♦r ❤❡✐❣❤t❀ • s♣❛❝❡ ❛♥❞ ❡q✉✐♣♠❡♥t ❛❧❧♦❝❛t✐♦♥ ❧✐♠✐t❛t✐♦♥s❀ • ♠✐♥✐♠✉♠ s❛❢❡t② ❞✐st❛♥❝❡s ❜❡t✇❡❡♥ ❡q✉✐♣♠❡♥t ✐t❡♠s❀

❞❡t❡r♠✐♥❡ ✿ • t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ r❡q✉✐r❡❞ ✢♦♦rs ❢♦r t❤❡ ❧❛②♦✉t❀ • t❤❡ ❜❛s❡ ❧❛♥❞ ❛r❡❛ ♦❝❝✉♣✐❡❞❀ ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

Page 6 of 33



• t❤❡ ❛r❡❛ ♦❢ ✢♦♦rs❀ • s♣❛t✐❛❧ ❡q✉✐♣♠❡♥t ❛❧❧♦❝❛t✐♦♥ t♦ ✢♦♦rs❀

s♦ ❛s t♦ ✿ ♠✐♥✐♠✐s❡ t❤❡ t♦t❛❧ ♣❧❛♥t ❧❛②♦✉t ❝♦st✳



▼❛t❤❡♠❛t✐❝❛❧ ❋♦r♠✉❧❛t✐♦♥

❚❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❢♦r♠✉❧❛t✐♦♥ ❝♦♥st✐t✉t❡s ❛♥ ❡①t❡♥s✐♦♥ t♦ t❤❡ ✇♦r❦ ♦❢ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r✲ ❣✐♦✉ ✶ ✳ ❆ ❢✉❧❧ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ ♣r♦♣♦s❡❞ ❜② P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✐s ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳ ❚✇♦ ❢♦r♠✉❧❛t✐♦♥s ✭❆ ✫ ❇✮ ❛r❡ ♣r♦♣♦s❡❞✱ ♣r✐♠❛r✐❧② ❞✐✛❡r✐♥❣ ✐♥ t❤❡ ♠❛♥♥❡r t❛❧❧ ❡q✉✐♣♠❡♥t ✭✇❤✐❝❤ s♣❛♥ ♠✉❧t✐♣❧❡ ✢♦♦rs✮ ❛r❡ ❤❛♥❞❧❡❞✳ ❚❤❡ ✜rst ❤❛♥❞❧❡s ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❛s ✐s✱ ❜② ❛ s❡t ♦❢ ❝♦♥str❛✐♥ts ❛s s✉♠♠❛r✐s❡❞ ✐♥ ❚❛❜❧❡ ✶ ❢♦r ❡❛❝❤ ♦❢ t❤❡ t❤r❡❡ ♠♦❞❡❧s ♣r♦♣♦s❡❞✳ ❚❤❡ s❡❝♦♥❞ ❢♦r♠✉❧❛t✐♦♥ ✐s ❛ ❧✐♥❡❛r✐s❡❞ ❢♦r♠ ♦❢ t❤❡ ♠♦❞❡❧ ♣r♦♣♦s❡❞ ❜② ❑✉ ❡t ❛❧✳ ✶✽ ✭❛ ❞✐r❡❝t ❡①t❡♥s✐♦♥ ♦❢ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✮✱ ✇✐t❤ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❞✐✈✐❞❡❞ ✐♥t♦ ♣s❡✉❞♦✲s✐♥❣❧❡ ✢♦♦r ✉♥✐ts ❡q✉✐✈❛❧❡♥t t♦ t❤❡ ♥✉♠❜❡r ♦❢ ❝♦♥s❡❝✉t✐✈❡ ✢♦♦rs t❤❡② r❡q✉✐r❡✳

❚❛❜❧❡ ✶✿ ❙✉♠♠❛r② ♦❢ ❡q✉❛t✐♦♥s ❛❞♦♣t❡❞ ✐♥ ♠♦❞❡❧s ❆✳✶ ✲ ❆✳✸ ❈♦♥str❛✐♥ts ❋❧♦♦r ❊q✉✐♣♠❡♥t ♦r✐❡♥t❛t✐♦♥ ▼✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❉✐st❛♥❝❡ ◆♦♥✲♦✈❡r❧❛♣♣✐♥❣ ❆r❡❛ ▲❛②♦✉t ❞❡s✐❣♥

❋♦r♠✉❧❛t✐♦♥ ❆ ♠♦❞❡❧ ❆✳✶ ❆✳✷ ❆✳✸ ✶ ✲ ✹✱ ✺ ✲ ✻ ✶ ✲ ✹✱ ✺ ✲ ✻ ✶ ✲ ✹✱ ✺ ✲ ✻ ✾✱ ✼ ✲ ✽ ✾✱ ✼ ✲ ✽ ✾✱ ✼ ✲ ✽ ✶✵✲✶✹ ✶✺ ✶✷✱ ✶✸ ❛♥❞ ✶✻ ✷✹✱✷✶✱ ✷✷✱ ✶✵✱ ✶✷✱ ✷✹ ❛♥❞ ✷✹✱✷✶✱ ✷✷✱ ✷✶✱ ✷✷✱ ✷✸✱ ❛♥❞ ✷✸ ❛♥❞ ✷✸ ✶✼ ✲ ✷✵ ✶✼ ✲ ✷✵ ✶✼ ✲ ✷✵ ✸✶ ✲ ✸✻ ✸✶ ✲ ✸✻ ✸✶ ✲ ✸✻ ✸✵✱ ✷✺ ✲ ✷✾ ✸✵✱ ✷✺ ✲ ✷✾ ✸✵✱ ✷✺ ✲ ✷✾

ACS Paragon Plus Environment

Page 7 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆ ◆♦♠❡♥❝❧❛t✉r❡

■♥❞✐❝❡s i,j

❡q✉✐♣♠❡♥t ✐t❡♠ ✐♥ ♠♦❞❡❧s ❆✳✶ ✲ ❆✳✸

i′ ,j ′

❡q✉✐♣♠❡♥t ✐t❡♠ ✐♥ ♠♦❞❡❧ ❇

k, k ′

✢♦♦r ♥✉♠❜❡r

p

♣s❡✉❞♦ ✉♥✐ts

s

r❡❝t❛♥❣✉❧❛r ❛r❡❛ s✐③❡s

❙❡ts I

s❡t ♦❢ ❡q✉✐♣♠❡♥t ✐t❡♠ ❢♦r ♠♦❞❡❧s ❆✳✶✲ ❆✳✸

I′

s❡t ♦❢ ❡q✉✐♣♠❡♥t ✐t❡♠ ❢♦r ♠♦❞❡❧ ❇

MF

s❡t ♦❢ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥ts

Pi

s❡ts ♦❢ ♣s❡✉❞♦ ✉♥✐ts ❢♦r ❡q✉✐♣♠❡♥t i

P❛r❛♠❡t❡rs αi ✱ βi ,γi

❞✐♠❡♥s✐♦♥s ♦❢ ✐t❡♠ i

Mi

♥✉♠❜❡r ♦❢ ✢♦♦rs r❡q✉✐r❡❞ ❜② ✐t❡♠ i

fij

✶ ✐❢ ✢♦✇ ❞✐r❡❝t✐♦♥ ❜❡t✇❡❡♥ i ❛♥❞ j ✐s ♣♦s✐t✐✈❡❀ ✵✱ ♦t❤❡r✇✐s❡

OPij

❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❜❛s❡ ❛♥❞ ♦✉t♣✉t ♣♦✐♥t ♦♥ ❡q✉✐♣♠❡♥t i

IPij

❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❜❛s❡ ❛♥❞ ✐♥♣✉t ♣♦✐♥t ♦♥ ❡q✉✐♣♠❡♥t j

BM

❛ ❧❛r❣❡ ♥✉♠❜❡r

FH

✢♦♦r ❤❡✐❣❤t

LC

❧❛♥❞ ❝♦st

F C1

✜①❡❞ ✢♦♦r ❝♦♥str✉❝t✐♦♥ ❝♦st

F C2

❛r❡❛✲❞❡♣❡♥❞❡♥t ✢♦♦r ❝♦♥str✉❝t✐♦♥ ❝♦st

Cijc

❝♦♥♥❡❝t✐♦♥✴♣✐♣✐♥❣ ❝♦sts ACS Paragon Plus Environment



Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

Cijh

❤♦r✐③♦♥t❛❧ ♣✉♠♣✐♥❣ ❝♦sts

Cijv

✈❡rt✐❝❛❧ ♣✉♠♣✐♥❣ ❝♦sts

■♥t❡❣❡r ✈❛r✐❛❜❧❡s NF

♥✉♠❜❡r ♦❢ ✢♦♦rs r❡q✉✐r❡❞ ❢♦r ❧❛②♦✉t

❇✐♥❛r② ✈❛r✐❛❜❧❡s Oi

✶ ✐❢ ❧❡♥❣t❤ ♦❢ ✐t❡♠ i ✐s ❡q✉❛❧ t♦ αi ❀ ✵✱ ♦t❤❡r✇✐s❡

Wk

✶ ✐❢ ✢♦♦r k ✐s ♦❝❝✉♣✐❡❞❀ ✵✱ ♦t❤❡r✇✐s❡

nijk

✶ ✐❢ ✐t❡♠s i ❛♥❞ j ❛r❡ ❛ss✐❣♥❡❞ t♦ ✢♦♦r k ❀ ✵✱ ♦t❤❡r✇✐s❡

Nij

✶ ✐❢ ✐t❡♠s i ❛♥❞ j ❛r❡ ❛ss✐❣♥❡❞ t♦ t❤❡ s❛♠❡ ✢♦♦r❀ ✵✱ ♦t❤❡r✇✐s❡

Vik

✶ ✐❢ ✐t❡♠ i ✐s ❛ss✐❣♥❡❞ t♦ ✢♦♦r k

Qs

✶ ✐❢ r❡❝t❛♥❣✉❧❛r ❛r❡❛ s ✐s s❡❧❡❝t❡❞ ❢♦r t❤❡ ❧❛②♦✉t❀ ✵✱ ♦t❤❡r✇✐s❡

E1ij ✱ E2ij

♥♦♥✲♦✈❡r❧❛♣♣✐♥❣ ❜✐♥❛r②✱ ❛ s❡t ♦❢ ✈❛❧✉❡s ♦❢ ✇❤✐❝❤ ♣r❡✈❡♥ts ❡q✉✐♣♠❡♥t ♦✈❡r❧❛♣ ✐♥ ♦♥❡ ❞✐r❡❝t✐♦♥ ✐♥ t❤❡ ①✲② ♣❧❛♥❡

s Sik

✶ ✐❢ ✐t❡♠ i s♣❛♥s ♠♦r❡ t❤❛♥ ♦♥❡ ✢♦♦r ❛♥❞ ❜❡❣✐♥s ❛t ✢♦♦r k ❀ ✵✱ ♦t❤❡r✇✐s❡

f Sik

✶ ✐❢ ✐t❡♠ i s♣❛♥s ♠♦r❡ t❤❛♥ ♦♥❡ ✢♦♦r ❛♥❞ t❡r♠✐♥❛t❡s ❛t ✢♦♦r k ❀ ✵✱ ♦t❤❡r✇✐s❡

❈♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s li

❧❡♥❣t❤ ♦❢ ✐t❡♠ i

di

❜r❡❛❞t❤ ♦❢ ✐t❡♠ i

hi

❤❡✐❣❤t ♦❢ ✐t❡♠ i

xi ✱ yi ✱ z i

❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ❣❡♦♠❡tr✐❝❛❧ ❝❡♥tr❡ ♦❢ ✐t❡♠ i

Rij

r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ① ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

ACS Paragon Plus Environment

Page 8 of 33



Page 9 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆



✐❢ i ✐s t♦ t❤❡ r✐❣❤t ♦❢ j r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ① ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

Lij

✐❢ i ✐s t♦ t❤❡ ❧❡❢t ♦❢ j r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ② ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

Aij

✐❢ i ✐s ❛❜♦✈❡ j r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ② ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

Bij

✐❢ i ✐s ❜❡❧♦✇ j r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ③ ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

