Table Of ContentS I M U L T A N E O U S
M A S S T R A N S F E R A N D
C H E M I C A L R E A C T I O N S
I N E N G I N E E R I N G
S C I E N C E
Solution Methods and
Chemical Engineering
Applications
BERTRAM K.C. CHAN
PhD (The University of Sydney, Australia)
PE (California, USA)
IEEE (Life Member)
Elsevier
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This book is dedicated to:
thegloryofGod,
mybetterhalfMarieNashedYacoubChan,and
thefondmemoriesof:
my physical science teacher Brother Vincent, B.Sc., at the De La Salle
College, Cronulla, Sydney, New South Wales, Australia, as well as
my professors in Chemical Engineering in Australia, including:
at the University of New South Wales:
Professor Geoffrey Harold Roper
and
Visiting Professor Thomas Hamilton Chilton, from the University of Delaware
and at the University of Sydney:
Professor Thomas Girvan Hunter
and
Professor Rudolf George Herman Prince
PREFACE
Among the unit operations in biomolecular, chemical, and
process engineering, the one item that has uniquely, funda-
mentally,andhistorically,belongedtothedisciplineofchemical
engineering is concerned with operations involving mass trans-
fer.Theprincipalmasstransferoperations,inalphabeticalorder,
include[*]:
(cid:129) Adsorption and fixed-bed separations;
(cid:129) Crystallization;
(cid:129) Distillation;
(cid:129) Drying ofsolids;
(cid:129) Equilibrium-stage operations;
(cid:129) Gasabsorption;
(cid:129) Humidification operations;
(cid:129) Leaching and extraction;
(cid:129) Membrane separation processes.
More often than not, such operations involve a combination
of both mass transfer and chemical reactions. Hence, analysis
and design of such unit operations should start with a basic
understanding of simultaneous mass transfer and chemical re-
actions. After about a century of the academic discipline of
chemicalengineering,tobringintofocusthetheoryandpractice
of the study and research into chemical engineering, it is useful
to take an in-depth look at this important subject, supported by
all available modern computational tools to bring to bear a
cogent review of the discipline. Theoretical approaches to
simultaneous mass transfer and chemical reactions often begin
with mass balances of each of the interacting species at the
differentiallevels,oftenresultinginasetofsimultaneouspartial
differential equations: usually one equation for each partici-
pating species.
In this work, theoretical and mathematical analyses of these
systems of differential equations are undertaken, resulting in
existence and uniqueness theorems for such systems.
Upon assuming a given set of initial and/or boundary con-
ditions, with respect to each system of partial differential
x Preface
equations in both space and time, the system solution is then
reduced to solving the resultant set of partial differential equa-
tions,withradicalbutrealisticassumptionsofasetofinitialand
boundary conditions with respect to space and time.
Solution methodologies, starting with numerical analyses,
and using various computer methodologies, including:
(1) Programming,in FORTRAN-IV, for digital computation,
(2) Curve fitting, with resultant graphical outputs, using the
open-sourced programR,
(3) Computation and curve fitting graphical outputs using the
programs written in some high-level language, such as
BASIC, etc.
are used to obtain useful parametric curves for equipment
design.
[*](i)McCabe,W.L.,andSmith,J.(1956).“UnitOperationsof
Chemical Engineering”, 1st Edition, The McGraw-Hill Com-
panies, Inc., Series in Chemical Engineering, McGraw-Hill Book
Company, New York.
(ii) McCabe, W. L., Smith, J. C., and Harriott, P. (2005). “Unit
OperationsofChemicalEngineering”,7thEdition,TheMcGraw-
Hill Companies, Inc., Series in Chemical Engineering, McGraw-
Hill Book Company, New York.
“Chemical Engineering Science”
A semiofficial recorded documentation of Chemical Engi-
neering Science may be represented by “Perry’s Chemical
Engineers’ Handbook,” published by McGraw-Hill Book Com-
pany,nowonitswaytotheNinethEdition,spanningoverabout
a century of the illustrious history of the profession. This latest
version, under the general editorship of Don W. Green and
Marylee Z. Southard, is scheduled to be published in 2019!