Uij

✐❢ i ✐s ❤✐❣❤❡r t❤❛♥ j r❡❧❛t✐✈❡ ❞✐st❛♥❝❡ ✐♥ ③ ❝♦♦r❞✐♥❛t❡s ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j ✱

Dij

✐❢ i ✐s ❧♦✇❡r t❤❛♥ j

T Dij

t♦t❛❧ r❡❝t✐❧✐♥❡❛r ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ✐t❡♠s i ❛♥❞ j

N Qs

❧✐♥❡❛r✐s❛t✐♦♥ ✈❛r✐❛❜❧❡ ❡①♣r❡ss✐♥❣ t❤❡ ♣r♦❞✉❝t ♦❢ N F ❛♥❞ Qs

ARs

♣r❡❞❡✜♥❡❞ r❡❝t❛♥❣✉❧❛r ✢♦♦r ❛r❡❛ s

FA

✢♦♦r ❛r❡❛

X max , Y max

❞✐♠❡♥s✐♦♥s ♦❢ ✢♦♦r ❛r❡❛

✸✳✶

❋♦r♠✉❧❛t✐♦♥ ❆

■♥ ❢♦r♠✉❧❛t✐♦♥ ❆✱ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥ts ❛r❡ tr❡❛t❡❞ ❛s ❛ s✐♥❣❧❡ ✉♥✐t st❛rt✐♥❣ ♦♥ ♦♥❡ ✢♦♦r

k ✱ s♣❛♥♥✐♥❣ t❤r♦✉❣❤ ❝♦♥s❡❝✉t✐✈❡ ✢♦♦rs ❛♥❞ t❡r♠✐♥❛t✐♥❣ ❛t ❛ ❤✐❣❤❡r ✢♦♦r k ′ ✳ ❋❧♦♦rs ❛r❡ ♥✉♠❜❡r❡❞ ❢r♦♠ ❜♦tt♦♠ t♦ t♦♣✳ ❚❤r❡❡ ❡q✉✐✈❛❧❡♥t ♠♦❞❡❧s ✲ ❆✳✶✱ ❆✳✷ ❛♥❞ ❆✳✸ ❛r❡ ❞❡s❝r✐❜❡❞ ✇❤✐❝❤ ♦♥❧② ❞✐✛❡r ❜② t❤❡ s❡ts ♦❢ ❝♦♥str❛✐♥ts ✉s❡❞ t♦ ♠♦❞❡❧ t❤❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t✳

✸✳✶✳✶ ❋❧♦♦r ❝♦♥str❛✐♥ts ❊✈❡r② ❡q✉✐♣♠❡♥t i ❛✈❛✐❧❛❜❧❡ ✐s ❛ss✐❣♥❡❞ t♦ ❛♥ ❡q✉✐✈❛❧❡♥t ♥✉♠❜❡r ♦❢ ✢♦♦rs✱ Mi ✳

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

X

Page 10 of 33

✶✵

Vik = Mi

∀i

✭✶✮

k

✇❤❡r❡ Vik ✐s ❛ ❜✐♥❛r② ✈❛r✐❛❜❧❡ ✇❤✐❝❤ ❞❡t❡r♠✐♥❡s ✐❢ ❛♥ ❡q✉✐♣♠❡♥t i ✐s ❛ss✐❣♥❡❞ t♦ ✢♦♦r k. ❆ ✈❛r✐❛❜❧❡✱ nijk ✱ ✐s ✐♥tr♦❞✉❝❡❞ t♦ ❞❡t❡r♠✐♥❡ ✐❢ ❡q✉✐♣♠❡♥t i ❛♥❞ j ❛r❡ ❛ss✐❣♥❡❞ t♦ ✢♦♦r k ✱ ❣✐✈❡♥ ❜②✿

nijk ≥ Vik + Vjk − 1

∀ i = 1, ..., N − 1, j 6= i, k = 1, ..., K ∀ i = 1, ..., N − 1, j 6= i, k = 1, ..., K

Nij ≥ nijk

✭✷✮ ✭✸✮

❚❤❡ ✈❛r✐❛❜❧❡ Nij t❛❦❡s t❤❡ ✈❛❧✉❡ ♦❢ ✶ ✐❢ ❛♥❞ ♦♥❧② ✐❢ ✐t❡♠s i ❛♥❞ j ❛r❡ ♦♥ ❛♥② s❛♠❡ ✢♦♦r✳ s ❋✉rt❤❡r♠♦r❡✱ ❛ ✢♦♦r ✇✐❧❧ ♦♥❧② ❡①✐st ✐❢ ❛♥ ❡q✉✐♣♠❡♥t st❛rts ♦♥ ✐t✳ ❋♦r t❤✐s✱ ♥❡✇ ✈❛r✐❛❜❧❡s Sik f ❛♥❞ Sik ′ ❛r❡ ✐♥tr♦❞✉❝❡❞ t❛❦✐♥❣ ✈❛❧✉❡s ♦❢ ✶ ✐❢ ❛♥ ❡q✉✐♣♠❡♥t i st❛rts ❛t ✢♦♦r k ❛♥❞ t❡r♠✐♥❛t❡s

❛t ✢♦♦r k ′ r❡s♣❡❝t✐✈❡❧②✳ ❚❤✉s✿ s ≤ Wk Sik

∀ i, k

✭✹✮

❆❧s♦✱ ❛ ✢♦♦r s❤♦✉❧❞ ❡①✐st ♦♥❧② ✐❢ ❛♥ ❡q✉✐♣♠❡♥t ✐s ❛ss✐❣♥❡❞ t♦ ✐t✱ ❛♥❞ ♥♦t ❥✉st ♣❛s✐♥❣ t❤r♦✉❣❤ ✐t ✭❢♦r ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t✮✱ ❛♥❞ t❤❛t t❤❡ ♣r❡❝❡❞✐♥❣ ✢♦♦r ✐s ❛❧s♦ ♦❝❝✉♣✐❡❞✳ ❚❤✐s ❝♦♥str❛✐♥t ✐s ♦❜t❛✐♥❡❞ ❢r♦♠ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✿

∀ k = 2, ..., K

Wk ≤ Wk−1

✭✺✮

❚❤❡ ♥✉♠❜❡r ♦❢ ✢♦♦rs r❡q✉✐r❡❞ ✐s t❤❡♥ ❞❡t❡r♠✐♥❡❞ ❜② ❡q✉❛t✐♦♥ ✻ ✶ ✳

NF ≥

X

Wk

k

ACS Paragon Plus Environment

✭✻✮

Page 11 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

✶✶

✸✳✶✳✷ ❊q✉✐♣♠❡♥t ♦r✐❡♥t❛t✐♦♥ ❝♦♥str❛✐♥ts ❆ ✾✵◦ r♦t❛t✐♦♥ ♦❢ ❡q✉✐♣♠❡♥t ♦r✐❡♥t❛t✐♦♥ ✐s ❛❧❧♦✇❡❞ ✐♥ t❤❡ ①✲② ♣❧❛♥❡✳ ❚❤✐s ✐s r❡♣r❡s❡♥t❡❞ ❜② ❡q✉❛t✐♦♥s ✼ ❛♥❞ ✽ ✶ ✳

li = αi Oi + βi (1 − Oi )

∀i

di = αi + βi − li

∀i

✭✼✮ ✭✽✮

❘♦t❛t✐♦♥ ✐♥ t❤❡ ③✲❛①✐s ✐s ❞❡❡♠❡❞ ✉♥r❡❛❧✐st✐❝ ❛s s✉❝❤ ❡q✉✐♣♠❡♥t ♦r✐❡♥t❛t✐♦♥ ✐s ✜①❡❞ ❢♦r ❝♦♥✲ str✉❝t✐♦♥ ✐♥ ✈✐rt✉❛❧❧② ❛❧❧ ❝❛s❡s✳

hi = γ i

✭✾✮

∀i

✸✳✶✳✸ ▼✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❝♦♥str❛✐♥ts ■♥ ♦r❞❡r ❢♦r ❡q✉✐♣♠❡♥t ✐t❡♠s r❡q✉✐r✐♥❣ ♠♦r❡ t❤❛♥ ♦♥❡ ✢♦♦r t♦ s♣❛♥ ❛❝r♦ss s✉❝❝❡ss✐✈❡ ✢♦♦rs✱ t❤❡ ❝♦♥str❛✐♥ts ❜❡❧♦✇ ❛r❡ ✐♥tr♦❞✉❝❡❞✳ ❚❤r❡❡ ❛❧t❡r♥❛t✐✈❡ ♠♦❞❡❧s ❛r❡ s❤♦✇♥ ✭▼♦❞❡❧s ❆✳✶✱ ❆✳✷ ❛♥❞ ❆✳✸✮✳

▼♦❞❡❧ ❆✳✶ ✐♥❝❧✉❞❡s ❡q✉❛t✐♦♥s ✶✵ ✲ ✶✹✳ s −Vik + Vi,k−1 + Sik ≥0

∀ i, k

✭✶✵✮

f ≥0 −Vik + Vi,k+1 + Sik

∀ i, k

✭✶✶✮

f s ❊q✉❛t✐♦♥s ✶✵ ❛♥❞ ✶✶ ❡♥s✉r❡s t❤❛t t❤❡ ❜✐♥❛r② ✈❛r✐❛❜❧❡s Sik t❛❦❡ ❛ ✈❛❧✉❡ ♦❢ ✶ ✐❢ ❛♥ ❛♥❞ Sik

❡q✉✐♣♠❡♥t st❛rts ❛♥❞ ❡♥❞s ♦♥ ❛ ♣❛rt✐❝✉❧❛r ✢♦♦r✱ ✇✐t❤ ❡❛❝❤ ❡q✉✐♣♠❡♥t ❜❡✐♥❣ r❡str✐❝t❡❞ t♦ st❛rt ❛♥❞ ❡♥❞ ♦♥ ♦♥❧② ♦♥❡ ✢♦♦r ❜②✿

X

s Sik =1

∀i

✭✶✷✮

X

f =1 Sik

∀i

✭✶✸✮

k

k

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 33

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

✶✷

❚❤❡ ❝♦♥str❛✐♥t t♦ r❡str✐❝t ❡q✉✐♣♠❡♥t t♦ ♦❝❝✉♣② s✉❝❝❡ss✐✈❡ ✢♦♦rs ✐s t❤❡♥ ❣✐✈❡♥ ❛s✿ k+M Xi

s Vik′ ≥ Mi .Sik

✭✶✹✮

∀ i, k

k′ =k

▼♦❞❡❧ ❆✳✷ ♠♦❞❡❧s t❤❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❝♦♥str❛✐♥t ❜② t❤❡ ❡q✉❛t✐♦♥ ❜❡❧♦✇✿ M i −1 X

Vi,k+θ ≥ (M i − 1).(Vik − Vi,k−1 )

∀ i, k

✭✶✺✮

θ=1

❊q✉❛t✐♦♥ ✶✺ ❡♥s✉r❡s t❤❛t ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ♦❝❝✉♣② ❝♦♥s❡❝✉t✐✈❡ ✢♦♦rs✱ t❤❡ t♦t❛❧ ♥✉♠❜❡r ❡q✉❛❧❧✐♥❣ t❤❡ r❡q✉✐r❡❞ ♥✉♠❜❡r ♦❢ ✢♦♦rs Mi ✳

▼♦❞❡❧ ❆✳✸ ♠❛❦❡s ✉s❡ ♦❢ t❤❡ ❜✐♥❛r② ✈❛r✐❛❜❧❡s Siks ❛♥❞ Sikf ❛♥❞ ✐s ❞❡s❝r✐❜❡❞ ✉s✐♥❣ ❡q✉❛t✐♦♥s ✶✷✱ ✶✸ ❛♥❞ ✶✻ ❜❡❧♦✇✳ f s Vik − Vi,k−1 = Sik − Si,k−1

∀ i, k

✭✶✻✮

■♥ ❛❧❧ ❝❛s❡s ✭♠♦❞❡❧s ❆✳✶✱ ❆✳✷✱ ❛♥❞ ❆✳✸✮ ❢♦r t❤❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t✱ ❡✈❡r② ❡q✉✐♣♠❡♥t s ✐t❡♠ i s♣❛♥♥✐♥❣ ♠♦r❡ t❤❛♥ ♦♥❡ ✢♦♦r st❛rts ♦♥ ❛ s✐♥❣❧❡ ✢♦♦r ✭Sik = 1✮ ❛♥❞ t❡r♠✐♥❛t❡s ♦♥ f ❛♥♦t❤❡r ✢♦♦r ✭Sik ′ = 1✮✱ ♦❝❝✉♣②✐♥❣ s✉❝❝❡ss✐✈❡ ✢♦♦rs✱ t❤❡ s✉♠ ♦❢ ✇❤✐❝❤ ✐s ❡q✉❛❧ t♦ ✐ts r❡q✉✐r❡❞

♥✉♠❜❡r ♦❢ ✢♦♦rs ✭Mi ✮✳

ACS Paragon Plus Environment

Page 13 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

✶✸

✸✳✶✳✹ ◆♦♥✲♦✈❡r❧❛♣♣✐♥❣ ❝♦♥str❛✐♥ts ❚♦ ♣r❡✈❡♥t t✇♦ ♦r ♠♦r❡ ❡q✉✐♣♠❡♥t t♦ ♦❝❝✉♣② t❤❡ s❛♠❡ s♣❛❝❡ ✇✐t❤✐♥ ❛ ✢♦♦r✱ ❝♦♥str❛✐♥ts ✶✼ ✲ ✷✵ ❛r❡ ✐♥tr♦❞✉❝❡❞ ✶ ✿

li + lj 2

xi − xj + BM (1 − Ni,j + E1ij + E2ij ) ≥

∀ i = 1, ..., N − 1, j = 2, ..., N ✭✶✼✮

xj − xi + BM (2 − Ni,j − E1ij + E2ij ) ≥

li + lj 2

∀ i = 1, ..., N − 1, j = 2, ..., N ✭✶✽✮

yi − yj + BM (2 − Ni,j + E1ij − E2ij ) ≥

di + dj 2

∀ i = 1, ..., N − 1, j = 2, ..., N ✭✶✾✮

yj − yi + BM (3 − Nij − E1ij − E2ij ) ≥

di + dj 2

∀ i = 1, ..., N − 1, j = 2, ..., N ✭✷✵✮

✸✳✶✳✺ ❉✐st❛♥❝❡ ❝♦♥str❛✐♥ts ❉✐st❛♥❝❡ ❝♦♥str❛✐♥ts ❛r❡ ❞❡s❝r✐❜❡❞ ❜② ❡q✉❛t✐♦♥s ✷✶✱ ✷✷ ❛♥❞ ✷✸ ✶ ✱ t♦ ❞❡t❡r♠✐♥❡ t❤❡ r❡❧❛t✐✈❡ ❞✐st❛♥❝❡s ✐♥ t❤❡ ① ❛♥❞ ② ❝♦♦r❞✐♥❛t❡s r❡s♣❡❝t✐✈❡❧②✳

Rij − Lij = xi − xj

∀(i, j) : fij = 1

✭✷✶✮

Aij − Bij = yi − yj

∀(i, j) : fij = 1

✭✷✷✮

T Dij = Rij + Lij + Aij + Bij + Uij + Dij

∀(i, j) : fij = 1

✭✷✸✮

Pr♦✈✐s✐♦♥ ✐s ♠❛❞❡ ❢♦r ❝♦♥♥❡❝t✐♦♥ ❜❡t✇❡❡♥ ❡q✉✐♣♠❡♥t i ❛♥❞ j ❛t ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❤❡✐❣❤ts ♦❢ ❡✐t❤❡r ❡q✉✐♣♠❡♥t ❛s ❞❡s❝r✐❜❡❞ ❜② ❡q✉❛t✐♦♥ ✷✹❀

Uij − Dij = F H

X

s s (k − 1)(Sik − Sjk ) + OPij − IPij

∀(i, j) : fij = 1

✭✷✹✮

k

✇❤❡r❡ OPij r❡♣r❡s❡♥ts t❤❡ ✈❡rt✐❝❛❧ ❞✐st❛♥❝❡ ❢r♦♠ t❤❡ ❜❛s❡ ♦❢ ❡q✉✐♣♠❡♥t i t♦ ✐ts ♦✉t♣✉t ♣♦✐♥t✱

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Paragon Plus Environment

Page 14 of 33

Page 15 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

✶✺

❚❤❡ ❧❛♥❞ ❛r❡❛ ✐s t❤❡♥ ❝❛❧❝✉❧❛t❡❞ ❛s✿

F A = X max Y max

✭✷✾✮

❆♥ ❛❞❞✐t✐♦♥❛❧ ❧❛②♦✉t ❞❡s✐❣♥ ❝♦♥str❛✐♥t ✐s ✐♥❝❧✉❞❡❞ ❢♦r t❤❡ ③✲❝♦♦r❞✐♥❛t❡s t♦ ❞❡✜♥❡ ✐ts ❣❡♦♠❡t✲ r✐❝❛❧ ❝❡♥tr❡✱ ❣✐✈❡♥ ❜②✿

zi =

hi 2

∀i

✭✸✵✮

❊q✉❛t✐♦♥ ✸✵ ❛❧s♦ ❡♥s✉r❡s ❡q✉✐♣♠❡♥t i st❛rts ❢r♦♠ t❤❡ ❜❛s❡ ♦❢ t❤❡ ✢♦♦r k ✇❤❡r❡ ✐t ✐s ♣❧❛❝❡❞✳

✸✳✶✳✼ ❆r❡❛ ❈♦♥str❛✐♥ts ■♥ ♦r❞❡r t♦ ❛✈♦✐❞ ❜✐❧✐♥❡❛r t❡r♠s ✐♥ ❝❛❧❝✉❧❛t✐♥❣ t❤❡ ✢♦♦r ❛r❡❛✱ F A ✭❡q✳ ✷✾✮✱ ❡q✉❛t✐♦♥s ✸✶ ✲ ✸✻ ✶ ❛r❡ ✐♥tr♦❞✉❝❡❞✳ ❚❤❡ ❛r❡❛ ♦❢ ❡❛❝❤ ✢♦♦r ✐s ❞❡t❡r♠✐♥❡❞ ❢r♦♠ ❛ s❡t ♦❢ S ♣r❡❞❡✜♥❡❞ r❡❝t❛♥❣✉❧❛r ❛r❡❛ s✐③❡s✱ ARs ✱ ✇✐t❤ ❞✐♠❡♥s✐♦♥s (X s , Y s )✳

FA =

X

ARs Qs

✭✸✶✮

s

X

Qs = 1

✭✸✷✮

s

❚❤❡ ✢♦♦r ❧❡♥❣t❤ ❛♥❞ ❜r❡❛❞t❤ ✐s s❡❧❡❝t❡❞ ❢r♦♠ t❤❡ ❝❤♦s❡♥ r❡❝t❛♥❣✉❧❛r ❛r❡❛ s✐③❡ ❞✐♠❡♥s✐♦♥s✿

X max =

X

X s Qs

✭✸✸✮

X

Y s Qs

✭✸✹✮

s

Y max =

s

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✸ ▼❆❚❍❊▼❆❚■❈❆▲ ❋❖❘▼❯▲❆❚■❖◆

Page 16 of 33

✶✻

❆❧s♦✱ ❛ ♥❡✇ t❡r♠ N Qs ✐s ✐♥tr♦❞✉❝❡❞ ✐♥ ♦r❞❡r t♦ ❧✐♥❡❛r✐s❡ t❤❡ ❝♦st t❡r♠ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ♥✉♠❜❡r ♦❢ ✢♦♦rs✿

N Qs ≤ K Qs ∀s X NF = N Qs

✭✸✺✮ ✭✸✻✮

s

✸✳✶✳✽ ❖❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ❚❤❡ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ✐s t❤❡ s❛♠❡ ❢♦r ❡❛❝❤ ♠♦❞❡❧ ✲ t♦ ♠✐♥✐♠✐③❡ t❤❡ t♦t❛❧ ❝♦st ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❝♦♥♥❡❝t✐♦♥ ❝♦st✱ ♣✉♠♣✐♥❣ ❝♦st✱ ❧❛♥❞ ❛r❡❛ ❝♦st✱ ✢♦♦r ❝♦♥str✉❝t✐♦♥ ❝♦st ❛♥❞ ✢♦♦r✲❛r❡❛ ❞❡♣❡♥❞❡♥t ❝♦st✳ ❚❤✐s ✐s ❣✐✈❡♥ ❛s✿

min

X X

[Cijc T Dij + Cijv Dij + Cijh (Rij + Lij + Aij + Bij )]

i j6=i:fij =1

✭✸✼✮

+F C1 · N F + F C2

X

ARs · N Qs + LC · F A

s

✸✳✷

❋♦r♠✉❧❛t✐♦♥ ❇

❋♦r♠✉❧❛t✐♦♥ ❇ ✐s ❛ ❧✐♥❡❛r✐s❡❞ ♠♦❞❡❧ ♦❢ ❑✉ ❡t ❛❧✳ ✶✽ ✇✐t❤ ❛❞❛♣t❛t✐♦♥s ❢r♦♠ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ❛s ❞❡s❝r✐❜❡❞ ✐♥ t❤❡ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❛❞❞✐t✐♦♥❛❧ ❝♦♥✲ str❛✐♥ts ❛r❡ ✐♥❝❧✉❞❡❞ t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❛♥❞ ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❝♦♥♥❡❝t✐♦♥ ❤❡✐❣❤t✳

✸✳✷✳✶ ▼✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❝♦♥str❛✐♥t ▼✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❛r❡ s♣❧✐t ✐♥t♦ ♣s❡✉❞♦ ✉♥✐ts ❡q✉✐✈❛❧❡♥t t♦ t❤❡ ♥✉♠❜❡r ♦❢ ✢♦♦rs t❤❡② ♦❝❝✉♣② ✭❋✐❣✉r❡ ✷✮✳ ❚❤✐s ❛♣♣r♦❛❝❤ ♣r❡s❡♥ts ❛ ♠♦r❡ ❛❝❝✉r❛t❡ r❡♣r❡s❡♥t❛t✐♦♥ ❢♦r ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t t❤❛t ❤❛✈❡ ✈❛r②✐♥❣ s✐③❡s ❛❧♦♥❣ ✐ts ❤❡✐❣❤t ✲ ❞✉❡ t♦ ❛ r❛♥❣❡ ✭✐♥ t②♣❡ ❛♥❞ s✐③❡✮ ♦❢ ❛✉①✐❧✐❛r② ✉♥✐ts ♣❧❛❝❡❞ ❜② s✉❝❤ ❡q✉✐♣♠❡♥t✳ ❚❤❡ ❞r❛✇❜❛❝❦✱ ❤♦✇❡✈❡r✱ ✐s t❤❛t ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♥✉♠❜❡r ♦❢ ✉♥✐ts ✐♥ t❤❡ ▼■▲P ♠♦❞❡❧ ✐s r❡❛❧✐s❡❞ ✇❤✐❝❤ ❝❛♥ ❧❡❛❞ t♦ ❧❛r❣❡r ❝♦♠♣✉t❛t✐♦♥❛❧ ACS Paragon Plus Environment

Page 17 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 33

✹ ❈❆❙❊ ❙❚❯❉■❊❙

✶✽

❆♥❞ ❢♦r ♣s❡✉❞♦ ✉♥✐ts t♦ ❜❡ ♣❧❛❝❡❞ ❞✐r❡❝t❧② ❛❜♦✈❡ ✐t✬s ♣r❡❝❡❞✐♥❣ ❝♦✉♥t❡r♣❛rt✿

xp = xp+1

∀ pǫPi

✭✸✾✮

yp = yp+1

∀ pǫPi

✭✹✵✮

❛♥❞ ✜♥❛❧❧②✱ ❝♦♥s✐st❡♥❝② ✐♥ ✾✵♦ r♦t❛t✐♦♥ ✐s ❡♥s✉r❡❞ ❢♦r ❛❧❧ ♣s❡✉❞♦ ✉♥✐ts ♦❢ ❛ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣✲ ♠❡♥t✿