Preface xi
“Perry’s Chemical Engineers’ Handbook,” 9th Edition
xii Preface
“Perry’s Chemical Engineers’ Handbook”, 1st through 8th
Editions
This monogram focuses on one single aspect of the vast
literature of chemical engineering science, known as “simulta-
neousmasstransferandchemicalreactions,”whichisdiscussed
as a critical theoretical analysis of the subject. It is to be hoped
that it will enhance an important aspect of this subject.
Special Note:
Some introductory materials are taken from well-known en-
gineering literatures, which are thoroughly referenced as they
occur in the text.
1
Introduction to simultaneous
mass transfer and chemical
reactions in engineering
science
Chapter outline
1.1 GaseLiquid Reactions 2
1.1.1 Simultaneous biomolecular reactions and mass transfer 2
1.1.1.1 Thebiomedicalenvironment 2
1.1.1.2 Theindustrial chemistry andchemical engineering environment 4
1.2 The modeling of gaseliquid reactions 10
1.2.1 Film theory of mass transfer 10
1.2.2 Surface renewal theory of mass transfer 12
1.2.3 Absorption into a quiescent liquid[*1] 15
1.2.3.1 Absorption accompanied bychemicalreactions[*1] 16
1.2.3.2 Irreversible reactions[*1] 17
1.2.4 Absorption into agitated liquids [*4] 21
1.2.4.1 Furtherreferences 24
1.2.5 The mathematical theory of simultaneous mass transfer and
chemical reactions[*1] 26
1.2.5.1 Physical absorption 26
1.2.6 Chemical absorption 27
1.2.6.1 Preliminary remarksonsimultaneous masstransfer (absorption)
with chemicalreactions 27
1.2.6.2 Some solutions tothemathematical modelsofthetheory of
simultaneous mass transferandchemicalreactions 28
1.2.6.3 Approximate closedformsolutions** 29
1.2.7 Numerical solutions 37
1.3 Diffusive models of environmental transport 37
In many biochemical, biomedical, and chemical processes, in
both physiological systems and in the chemical industry,
including environmental sciences, mass transfer accompanied
SimultaneousMassTransferandChemicalReactionsinEngineeringScience.https://doi.org/10.1016/B978-0-12-819192-7.00001-1 1
Copyright©2020ElsevierInc.Allrightsreserved.
2 Chapter 1 Introductiontosimultaneous masstransferandchemicalreactions
with reversible, complex biochemical or chemical reactions in
gaseliquid systems are frequently found. From the viewpoint of
biochemical and/or chemicalpurposesindesign, the absorption
rates of the participating reactants should be accurately esti-
mated.Theassociatedmasstransferratesmaysignificantlyaffect
the process, such as the yield and selectivity. Much work had
been done in describing these processes analytically. These ap-
proaches will be used later in this work.
For example, the absorption of a gas is followed by a first-
order reversible reaction.
Thus, for all mass transfer models, including the penetration
and surface-renewal models, analytical solutions have been ob-
tained. For other models, limited work had been done, except
for special cases.
In this work, both analytical and numerical solutions are pre-
sented in some detail.
1.1 GaseLiquid Reactions
Reference:
[*1]Danckwerts,P.V.(1970).GasLiquidReactions,McGraw-Hill,
NY; van Elk, E. P. (2001). Gas-Liquid ReactionsdInfluence of
Liquid Bulk and Mass Transfer on Process Performance. http://
www.vanelk.nl/edwin/cv/thesis.pdf. It is well-known that many
biochemical and chemical processes involve mass transfer of
one or more species from the gas phase into the liquid phase.In
the liquid phase the species from the gas phase is converted by
oneormore(possiblyirreversible)biochemicalorchemicalreac-
tions with certain species present inthe liquidphase.
Typical of such examples are the following.
1.1.1 Simultaneous biomolecular reactions and
mass transfer
1.1.1.1 The biomedical environment
In epidemiologic investigations, occurrences of simultaneous
biomolecular reactions and mass transfer are common in many
biomedical environments. Some typical examples are:
(1) Intestinal drugabsorption involving bio-transportersand
metabolic reactions with enzymes[*2]: the absorption of
drugsviatheoralrouteisasubjectofon-goingandseriousin-
vestigations in the pharmaceutical industry since good bio-
availabilityimpliesthatthedrugisabletoreachthesystemic
circulationviatheoralpath.Oralabsorptiondependsonboth