Op = Op+1

✭✹✶✮

∀ pǫPi

✸✳✷✳✷ ❉✐st❛♥❝❡ ❝♦♥str❛✐♥ts ❋♦r ❝♦♥♥❡❝t✐♦♥ ❜❡t✇❡❡♥ ❡q✉✐♣♠❡♥t i′ ❛♥❞ j ′ ❛t ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ❤❡✐❣❤ts ♦❢ ❡✐t❤❡r ❡q✉✐♣♠❡♥t✱ t❤❡ ❝♦♥str❛✐♥t ❜❡❧♦✇ ✐s ✉s❡❞❀

Ui′ j ′ − Di′ j ′ = F H

X

∀(i′ , j ′ )ǫI ′ : fi′ j ′ = 1 ✭✹✷✮

(k − 1)(Vi′ k − Vj ′ k ) + OPi′ j ′ − IPi′ j ′

k

❚❤❡ r❡s✉❧t✐♥❣ ♠♦❞❡❧ ✭❇✮ t❤✉s ❝♦♥s✐sts ♦❢ ❝♦♥str❛✐♥ts ✸✽ ✲ ✹✷❀ ❛♥❞ ❡q✉❛t✐♦♥s ❙✶✲❙✶✺❀ ❙✶✼✲❙✷✽ ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ♠♦❞❡❧ ♦❢ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ❞❡s❝r✐❜❡❞ ✐♥ t❤❡ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ∀ i′ , j ′ ǫ I ′ ❀ ❛♥❞ ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥✿

min

X

X

[Cic′ j ′ T Di′ j ′ + Civ′ j ′ Di′ j ′ + Cih′ j ′ (Ri′ j ′ + Li′ j ′ + Ai′ j ′ + Bi′ j ′ )]

i′ j ′ 6=i′ :fi′ j ′ =1

✭✹✸✮

+F C1 · N F + F C2

X

ARs · N Qs + LC · F A

s



❈❛s❡ ❙t✉❞✐❡s

■♥ t❤✐s s❡❝t✐♦♥✱ ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❝❛s❡ st✉❞✐❡s ❛♣♣❧✐❡❞ t♦ ❡❛❝❤ ❢♦r♠✉❧❛t✐♦♥ ✐s s❤♦✇♥✳ ❊❛❝❤ ❡①❛♠♣❧❡ ✇❛s ♠♦❞❡❧❧❡❞ ✉s✐♥❣ ●❆▼❙ ✷✻ ♠♦❞❡❧❧✐♥❣ s②st❡♠ ✈✷✹✳✼✳✶ ✇✐t❤ t❤❡ ❈P▲❊❳ ✈✶✷✳✻ ❘ ❊✺✲✶✻✺✵ ❈P❯ ✇✐t❤ ✸✷●❇ ❘❆▼✱ ❛♥❞ t❤❡ ❧❛②♦✉t ♣❧♦tt❡❞ ✉s✐♥❣ ❘ ❳❡♦♥ s♦❧✈❡r ♦♥ ❛♥ ■♥t❡❧ ❘ ✷✵✶✼✳ ❊❛❝❤ r✉♥ ✇❛s s♦❧✈❡❞ t♦ ❣❧♦❜❛❧ ♦♣t✐♠❛❧✐t②✳ ❋♦r t❤❡ ✢♦♦r ❛r❡❛✱ ❆✉t♦❞❡s❦ ❆✉t♦❈❆❉

ACS Paragon Plus Environment

Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✹ ❈❆❙❊ ❙❚❯❉■❊❙

✶✾

✜✈❡ ❛❧t❡r♥❛t✐✈❡ s✐③❡s ✭✶✵♠✱ ✷✵♠✱ ✸✵♠✱ ✹✵♠ ❛♥❞ ✺✵♠✮ ✇❡r❡ ✉s❡❞ ✐♥ ❡①❛♠♣❧❡s ✶ ❛♥❞ ✷✱ s❡✈❡♥ ❛❧t❡r♥❛t✐✈❡ s✐③❡s ✭✶✵♠✱ ✷✵♠✱ ✸✵♠✱ ✹✵♠✱ ✺✵♠✱ ✻✵♠ ❛♥❞ ✼✵♠✮ ✐♥ ❡①❛♠♣❧❡ ✸✱ ❣✐✈✐♥❣ ❛ t♦t❛❧ ♦❢ ✷✺ ❛♥❞ ✹✾ ♣♦ss✐❜❧❡ ❛r❡❛ s✐③❡s r❡s♣❡❝t✐✈❡❧②✱ ❡①❝❡♣t ♦t❤❡r✇✐s❡ st❛t❡❞✳ ❉❛t❛ ♦♥ ❝♦♥♥❡❝t✐✈✐t② ❝♦sts ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❢r♦♠ ♣r♦❝❡ss s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ♦❢ ❛ ❝❛s❡ st✉❞②✳ P✐♣❡ s✐③✐♥❣ ✈❛❧✉❡s ❛r❡ ♦❜t❛✐♥❡❞ ❢r♦♠ ❞❡s✐❣♥ ❡q✉❛t✐♦♥s✱ ♠❛t❝❤❡❞ ✇✐t❤ ❝♦♠♠❡r❝✐❛❧❧② ❛✈❛✐❧❛❜❧❡ ♣✐♣❡ s✐③❡s ❛♥❞ t❤❡ ❝♦sts ❡st✐♠❛t❡❞ ♣❡r ✉♥✐t ❧❡♥❣t❤ ❢♦r ❛ s❡❧❡❝t❡❞ ♠❛t❡r✐❛❧ ♦❢ ❝♦♥str✉❝t✐♦♥ ❜❛s❡❞ ♦♥ t❤❡ ❝♦♠♣♦♥❡♥ts ✐♥ ❡❛❝❤ str❡❛♠✳ P✉♠♣✐♥❣ ❝♦sts ❛r❡ ❡st✐♠❛t❡❞ ❜❛s❡❞ ♦♥ ❝✉rr❡♥t ❡❧❡❝tr✐❝✐t② ♣r✐❝❡s ❛♥❞ ♠❛t❡r✐❛❧ ✢♦✇ r❛t❡ ✐♥ ❡❛❝❤ str❡❛♠✱ ❛♥❞ ❝♦♥str✉❝t✐♦♥ ❝♦sts ❛r❡ ❡①tr❛♣♦❧❛t❡❞ ❢r♦♠ ♣❛st ❞❛t❛ ♦♥ s✐♠✐❧❛r ♣❧❛♥t ❞❡s✐❣♥ ❜❛s❡❞ ♦♥ str✉❝t✉r❛❧ ❡♥❣✐♥❡❡r✐♥❣ ❝❛❧❝✉❧❛t✐♦♥s✳ ❋♦r ❛❧❧ ❝❛s❡ st✉❞✐❡s✱ ❞❛t❛ ♦♥ ❡q✉✐♣♠❡♥t ❞✐♠❡♥s✐♦♥s✱ ❝♦♥♥❡❝t✐✈✐t② ❛♥❞ ❝♦♥str✉❝t✐♦♥ ❝♦sts✱ ❛♥❞ ✈❡rt✐❝❛❧ ❝♦♥♥❡❝t✐♦♥ ♣♦✐♥ts ❛r❡ ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳ ❋♦r ❛❧❧ t❤r❡❡ ❡①❛♠♣❧❡s ✐♥✈❡st✐❣❛t❡❞ ✐♥ t❤✐s ✇♦r❦✱ ❜♦t❤ ❢♦r♠✉❧❛t✐♦♥s ❆ ❛♥❞ ❇ ②✐❡❧❞ ❡q✉✐✈❛❧❡♥t ♦♣t✐♠❛❧ ♣❧❛♥t ❧❛②♦✉ts ❛♥❞ t❤❡ s❛♠❡ ♦❜❥❡❝t✐✈❡ ✈❛❧✉❡✱ ✇✐t❤ ♠❛✐♥ ❞✐✛❡r❡♥❝❡s ✐♥ ❧❛②♦✉t ♦r✐❡♥t❛t✐♦♥ ❛♥❞ r❡✢❡❝t✐♦♥✳ ❚❤✉s✱ ♦♥❧② t❤❡ ♦♣t✐♠❛❧ ❧❛②♦✉t r❡s✉❧t ❢♦r ♠♦❞❡❧ ❆✳✶ ✐s ♣r❡s❡♥t❡❞ ❢♦r ❡❛❝❤ ❡①❛♠♣❧❡✳ ▲❛②♦✉t r❡s✉❧ts ❢♦r t❤❡ ♦t❤❡r ♠♦❞❡❧s ❛r❡ ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳

✹✳✶

❊①❛♠♣❧❡ ✶

❊①❛♠♣❧❡ ✶ ✐s ❛♥ ❊t❤②❧❡♥❡ ♦①✐❞❡ ♣❧❛♥t ✉s❡❞ ✐♥ t❤❡ ✇♦r❦ ♦❢ P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶✵ ✱ ♦r✐❣✐♥❛❧❧② ♣r❡s❡♥t❡❞ ❜② P❡♥t❡❛❞♦ ❛♥❞ ❈✐r✐❝ ✺ ✳ ❚❤❡ ♣❧❛♥t ❝♦♥s✐sts ♦❢ ✼ ✉♥✐ts ✇✐t❤ ♣r♦❝❡ss ✢♦✇ ❞✐❛❣r❛♠ s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✸✳ ❚❤❡ s✉♠♠❛r② ♦❢ t❤❡ ♠♦❞❡❧ st❛t✐st✐❝s ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❡r❢♦r♠❛♥❝❡ ✐s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✷ ❛♥❞ t❤❡ ♦♣t✐♠❛❧ ❧❛②♦✉t ✐♥ ❋✐❣✉r❡ ✹✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❣❛✈❡ ❛ t♦t❛❧ ❝♦st ♦❢ ✻✻✱✷✻✷✳✵ r♠✉ ✲ ✷✷✪ ❝♦♥♥❡❝t✐♦♥ ❝♦sts✱ ✹✹✪ ♣✉♠♣✐♥❣ ❝♦sts ❛♥❞ ✸✹✪ ❝♦♥str✉❝t✐♦♥ ❝♦sts✳ ❊❛❝❤ ✢♦♦r ❤❛❞ ❛♥ ❛r❡❛ ♠❡❛s✉r✐♥❣ ✷✵♠①✷✵♠✱ t♦t❛❧❧✐♥❣ t✇♦ ✢♦♦rs s❡❧❡❝t❡❞ ❢♦r ❝♦♥str✉❝t✐♦♥ ♦✉t ♦❢ ❢♦✉r ♣r♦✈✐❞❡❞ t♦ t❤❡ ♠♦❞❡❧✳ ❚❛❜❧❡ ✷ s❤♦✇s t❤❛t t❤❡ ♠♦❞❡❧s ✐♥ ❢♦r♠✉❧❛t✐♦♥ ❆ ❛r❡ ♠♦r❡ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡✣❝✐❡♥t✳ ❋♦r♠✉❧❛t✐♦♥ ❇ ✇❛s ✐♥❤❡r❡♥t❧② ❧❛r❣❡r ✐♥ s✐③❡ ❢♦r ❡❛❝❤ ❝❛s❡ st✉❞②✱ ❛s ❛ ❣r❡❛t❡r ♥✉♠❜❡r ♦❢ ✉♥✐ts ♥❡❡❞❡❞ t♦ ❜❡ ❤❛♥❞❧❡❞ t❤❛♥ ✐♥ ❢♦r♠✉❧❛t✐♦♥s ❆✳

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Paragon Plus Environment

Page 20 of 33

Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✹ ❈❆❙❊ ❙❚❯❉■❊❙

✷✶

❋✐❣✉r❡ ✹✿ ❊①❛♠♣❧❡ ✶ ❧❛②♦✉t r❡s✉❧ts ✹✳✷

❊①❛♠♣❧❡ ✷

❘ ✈✽✳✵✳ ■t ❝♦♥s✐sts ♦❢ ❊①❛♠♣❧❡ ✷ ✐s ❛♥ ❯r❡❛ ♣r♦❞✉❝t✐♦♥ ♣❧❛♥t✱ s✐♠✉❧❛t❡❞ ✇✐t❤ ❆s♣❡♥ P▲❯❙

✽ ✉♥✐ts✱ ✷ ♦❢ ✇❤✐❝❤ ❡①❝❡❡❞ t❤❡ ✢♦♦r ❤❡✐❣❤t ♦❢ ✽♠✳ ❚❤❡ ♣r♦❝❡ss ✢♦✇ ❞✐❛❣r❛♠ ♦❢ t❤❡ ♣❧❛♥t ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✺✳ ❆ t♦t❛❧ ♦❢ ✷✺ ♣♦ss✐❜❧❡ ❛r❡❛ s✐③❡s ✇❡r❡ ✉s❡❞ r❛♥❣✐♥❣ ❢r♦♠ ✺♠ ✲ ✹✺♠✳ ❊❛❝❤ ✉♥✐t ❤❛❞ t♦ ❜❡ ♣❧❛❝❡❞ ❛ ♠✐♥✐♠✉♠ ♦❢ ✹♠ ❢r♦♠ ❛♥♦t❤❡r ✐♥ ❡✐t❤❡r ❞✐r❡❝t✐♦♥✳ ❚❤❡ s✉♠♠❛r② ♦❢ t❤❡ ♠♦❞❡❧ st❛t✐st✐❝s ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❡r❢♦r♠❛♥❝❡ ✐s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✸✳ ❚❤❡ ❧❛②♦✉t r❡s✉❧t ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✻✳ ❆❧❧ ✹ ✢♦♦rs ✇❡r❡ ❛ss✐❣♥❡❞ ✉♥✐ts✱ ✇✐t❤ ❡❛❝❤ ✢♦♦r ❤❛✈✐♥❣ ❛♥ ❛r❡❛ ♠❡❛s✉r✐♥❣ ✶✺♠①✺♠✱ ❛♥❞ ❛ t♦t❛❧ ❝♦st ♦❢ ✶✶✼✱✹✸✶✳✵ r♠✉ ✲ ✻✪ ❝♦♥♥❡❝t✐♦♥✱ ✷✻✪ ♣✉♠♣✐♥❣ ❛♥❞ ✻✽✪ ❝♦♥str✉❝t✐♦♥ ❝♦sts✳ ❚❤❡ t✇♦ ♠✉❧t✐✲✢♦♦r ✉♥✐ts ✭✉♥✐ts ✷ ❛♥❞ ✹✮ ♦❝❝✉♣✐❡❞ s✉❝❝❡ss✐✈❡ ✢♦♦rs ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡✐r ❤❡✐❣❤t ✭✢♦♦rs ✶✲✹ ❛♥❞ ✷✲✸ r❡s♣❡❝t✐✈❡❧②✮✳ ❈♦♠♣✉t❛t✐♦♥❛❧ r❡s✉❧ts s❤♦✇❡❞ ❣❧♦❜❛❧ ♦♣t✐♠❛❧✐t② ✇❛s ❛❝❤✐❡✈❡❞ ❜② ❛❧❧ ♠♦❞❡❧s ✐♥ ❛ r❡❧❛t✐✈❡❧② s❤♦rt t✐♠❡ ✭✉♥❞❡r ✺s✮✳ ❖✈❡r❛❧❧ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ♠♦❞❡❧ ✐s ❝❛♣❛❜❧❡ ♦❢ ❤❛♥❞❧✐♥❣ ♣r♦❝❡ss✲s♣❡❝✐✜❝ ❝♦♥❞✐t✐♦♥s ✇❤✐❧st ❞❡❝✐❞✐♥❣ ✢♦♦r ♣❧❛❝❡♠❡♥t ❡✈❡♥ ❢♦r ♠✉❧t✐✲✢♦♦r ✉♥✐ts✳

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✹ ❈❆❙❊ ❙❚❯❉■❊❙

Page 22 of 33

✷✷

❋✐❣✉r❡ ✺✿ ❋❧♦✇ ❞✐❛❣r❛♠ ♦❢ ❯r❡❛ Pr♦❞✉❝t✐♦♥

❚❛❜❧❡ ✸✿ ❙✉♠♠❛r② ♦❢ ♠♦❞❡❧ st❛t✐st✐❝s ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❡r❢♦r♠❛♥❝❡ ❢♦r ❊①❛♠♣❧❡ ✷

❚♦t❛❧ ❈♦st ❈P❯ ✭s✮ ◆✉♠❜❡r ♦❢ ◆✉♠❜❡r ♦❢ ◆✉♠❜❡r ♦❢

✭r♠✉✮ ❜✐♥❛r② ✈❛r✐❛❜❧❡s ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s ❡q✉❛t✐♦♥s

❯r❡❛ Pr♦❞✉❝t✐♦♥ ✭✽ ✉♥✐ts✮ ❆✳✶ ❆✳✷ ❆✳✸ ❇ ✶✶✼✱✹✸✶✳✵ ✹✳✽ ✹✳✾ ✷✳✾ ✹✳✵ ✶✹✺ ✶✹✺ ✶✹✺✸ ✷✽✶ ✸✶✺ ✷✽✸ ✸✶✺ ✶✺✾ ✻✶✶ ✺✹✼ ✺✹✼ ✶✱✷✼✾

ACS Paragon Plus Environment

Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✹ ❈❆❙❊ ❙❚❯❉■❊❙

✷✸

❋✐❣✉r❡ ✻✿ ❊①❛♠♣❧❡ ✷ ❧❛②♦✉t r❡s✉❧ts

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Paragon Plus Environment

Page 24 of 33

Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✹ ❈❆❙❊ ❙❚❯❉■❊❙

✷✺

✇✐t❤ ♣r❡✈✐♦✉s ❡①❛♠♣❧❡s ✐s ❛ttr✐❜✉t❡❞ t♦ t❤❡ ❣r❡❛t❡r ♥✉♠❜❡r ♦❢ ✉♥✐ts ❝♦♥s✐❞❡r❡❞✳ ❈♦♥♥❡❝t✐♦♥ ❛♥❞ ❝♦♥str✉❝t✐♦♥ ❝♦sts ❝♦♥st✐t✉t❡❞ ✻✪ ❛♥❞ ✹✹✪ ♦❢ t❤❡ t♦t❛❧ ❝♦st r❡s♣❡❝t✐✈❡❧②✳ ❚❛❜❧❡ ✹✿ ❙✉♠♠❛r② ♦❢ ♠♦❞❡❧ st❛t✐st✐❝s ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❡r❢♦r♠❛♥❝❡ ❢♦r ❊①❛♠♣❧❡ ✸

❚♦t❛❧ ❈♦st ❈P❯ ✭s✮ ◆✉♠❜❡r ♦❢ ◆✉♠❜❡r ♦❢ ◆✉♠❜❡r ♦❢

✭r♠✉✮ ❜✐♥❛r② ✈❛r✐❛❜❧❡s ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s ❡q✉❛t✐♦♥s

❈❉❯ P❧❛♥t ✭✶✼ ✉♥✐ts✮ ❆✳✶ ❆✳✷ ❆✳✸ ❇ ✼✹✾✱✻✾✶✳✹ ✷✾✷✳✸ ✶✵✺✳✵ ✹✹✳✶ ✶✸✶✳✻ ✺✻✽ ✺✻✽ ✺✻✽ ✶✱✺✻✾ ✶✱✺✵✼ ✶✱✸✽✽ ✶✱✺✵✼ ✸✽✼ ✸✱✷✶✸ ✷✱✾✾✸ ✷✱✾✼✺ ✶✶✱✹✽✸

❚❤❡ ❧❛②♦✉t ♦❢ ❡q✉✐♣♠❡♥t ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✽✳ ❆s ❛❧❧ t❤❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ✭✺✱ ✻✱ ✼✱ ✶✷ ❛♥❞ ✶✺✮ st❛rt✐♥❣ ✢♦♦rs ✇❡r❡ ♣r❡❞❡✜♥❡❞✱ t❤❡② ❛❧❧ st❛rt❡❞ ❢r♦♠ t❤❡ ✜rst ✢♦♦r t❤r♦✉❣❤ t❤❡ ♥✉♠❜❡r ♦❢ ✢♦♦rs r❡q✉✐r❡❞ ❜❛s❡❞ ♦♥ t❤❡✐r ❤❡✐❣❤t✳ ■t ✐s ✇♦rt❤② ♦❢ ♥♦t✐♥❣ t❤❛t ❛❧t❤♦✉❣❤ ❡q✉✐♣♠❡♥t ✶✹ r❡q✉✐r❡❞ ✺ ✢♦♦rs ❜❛s❡❞ ♦♥ ✐ts ❤❡✐❣❤t✱ ❛ t♦t❛❧ ♦❢ ✹ ✢♦♦rs ✇❛s ❞❡❝✐❞❡❞ ❜② ❛❧❧ ❢♦r♠✉❧❛t✐♦♥s✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ❛ ✜❢t❤ ✢♦♦r ✇❛s ❞❡❡♠❡❞ ✉♥♥❡❝❡ss❛r② ❛s ♥♦ ♦t❤❡r ❡q✉✐♣♠❡♥t ♦t❤❡r t❤❛♥ ❡q✉✐♣♠❡♥t ✶✹ ✇❛s t♦ ❜❡ ♣❧❛❝❡❞ ♦♥ s✉❝❤ ✢♦♦r ✐♥ ♦r❞❡r t♦ ♦❜t❛✐♥ ❛♥ ♦♣t✐♠❛❧ s♦❧✉t✐♦♥✱ ❛♥❞ t❤❡ ❛❞❞✐t✐♦♥❛❧ ❝♦♥str✉❝t✐♦♥ ❝♦st ❢♦r ❛ ✜❢t❤ ✢♦♦r ✇❛s ❡❧✐♠✐♥❛t❡❞✳ ❙♦✱ ❛❧t❤♦✉❣❤ ❛ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❝❛♥ s♣❛♥ ❛ s♣❡❝✐✜❡❞ ♥✉♠❜❡r ♦❢ ✢♦♦rs ❜❛s❡❞ ♦♥ ✐ts ❤❡✐❣❤t✱ ♥♦t ❡✈❡r② ♦♥❡ ♦❢ t❤♦s❡ ✢♦♦rs ♥❡❡❞ t♦ ❜❡ ❝♦♥str✉❝t❡❞✳ Pr❛❝t✐❝❛❧ ❡①❛♠♣❧❡s ✐♥❝❧✉❞❡ ♠✉❧t✐✲✢♦♦r ❧❛②♦✉ts ❛❜♦✉t ✜r❡❞ ❤❡❛t❡rs ✇✐t❤ ❧♦♥❣ st❛❝❦s✱ ❞✐st✐❧❧❛t✐♦♥ ❝♦❧✉♠♥s ❛♥❞ ✢❛r❡ st❛❝❦s✳

❋✐❣✉r❡ ✽✿ ❊①❛♠♣❧❡ ✸ ❧❛②♦✉t r❡s✉❧ts

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✹ ❈❆❙❊ ❙❚❯❉■❊❙

Page 26 of 33

✷✻

✹✳✸✳✶ ❙②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ❋♦r ❡❛❝❤ ♦❢ t❤❡ ❝❛s❡ st✉❞✐❡s s♦❧✈❡❞✱ ✐t ❜❡❝♦♠❡s ❡✈✐❞❡♥t ❢r♦♠ t❤❡ ❧❛②♦✉t r❡s✉❧ts ✭♣r❡s❡♥t❡❞ ❛❜♦✈❡ ❛♥❞ ✐♥ s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✮ t❤❛t t❤❡r❡ ❝❛♥ ❡①✐st ♠✉❧t✐♣❧❡ ♦♣t✐♠❛❧ s♦❧✉t✐♦♥s ❢♦r ❡❛❝❤ ♣r♦❜❧❡♠✳ ❚❤❡s❡ ♠✉❧t✐♣❧❡ ♦♣t✐♠❛❧ s♦❧✉t✐♦♥s ❞✐✛❡r ♦♥❧② ✐♥ ❧❛②♦✉t ♦r✐❡♥t❛t✐♦♥✴r❡✢❡❝t✐♦♥ ❛♥❞✴♦r tr❛♥s❧❛t✐♦♥ ♦❢ ❡q✉✐♣♠❡♥t ♦♥ t❤❡ ❧❛②♦✉t ❛r❡❛✱ r❡s✉❧t✐♥❣ ✐♥ ✐♥❡✣❝✐❡♥t ❈P❯ ✉s❛❣❡ ✷✼ ✱ ❡s♣❡❝✐❛❧❧② ❢♦r ❧❛r❣❡r ♣r♦❜❧❡♠ ✐♥st❛♥❝❡s✳ ■♥ ♦r❞❡r t♦ ✐♥❝r❡❛s❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡✣❝✐❡♥❝② ❛♥❞ r❡❞✉❝❡ s②♠♠❡tr②✱ ❛❞❞✐t✐♦♥❛❧ ❝♦♥str❛✐♥ts✱ ❛❞❛♣t❡❞ ❢r♦♠ ❲❡st❡r❧✉♥❞ ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✷✼ ❛r❡ ✐♥tr♦❞✉❝❡❞✿

✇❤❡r❡ α = min



li d i , 2 2



+ min



xi + yi − xj − yj ≥ α · Nij

✭✹✹✮

E1ij = 0

✭✹✺✮

lj d j , 2 2



✳ ❚❤❡s❡ ✜① t❤❡ r❡❧❛t✐✈❡ ♣♦s✐t✐♦♥ ♦❢ i ❛♥❞ j ❛s ✇❡❧❧ ❛s ♦♥❡

♦❢ t❤❡ ♥♦♥✲♦✈❡r❧❛♣♣✐♥❣ ❜✐♥❛r② ✈❛r✐❛❜❧❡s✱ E1ij = 0✳ ❚❤❡ ❧❛tt❡r ❡♥❢♦r❝❡s ❡✐t❤❡r ♦❢ xi −xj ≥ ♦r yi − yj ≥

di +dj 2

li +lj 2

❛❝❝♦r❞✐♥❣ t♦ ❡q✉❛t✐♦♥s ✶✼ ✲ ✷✵✱ ✐✳❡✳✱ ✉♥✐t i ✐s r❡❧❛t✐✈❡❧② ❧♦❝❦❡❞ ✐♥ ❛ ❝♦♠♣❛ss

♣♦✐♥t ◆♦rt❤ ❊❛st ♦❢ ✉♥✐t j ❤❡♥❝❡ ❜r❡❛❦✐♥❣ t❤❡ s②♠♠❡tr②✳ ❚❤❡ ❛❜♦✈❡ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ✇❡r❡ ❛♣♣❧✐❡❞ t♦ ❡①❛♠♣❧❡ ✸ ✲ ❈r✉❞❡ ❞✐st✐❧❧❛t✐♦♥ ♣❧❛♥t ✇✐t❤ ♣r❡✲❤❡❛t✐♥❣ tr❛✐♥ ✲ ❜② ✐♥❝♦r♣♦r❛t✐♥❣ ❡q✉❛t✐♦♥s ✹✹ ❛♥❞ ✹✺ ✐♥ ▼♦❞❡❧ ❆✳✶ ✇❤❡r❡ t❤❡ ❝❤♦✐❝❡ ♦❢ ❡q✉✐♣♠❡♥t i ❛♥❞ j ❛r❡ ❛♠♦♥❣ ♠✉❧t✐✲✢♦♦r ✉♥✐ts ♦♥❧②✱ ❜❛s❡❞ ♦♥ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ❝r✐t❡r✐❛ ✷✼ ✿ ❛ ✲ ❊q✉✐♣♠❡♥t i ❛♥❞ j ❤❛✈✐♥❣ t❤❡ ❤✐❣❤❡st ❝♦♥♥❡❝t✐♦♥ ❝♦st✿ ✉♥✐ts ✺ ❛♥❞ ✻❀ ❜ ✲ ❚✇♦ ❡q✉✐♣♠❡♥t ✇✐t❤ t❤❡ ❧❛r❣❡st ❛r❡❛✿ ✉♥✐ts ✼ ❛♥❞ ✶✺❀ ❝ ✲ ❚✇♦ ❡q✉✐♣♠❡♥t ✇✐t❤ t❤❡ s♠❛❧❧❡st ❛r❡❛✿ ✉♥✐ts ✻ ❛♥❞ ✶✷✳ ❚❤❡ r❡s✉❧t✐♥❣ ♠♦❞❡❧s ✇❡r❡ s♦❧✈❡❞ t♦ ❣❧♦❜❛❧ ♦♣t✐♠❛❧✐t② ❛♥❞ ❛ s♦❧✉t✐♦♥ ♦❢ ✼✹✾✱✻✾✶✳✹ r♠✉ ✇❛s ♦❜t❛✐♥❡❞ ✐♥ ❛❧❧ ❛❧t❡r♥❛t✐✈❡ ❝❤♦✐❝❡s ♦❢ ❡q✉✐♣♠❡♥t✱ t❤❡ s❛♠❡ ❛s ♠♦❞❡❧ ❆✳✶ ✇✐t❤♦✉t t❤❡s❡ ❝♦♥✲ str❛✐♥ts✳ ❚❤❡✐r ❝♦♠♣✉t❛t✐♦♥❛❧ ❈P❯ t✐♠❡s ❛r❡ s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✺ ✲ ✇❤❡r❡ ❢♦r ❡❛❝❤ ✉♥✐t s❡❧❡❝t✐♦♥ ACS Paragon Plus Environment

Page 27 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✺ ❈❖◆❈▲❯❉■◆● ❘❊▼❆❘❑❙

✷✼

❛❧t❡r♥❛t✐✈❡✱ t❤❡ r❡s✉❧t✐♥❣ ♠♦❞❡❧ ✐s ♥❛♠❡❞ ❛♣♣r♦♣r✐❛t❡❧② ✲ ♠♦❞❡❧ ❆✳✶❛ ❢♦r ♠♦❞❡❧ ❆✳✶ ✇✐t❤ s②♠✲ ♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ✇✐t❤ ❡q✉✐♣♠❡♥t i ❛♥❞ j ❝❤♦s❡♥ ❜② ❝r✐t❡r✐♦♥ ❛✱ ❤❛✈✐♥❣ t❤❡ ❤✐❣❤❡st ❝♦♥♥❡❝t✐♦♥ ❝♦st✱ ❛♥❞ s♦ ♦♥✳ ❚❤❡ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ♥❡✇ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ❤❛s ✐♠♣r♦✈❡❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡✣❝✐❡♥❝② ❜② ♦♥❡ ♦r❞❡r ♦❢ ♠❛❣♥✐t✉❞❡✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ✐♠♣r♦✈❡♠❡♥ts ✇❡r❡ ❛❧s♦ ❢♦✉♥❞ ❢♦r t❤❡ ♦t❤❡r ♠♦❞❡❧s ❞❡✈❡❧♦♣❡❞ ❛♥❞ ❡①❛♠♣❧❡s ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ✇♦r❦✳ ❚❛❜❧❡ ✺✿ ❙✉♠♠❛r② ♦❢ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❡r❢♦r♠❛♥❝❡ ❢♦r ❊①❛♠♣❧❡ ✸❀ ▼♦❞❡❧ ❆✳✶ ✇✐t❤ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥tr❛✐♥ts ▼♦❞❡❧ ❆✳✶ ❆✳✶❛ ❆✳✶❜ ❆✳✶❝



❈P❯ ✭s✮ ✷✾✷✳✸ ✸✶✳✷ ✸✸✳✼ ✼✶✳✷

❈♦♥❝❧✉❞✐♥❣ r❡♠❛r❦s

❆♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ▼■▲P ♠♦❞❡❧ ❜② P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✇❛s ♣r♦♣♦s❡❞ t♦ ❛❞❞r❡ss ♥❡✇ ❝♦♥❝❡r♥s ✐♥ t❤❡ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ♣r♦❜❧❡♠✳ ❚❤❡s❡ ❝♦♥❝❡r♥s ✐♥❝❧✉❞❡❞ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ✐♥ ❝❡rt❛✐♥ ♣r♦❝❡ss ♣❧❛♥ts ✇✐t❤ ❞❡s✐❣♥✲s♣❡❝✐✜❡❞ ✐♥♣✉t ❛♥❞ ♦✉t♣✉t ❝♦♥♥❡❝t✐♦♥ ♣♦✐♥ts ❛❧♦♥❣ t❤❡ ❤❡✐❣❤t ♦❢ ❛♥ ❡q✉✐♣♠❡♥t✳ ❆ t♦t❛❧ ♦❢ ❢♦✉r ✭✹✮ ♠♦❞❡❧s ✇❡r❡ ♣r♦♣♦s❡❞✱ ❣r♦✉♣❡❞ ✐♥ t✇♦ ❜r♦❛❞ ❝❧❛ss❡s✳ ❚❤❡ ✜rst ❝❧❛ss ❤❛♥❞❧❡❞ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ❛s t❤❡② ✇❡r❡ ✭s✐♥❣❧❡ t❛❧❧ ✉♥✐ts✮ ❤❛✈✐♥❣ ❝♦♥str❛✐♥ts t♦ ❡♥s✉r❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ✇❡r❡ ❛ss✐❣♥❡❞ t♦ ❝♦♥s❡❝✉t✐✈❡ ✢♦♦rs✱ ✇✐t❤ t❤r❡❡ ✭✸✮ ❛❧t❡r♥❛t✐✈❡ ♠♦❞❡❧s r❡s✉❧t✐♥❣✳ ❋♦r t❤❡ s❡❝♦♥❞ ❝❧❛ss✱ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ✇❡r❡ ❜r♦❦❡♥ ✉♣ t♦ s✐♥❣❧❡✲✢♦♦r✲♣s❡✉❞♦✲ ✉♥✐ts ❛♥❞ t❤❡ ❧❛②♦✉t s♦❧✈❡❞ ❜❛s❡❞ ♦♥ ❛ ❧✐♥❡❛r✐s❡❞ ♠♦❞❡❧ ♦❢ ❑✉ ❡t ❛❧✳ ✶✽ ✳ ❊❛❝❤ ♦❢ t❤❡ ❢♦✉r ✭✹✮ ♠♦❞❡❧s ✇❡r❡ ✈❛❧✐❞❛t❡❞ ✇✐t❤ ❝❛s❡ st✉❞✐❡s ❛♥❞ ♠♦❞❡❧ ♣❡r❢♦r♠❛♥❝❡ ✇❡r❡ ❛s❝❡rt❛✐♥❡❞ ❛♥❞ ❝♦♠♣❛r❡❞✳ ❆❧❧ ♠♦❞❡❧s s♦❧✈❡❞ ♣r♦❜❧❡♠s ♦❢ ✉♣ t♦ ✶✼ ✉♥✐ts ✇❡❧❧ ✉♥❞❡r ✼ ♠✐♥✉t❡s✱ ❛s ❝♦♠♣❛r❡❞ t♦ ♣r❡✈✐♦✉s ✇♦r❦ ✶ ✇❤✐❝❤ ♦♥❧② ❤❛♥❞❧❡❞ ❛ ♠❛①✐♠✉♠ ♦❢ ✶✶ ✉♥✐ts s✐♠✉❧t❛♥❡♦✉s❧②✳ ❚♦t❛❧ ❝♦st ❞✐str✐❜✉t✐♦♥ ✇❡r❡ ❝♦♥s✐st❡♥t ✇✐t❤ ❡①♣❡❝t❡❞ ✈❛❧✉❡s ✲ ❝♦♥str✉❝t✐♦♥ ❛♥❞ ♣✉♠♣✐♥❣ ❝♦sts t❛❦❡♥ ✉♣ t❤❡ ❧❛r❣❡r ♣♦rt✐♦♥✱ ✇✐t❤ ❝♦♥♥❡❝t✐♦♥ ❝♦sts ❢♦❧❧♦✇✐♥❣✳ ❆❧❧ ♠♦❞❡❧s ✇❡r❡ ❛❜❧❡ t♦ ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

✺ ❆❈❑◆❖❲▲❊❉●❊▼❊◆❚

Page 28 of 33

✷✽

❤❛♥❞❧❡ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t✱ ❛♥❞ ❞❡❝✐❞❡ ✇❤❡t❤❡r ❛ ✢♦♦r ❜❡ ❝♦♥str✉❝t❡❞ ❛♥❞ ✉s❡❞ ❡✈❡♥ ✐❢ ❛ ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t ✇❡r❡ ❛ss✐❣♥❡❞ t♦ ✐t✳ ■♥ ♠♦st ❝❛s❡s t❤♦✉❣❤✱ ❢♦r♠✉❧❛t✐♦♥s ❆ ✇❛s ❢♦✉♥❞ t♦ ❜❡ ♠♦r❡ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡✣❝✐❡♥t t❤❛♥ ❇✳ ❋✐♥❛❧❧②✱ s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts ✇❡r❡ ✐♥tr♦❞✉❝❡❞ r❡❞✉❝✐♥❣ t❤❡ ❛✈❛✐❧❛❜✐❧✐t② ♦❢ ♠✉❧t✐♣❧❡ ♦♣t✐♠❛❧ s♦❧✉t✐♦♥s t❤❛t ❧❡❛❞ t♦ ❣r❡❛t❡r ❈P❯ ✉s❛❣❡✳ ❚❤❡s❡ ❝♦♥str❛✐♥ts ✜①❡❞ t❤❡ r❡❧❛t✐✈❡ ♣♦s✐t✐♦♥s ♦❢ t✇♦ ✉♥✐ts i ❛♥❞ j ✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ ✉♥✐ts i ❛♥❞ j ✇❡r❡ ❜❛s❡❞ ♦♥ t❤r❡❡ ❝r✐t❡r✐❛✿ ❧❛r❣❡st ❝♦♥♥❡❝t✐♦♥✱ ❧❛r❣❡st ❛r❡❛s ♦r s♠❛❧❧❡st ❛r❡❛ ❛♠♦♥❣st ♠✉❧t✐✲✢♦♦r ❡q✉✐♣♠❡♥t✳ ❆ r❡❞✉❝t✐♦♥ ✐♥ ❝♦♠♣✉t❛t✐♦♥❛❧ t✐♠❡ ✉♣ t♦ ✸✶✳✷s ✇❛s ♦❜t❛✐♥❡❞ ❢♦r ❡①❛♠♣❧❡ ✸✱ ❛s ❝♦♠♣❛r❡❞ t♦ ✷✾✷✳✸s ✇✐t❤♦✉t s②♠♠❡tr② ❜r❡❛❦✐♥❣✳ ❋✉rt❤❡r ✇♦r❦ ✇✐❧❧ ❡♥t❛✐❧ ♠♦❞❡❧ ✈❛❧✐❞❛t✐♦♥ ✇✐t❤ ❧❛r❣❡r ❝❛s❡ st✉❞✐❡s ❛♥❞ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❡✣❝✐❡♥t ❝♦♠♣✉t❛t✐♦♥❛❧ ♠❡t❤♦❞s✱ ❡✳❣✳ ❞❡❝♦♠♣♦s✐t✐♦♥ t❡❝❤♥✐q✉❡s✳

❆❝❦♥♦✇❧❡❞❣❡♠❡♥t ❏❖❊ ❛❝❦♥♦✇❧❡❞❣❡s t❤❡ ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ♦❢ t❤❡ P❡tr♦❧❡✉♠ ❚❡❝❤♥♦❧♦❣② ❉❡✈❡❧♦♣♠❡♥t ❋✉♥❞ ✭P❚❉❋✮✱ ◆✐❣❡r✐❛✳

❙✉♣♣♦rt✐♥❣ ■♥❢♦r♠❛t✐♦♥ ❆✈❛✐❧❛❜❧❡ ❆ ❢✉❧❧ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ ♣r♦♣♦s❡❞ ❜② P❛ts✐❛t③✐s ❛♥❞ P❛♣❛❣❡♦r❣✐♦✉ ✶ ✱ ❞❛t❛ ❢♦r t❤❡ ❝❛s❡ st✉❞✐❡s ♣r❡s❡♥t❡❞✱ ❛♥❞ ❧❛②♦✉t r❡s✉❧ts ❢♦r ♠♦❞❡❧s ❆✳✷✱ ❆✳✸ ❛♥❞ ❇ ✐s ❛✈❛✐❧❛❜❧❡ ❛s s✉♣♣♦rt✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳

❆✉t❤♦r ■♥❢♦r♠❛t✐♦♥ ❈♦rr❡s♣♦♥❞✐♥❣ ❆✉t❤♦r

✯❊♠❛✐❧✿ ❧✳♣❛♣❛❣❡♦r❣✐♦✉❅✉❝❧✳❛❝✳✉❦❀ P❤♦♥❡✿ ✰✹✹ ✭✵✮✷✵ ✼✻✼✾ ✷✺✻✸✳

ACS Paragon Plus Environment

Page 29 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✺ ❆❯❚❍❖❘ ■◆❋❖❘▼❆❚■❖◆

✷✾

❖❘❈■❉

❙♦♥❣s♦♥❣ ▲✐✉✿ ✵✵✵✵✲✵✵✵✶✲✽✹✶✷✲✷✼✹❳ ▲❛③❛r♦s ●✳ P❛♣❛❣❡♦r❣✐♦✉✿ ✵✵✵✵✲✵✵✵✸✲✹✻✺✷✲✻✵✽✻

◆♦t❡s

❚❤❡ ❛✉t❤♦rs ❞❡❝❧❛r❡ ♥♦ ❝♦♠♣❡t✐♥❣ ✜♥❛♥❝✐❛❧ ✐♥t❡r❡st✳

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 33

✺ ❘❊❋❊❘❊◆❈❊❙

✸✵

❘❡❢❡r❡♥❝❡s ✭✶✮ P❛ts✐❛t③✐s✱ ❉✳ ■✳❀ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳ ❊✣❝✐❡♥t ❙♦❧✉t✐♦♥ ❆♣♣r♦❛❝❤❡s ❢♦r t❤❡ ▼✉❧t✐✢♦♦r Pr♦❝❡ss P❧❛♥t ▲❛②♦✉t Pr♦❜❧❡♠✳

■♥❞✉str✐❛❧ ✫ ❊♥❣✐♥❡❡r✐♥❣ ❈❤❡♠✐str② ❘❡s❡❛r❝❤ ✷✵✵✸✱

✹✷✱ ✽✶✶✕✽✷✹✳ ✭✷✮ ❆♥❥♦s✱ ▼✳ ❋✳❀ ❱✐❡✐r❛✱ ▼✳ ❱✳ ❈✳ ▼❛t❤❡♠❛t✐❝❛❧ ❖♣t✐♠✐③❛t✐♦♥ ❆♣♣r♦❛❝❤❡s ❢♦r ❋❛❝✐❧✐t② ▲❛②✲ ♦✉t Pr♦❜❧❡♠s✿ ❚❤❡ ❙t❛t❡✲♦❢✲t❤❡✲❆rt ❛♥❞ ❋✉t✉r❡ ❘❡s❡❛r❝❤ ❉✐r❡❝t✐♦♥s✳ ❊✉r♦♣❡❛♥

❏♦✉r♥❛❧

♦❢ ❖♣❡r❛t✐♦♥❛❧ ❘❡s❡❛r❝❤ ✷✵✶✼✱ ✷✻✶✱ ✶✕✶✻✳ ✭✸✮ ▼❡❝❦❧❡♥❜✉r❣❤✱ ❏✳

Pr♦❝❡ss ♣❧❛♥t ❧❛②♦✉t✱ ✷♥❞ ❡❞✳❀ ▲♦♥❣♠❛♥✿ ◆❡✇ ❨♦r❦✱ ✶✾✽✺❀ ♣ ✻✷✺✳

✭✹✮ ❉r✐r❛✱ ❆✳❀ P✐❡rr❡✈❛❧✱ ❍✳❀ ❍❛❥r✐✲●❛❜♦✉❥✱ ❙✳ ❋❛❝✐❧✐t② ❧❛②♦✉t ♣r♦❜❧❡♠s✿ ❆ s✉r✈❡②✳

❆♥♥✉❛❧

❘❡✈✐❡✇s ✐♥ ❈♦♥tr♦❧ ✷✵✵✼✱ ✸✶✱ ✷✺✺✕✷✻✼✳ ✭✺✮ P❡♥t❡❛❞♦✱ ❋✳ ❉✳❀ ❈✐r✐❝✱ ❆✳ ❘✳ ❆♥ ▼■◆▲P ❆♣♣r♦❛❝❤ ❢♦r ❙❛❢❡ Pr♦❝❡ss P❧❛♥t ▲❛②♦✉t✳

■♥❞✉str✐❛❧ ✫ ❊♥❣✐♥❡❡r✐♥❣ ❈❤❡♠✐str② ❘❡s❡❛r❝❤ ✶✾✾✻✱ ✸✺✱ ✶✸✺✹✕✶✸✻✶✳ ✭✻✮ ●✉✐r❛r❞❡❧❧♦✱ ❘✳❀ ❙✇❛♥❡②✱ ❘✳ ❊✳ ❖♣t✐♠✐③❛t✐♦♥ ♦❢ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ✇✐t❤ ♣✐♣❡ r♦✉t✐♥❣✳

❈♦♠♣✉t❡rs ✫ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✷✵✵✺✱ ✸✵✱ ✾✾✕✶✶✹✳ ✭✼✮ ❇❛r❜♦s❛✲P♦✈♦❛✱ ❆✳ P✳❀ ▼❛t❡✉s③✱ ❘✳❀ ◆♦✈❛✐s③✱ ❆✳ ◗✳ ❖♣t✐♠❛❧ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ❧❛②♦✉t ♦❢ ✐♥❞✉str✐❛❧ ❢❛❝✐❧✐t✐❡s✳

■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ Pr♦❞✉❝t✐♦♥ ❘❡s❡❛r❝❤ ✷✵✵✶✱ ✸✾✶✷✱ ✷✺✻✼✕

✷✺✾✸✳ ✭✽✮ ❇❛r❜♦s❛✲Pó✈♦❛✱ ❆✳ P✳❀ ▼❛t❡✉s✱ ❘✳❀ ◆♦✈❛✐s✱ ❆✳ ◗✳ ❖♣t✐♠❛❧ ✸❉ ❧❛②♦✉t ♦❢ ✐♥❞✉str✐❛❧ ❢❛❝✐❧✐t✐❡s✳

■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ Pr♦❞✉❝t✐♦♥ ❘❡s❡❛r❝❤ ✷✵✵✷✱ ✹✵✱ ✶✻✻✾✕✶✻✾✽✳

✭✾✮ ●❡♦r❣✐❛❞✐s✱ ▼✳❀ ▼❛❝❝❤✐❡tt♦✱ ❙✳ ▲❛②♦✉t ♦❢ ♣r♦❝❡ss ♣❧❛♥ts✿ ❆ ♥♦✈❡❧ ❛♣♣r♦❛❝❤✳ ❈♦♠♣✉t❡rs

✫ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✶✾✾✼✱ ✷✶✱ ❙✸✸✼✕❙✸✹✷✳ ✭✶✵✮ P❛ts✐❛t③✐s✱ ❉✳ ■✳❀ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳ ❖♣t✐♠❛❧ ♠✉❧t✐✲✢♦♦r ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t✳

♣✉t❡rs ✫ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✷✵✵✷✱ ✷✻✱ ✺✼✺✕✺✽✸✳ ACS Paragon Plus Environment

❈♦♠✲

Page 31 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

✺ ❘❊❋❊❘❊◆❈❊❙

✸✶

✭✶✶✮ P❛ts✐❛t③✐s✱ ❉✳ ■✳❀ ❑♥✐❣❤t✱ ●✳❀ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳ ❆♥ ▼■▲P ❛♣♣r♦❛❝❤ t♦ s❛❢❡ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t✳

❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❘❡s❡❛r❝❤ ❛♥❞ ❉❡s✐❣♥ ✷✵✵✹✱ ✽✷✱ ✺✼✾✕✺✽✻✳

✭✶✷✮ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳❀ ❘♦tst❡✐♥✱ ●✳ ❊✳ ❈♦♥t✐♥✉♦✉s✲❞♦♠❛✐♥ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s ❢♦r ♦♣✲ t✐♠❛❧ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉t✳

■♥❞✉str✐❛❧ ✫ ❊♥❣✐♥❡❡r✐♥❣ ❈❤❡♠✐str② ❘❡s❡❛r❝❤ ✶✾✾✽✱ ✺✽✽✺✱

✸✻✸✶✕✸✻✸✾✳ ✭✶✸✮ ❳✉✱ ●✳❀ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳ Pr♦❝❡ss ♣❧❛♥t ❧❛②♦✉t ✉s✐♥❣ ❛♥ ✐♠♣r♦✈❡♠❡♥t✲t②♣❡ ❛❧❣♦r✐t❤♠✳

❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❘❡s❡❛r❝❤ ❛♥❞ ❉❡s✐❣♥ ✷✵✵✾✱ ✽✼✱ ✼✽✵✕✼✽✽✳ ✭✶✹✮ ▼❡❞✐♥❛✲❍❡rr❡r❛✱ ◆✳❀ ❏✐♠é♥❡③✲●✉t✐érr❡③✱ ❆✳❀ ●r♦ss♠❛♥♥✱ ■✳ ❊✳ ❆ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦❣r❛♠✲ ♠✐♥❣ ♠♦❞❡❧ ❢♦r ♦♣t✐♠❛❧ ❧❛②♦✉t ❝♦♥s✐❞❡r✐♥❣ q✉❛♥t✐t❛t✐✈❡ r✐s❦ ❛♥❛❧②s✐s✳

❈♦♠♣✉t❡rs ❛♥❞

❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✷✵✶✹✱ ✻✽✱ ✶✻✺✕✶✽✶✳ ✭✶✺✮ ❍✉❛♥❣✱ ❈✳❀ ❲♦♥❣✱ ❈✳ ❑✳ ❖♣t✐♠✐s❛t✐♦♥ ♦❢ s✐t❡ ❧❛②♦✉t ♣❧❛♥♥✐♥❣ ❢♦r ♠✉❧t✐♣❧❡ ❝♦♥str✉❝t✐♦♥ st❛❣❡s ✇✐t❤ s❛❢❡t② ❝♦♥s✐❞❡r❛t✐♦♥s ❛♥❞ r❡q✉✐r❡♠❡♥ts✳ ❆✉t♦♠❛t✐♦♥

✐♥ ❈♦♥str✉❝t✐♦♥ ✷✵✶✺✱

✺✸✱ ✺✽✕✻✽✳ ✭✶✻✮ ❏✉♥❣✱ ❙✳ ❋❛❝✐❧✐t② s✐t✐♥❣ ❛♥❞ ♣❧❛♥t ❧❛②♦✉t ♦♣t✐♠✐③❛t✐♦♥ ❢♦r ❝❤❡♠✐❝❛❧ ♣r♦❝❡ss s❛❢❡t②✳ ❑♦r❡❛♥

❏♦✉r♥❛❧ ♦❢ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✷✵✶✻✱ ✸✸✱ ✶✕✼✳ ✭✶✼✮ ❳✐♥✱ P✳❀ ❑❤❛♥✱ ❋✳❀ ❆❤♠❡❞✱ ❙✳ ▲❛②♦✉t ❖♣t✐♠✐③❛t✐♦♥ ♦❢ ❛ ❋❧♦❛t✐♥❣ ▲✐q✉❡✜❡❞ ◆❛t✉r❛❧ ●❛s ❋❛❝✐❧✐t② ❯s✐♥❣ ■♥❤❡r❡♥t ❙❛❢❡t② Pr✐♥❝✐♣❧❡s✳

❏♦✉r♥❛❧ ♦❢ ❖✛s❤♦r❡ ▼❡❝❤❛♥✐❝s ❛♥❞ ❆r❝t✐❝

❊♥❣✐♥❡❡r✐♥❣ ✷✵✶✻✱ ✶✸✽✱ ✵✹✶✻✵✷✳ ✭✶✽✮ ❑✉✱ ◆✳✲❑✳❀ ❍✇❛♥❣✱ ❏✳✲❍✳❀ ▲❡❡✱ ❏✳✲❈✳❀ ❘♦❤✱ ▼✳✲■✳❀ ▲❡❡✱ ❑✳✲❨✳ ❖♣t✐♠❛❧ ♠♦❞✉❧❡ ❧❛②♦✉t ❢♦r ❛ ❣❡♥❡r✐❝ ♦✛s❤♦r❡ ▲◆● ❧✐q✉❡❢❛❝t✐♦♥ ♣r♦❝❡ss ♦❢ ▲◆●✲❋P❙❖✳ ❙❤✐♣s ❛♥❞ ❖✛s❤♦r❡ ❙tr✉❝t✉r❡s

✷✵✶✸✱ ✾✱ ✸✶✶✕✸✸✷✳ ✭✶✾✮ ❍✇❛♥❣✱ ❏✳❀ ▲❡❡✱ ❑✳ ❨✳ ❖♣t✐♠❛❧ ❧✐q✉❡❢❛❝t✐♦♥ ♣r♦❝❡ss ❝②❝❧❡ ❝♦♥s✐❞❡r✐♥❣ s✐♠♣❧✐❝✐t② ❛♥❞ ❡✣❝✐❡♥❝② ❢♦r ▲◆● ❋P❙❖ ❛t ❋❊❊❉ st❛❣❡✳

❈♦♠♣✉t❡rs ❛♥❞ ❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✷✵✶✹✱

✻✸✱ ✶✕✸✸✳ ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 33

✺ ❘❊❋❊❘❊◆❈❊❙

✸✷

✭✷✵✮ ❑✉✱ ◆✳❀ ❏❡♦♥❣✱ ❙✳✲❨✳❀ ❘♦❤✱ ▼✳✲■✳❀ ❙❤✐♥✱ ❍✳✲❑✳❀ ❍❛✱ ❙✳❀ ❍♦♥❣✱ ❏✳✲✇✳ ▲❛②♦✉t ▼❡t❤♦❞ ♦❢ ❛ ❋P❙❖ ✭❋❧♦❛t✐♥❣✱ Pr♦❞✉❝t✐♦♥✱ ❙t♦r❛❣❡✱ ❛♥❞ ❖✛✲▲♦❛❞✐♥❣ ❯♥✐t✮ ❯s✐♥❣ t❤❡ ❖♣t✐♠✐③❛t✐♦♥ ❚❡❝❤♥✐q✉❡✳ ❱♦❧✉♠❡ ✶❇✿ ❖✛s❤♦r❡ ❚❡❝❤♥♦❧♦❣②✳ ✷✵✶✹❀ ♣♣ ✶✕✶✶✳ ✭✷✶✮ P❛r❦✱ P✳ ❏✳❀ ▲❡❡✱ ❈✳ ❏✳ ❚❤❡ ❘❡s❡❛r❝❤ ♦❢ ❖♣t✐♠❛❧ P❧❛♥t ▲❛②♦✉t ❖♣t✐♠✐③❛t✐♦♥ ❜❛s❡❞ ♦♥ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ❢♦r ❊t❤②❧❡♥❡ ❖①✐❞❡ P❧❛♥t✳

❏♦✉r♥❛❧ ♦❢ t❤❡ ❑♦r❡❛♥ ❙♦❝✐❡t②

♦❢ ❙❛❢❡t② ✷✵✶✺✱ ✸✵✱ ✸✷✕✸✼✳ ✭✷✷✮ ❑❤❡✐r❦❤❛❤✱ ❆✳❀ ◆❛✈✐❞✐✱ ❍✳❀ ▼❡ss✐ ❇✐❞❣♦❧✐✱ ▼✳ ❉②♥❛♠✐❝ ❢❛❝✐❧✐t② ❧❛②♦✉t ♣r♦❜❧❡♠✿ ❛ ♥❡✇ ❜✐❧❡✈❡❧ ❢♦r♠✉❧❛t✐♦♥ ❛♥❞ s♦♠❡ ♠❡t❛❤❡✉r✐st✐❝ s♦❧✉t✐♦♥ ♠❡t❤♦❞s✳

■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥

❊♥❣✐♥❡❡r✐♥❣ ▼❛♥❛❣❡♠❡♥t ✷✵✶✺✱ ✻✷✱ ✸✾✻✕✹✶✵✳ ✭✷✸✮ ◆❛✈✐❞✐✱ ❍✳❀ ❇❛s❤✐r✐✱ ▼✳❀ ❇✐❞❣♦❧✐✱ ▼✳ ▼✳ ❆ ❤❡✉r✐st✐❝ ❛♣♣r♦❛❝❤ ♦♥ t❤❡ ❢❛❝✐❧✐t② ❧❛②♦✉t ♣r♦❜❧❡♠ ❜❛s❡❞ ♦♥ ❣❛♠❡ t❤❡♦r②✳

■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ Pr♦❞✉❝t✐♦♥ ❘❡s❡❛r❝❤ ✷✵✶✷✱

✺✵✱ ✶✺✶✷✕✶✺✷✼✳ ✭✷✹✮ ◆❛❜❛✈✐✱ ❙✳ ❘✳❀ ❚❛❣❤✐♣♦✉r✱ ❆✳ ❍✳❀ ▼♦❤❛♠♠❛❞♣♦✉r ●♦r❥✐✱ ❆✳ ❖♣t✐♠✐③❛t✐♦♥ ♦❢ ❋❛❝✐❧✐t② ▲❛②♦✉t ♦❢ ❚❛♥❦ ❢❛r♠s ✉s✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ❛♥❞ ❋✐r❡❜❛❧❧ ❙❝❡♥❛r✐♦✳ ❈❤❡♠✐❝❛❧ Pr♦❞✉❝t

❛♥❞ Pr♦❝❡ss ▼♦❞❡❧✐♥❣ ✷✵✶✻✱ ✶✶ ✳ ✭✷✺✮ ❋✉r✉❤♦❧♠❡♥✱ ▼✳❀ ●❧❡tt❡✱ ❑✳❀ ❍♦✈✐♥✱ ▼✳❀ ❚♦rr❡s❡♥✱ ❏✳ ❆ ❝♦❡✈♦❧✉t✐♦♥❛r②✱ ❤②♣❡r ❤❡✉r✐st✐❝ ❛♣♣r♦❛❝❤ t♦ t❤❡ ♦♣t✐♠✐③❛t✐♦♥ ♦❢ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ♣r♦❝❡ss ♣❧❛♥t ❧❛②♦✉ts ✲ ❆ ❝♦♠♣❛r❛t✐✈❡ st✉❞②✳

✷✵✶✵ ■❊❊❊ ❲♦r❧❞ ❈♦♥❣r❡ss ♦♥ ❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ❲❈❈■ ✷✵✶✵ ✲ ✷✵✶✵

■❊❊❊ ❈♦♥❣r❡ss ♦♥ ❊✈♦❧✉t✐♦♥❛r② ❈♦♠♣✉t❛t✐♦♥✱ ❈❊❈ ✷✵✶✵ ✷✵✶✵✱ ✭✷✻✮ ❘♦s❡♥t❤❛❧✱ ❊✳ ●❆▼❙✲❆ ✉s❡r✬s ❣✉✐❞❡✳ ●❆▼❙ ❉❡✈❡❧♦♣♠❡♥t ❈♦r♣♦r❛t✐♦♥✳ ❲❛s❤✐♥❣t♦♥✱ ❉❈✱ ❯❙❆✱ ✷✵✵✽✳ ✭✷✼✮ ❲❡st❡r❧✉♥❞✱ ❏✳❀ P❛♣❛❣❡♦r❣✐♦✉✱ ▲✳ ●✳ ■♠♣r♦✈❡❞ P❡r❢♦r♠❛♥❝❡ ✐♥ Pr♦❝❡ss P❧❛♥t ▲❛②♦✉t Pr♦❜❧❡♠s ❯s✐♥❣ ❙②♠♠❡tr②✲❜r❡❛❦✐♥❣ ❝♦♥str❛✐♥ts✳

❉❡s✐❣♥ ✷✵✵✷✱ ✹✽✺✕✹✽✽✳

ACS Paragon Plus Environment

Page 33 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

ACS Paragon Plus Environment