(354d) Concepts Rendered False by Advances In Understanding and Obsolete by Advances In Computation

          The formulation  and adoption of useful concepts and generalizations, and in many instances unique ones, have helped chemical engineering to flourish as an academic subject and as a profession. The broadest ones are illustrated by unit operations, unit processes, and transport phenomena. Narrower ones are illustrated by the equilibrium stage,  the perfectly mixed continuous reactor, and the Colburn j-factor. These latter concepts have resulted from observations in plant operations and in the laboratory as well as from theoretical analyses and flashes of insight. All in all, they constitute an essential element of both education and practice in chemical engineering.

          With the passage of time, most of the broad  concepts have been replaced, modified, or supplemented.  Many of the specific ones  have been found to be false or unnecessary yet  remain in textbooks and  computer packages  out of inertia and/or out of misdirected respect for those who originated them. The objective of this presentation is to identify some of the  obsolete and/or false ones. Within this restricted space, identifications can only be illustrative, so an attempt has been made to choose examples that are diverse in subject and in the nature of the shortcomings. The results of the advances by virtue of computation will be shown graphically in the presentation. It is hoped that these examples will inspire each of you to question the continued viability of the concepts and idealizations in your personal professional portfolio, including  the books you depend upon.

          The formulation of each of the concepts discussed herein depends upon one or more ingenious idealizations and/or simplifications. With time some of these have become unnecessary because of  advances in computer hardware and software, and some  have been proven to be false by advances in understanding. Their identification is an essential part of the process of re-examination of a concept, and often the critical one.

Reaction engineering

The concept of reaction engineering was a great advance over chemical kinetics, which was

originally taught as a subtopic in physical chemistry.  It continues to have vitality  but  has accumulated a number of false concepts, a few examples of which are noted here.

Plug flow

This is a misleading, inaccurate, and totally unnecessary concept. It should be excised from our literature and replaced by realistic  fluid-mechanical models.

Space velocity and space time

These concepts invoke a Lagrangian framework and thereby the shortcomings of plug flow.

They too should be excised.

Perfect radial mixing in tubular flow

This is a more accurate verbal description of the behavior resulting from the postulate of plug flow in that it can be considered as an asymptote for Pr → 0   and Sc→ 0,  but it does not ameliorate the errors in the model.

Fully developed flow with no radial mixing

This is the counterpart of perfect radial mixing, that is, it corresponds to Pr→ ∞ and Sc→ ∞, and as such is physically conceivable. It is useful as a lower-bound for the conversion and as an upper-bound for the length of the  reactor, which are conservative predictions and thereby good engineering as contrasted with the predictions of perfect radial mixing which are non-conservative and thereby poor engineering.

Turbulent tubular flow

Chemical conversions rarely occur in the turbulent regime because the  reactor is then almost

certainly of excessive length. Plug  flow is not approached; the velocity remains nearly parabolic.

Initiation

The initiation of a reaction over the entire cross-section at the inlet is implied in most models

although it is impossible to achieve physically. This idealization is difficult to replace, because

the alternatives involve developing flow and thereby an increase of an order of magnitude in

complexity of the numerical modeling. Until such modeling is included in computer

packages, the affects of this non-conservative idealization should not be ignored.

Rate mechanisms

The expression of reaction rates in terms of molecular concentrations rather than  activities

betrays the principles of chemical engineering thermodynamics. To brag about its rigor and

generality as  compared  to that  of mechanical engineering and chemistry and then cling

to this erroneous concept is untenable. It is difficult to re-do rate constants in terms of

concentrations because that requires a knowledge of the pressure, temperature, and

composition at which the measurements  were made. The error in the predictions is serious

only if the conditions differ significantly from those of the measurements, but the time

has come  for the editors of chemical engineering publications to establish a new standard.

Over-correlation

As shown definitively in an article by Mayer and Stowe, models of the type proposed by

Hougen and Watson for chemical conversions in flow through a bed of catalyst particles

introduce more empirical coefficients than can be justified by the precision and extent of the

experimental data. It follows that the resulting models have no physical significance. This

approach should have been abandoned long ago. This is an example of the misuse of

numerical computation. This listing could go on and on and on; the number of obsolete and

false concepts and the unnecessary idealizations and simplifications in reaction engineering is

almost endless, but some space must be reserved for other topics.

Combustion

Combustion has progressed from art to an engineering science by virtue of advances in

computation and in the determination of free-radical mechanisms. It should be a sub-topic,

such as Separations, within chemical engineering but because of the failure to encompass it

in reaction engineering it has become a separate profession. The probable reason for such

short-sightedness  is that combustion occurs primarily in unconfined flow whereas chemical

engineers are more comfortable with tubular flow. Two false concepts related to the

modeling of combustion deserve mention.  First, solids, liquids, and gases do not burn – only

free radicals; therefore combustion must be preceded by pyrolysis. Second, the concentration

of free radicals never attains a stationary state. Global modeling should be abandoned.

Separations

Molecular separations are, along with  reaction engineering, unique to chemical engineering.

There is space to  mention only one ingenious but now obsolete concept, namely, the ideal-

stage. The many inherent idealizations, most of which are now avoidable owing to advances

in computation, should not go unmentioned.

Heat Transfer

Chemical engineers have more or less ceded leadership in heat transfer to mechanical

engineers although heat exchange remains essential in chemical processing and in

petroleum refining. Space allows the mention of only two obsolete concepts and one

overlooked effect.

Correlations in the form of products of powers of Re and Pr

A power-dependence actually occurs, if at all, only in an asymptotic sense. As an example,

the Colburn analogy is functionally in error in every respect and, as a consequence,

seriously in error numerically. The formulation and use of far more accurate correlating

equations in the form of power-means of the asymptotes has been encouraged and abetted

by advances in computation.

The hyperbolic equation of conduction

This model is totally false. In the instance of a pressure wave generated by impulsive

heating, such as thunder by lightning, the behavior can be predicted exactly by

taking the compressibility and the conservation of momentum into account. The

computational investment is however high owing to stiffness.

The enhancement of convection by an energetic reaction

This effect, which is completely overlooked in all textbooks has been resolved by differential

models and finite-difference computations.

Fluid Mechanics

This subject is shared with mechanical engineers, civil  engineers, and others but chemical

engineers remain the pace-setters in special topics such as  non-Newtonian fluids, packed

beds, and fluidized beds. Obsolete concepts are illustrated by the following examples.

The power-law fluid

Such behavior is simply a necessary  artifact of the transition between pseudoplastic and

dilatant behavior.

The orifice coefficient

The numerical expression derived for a sharp-edged orifice on the basis of a free streamline is a misleading approximation. The coefficient, including its asymptotic value, varies with D_o/D and Re, and should be computed numerically.

The Ergun equation

The attribution of the Re²  term of the Ergun equation to turbulent rather than inertial flow is

an example of a pervasive misinterpretation.

DNS (direct numerical simulation) and LES (large eddy simulation)

These methodologies exemplify  self-defeating limitations. DNS has proven to be viable only

for the hypothetical case of a parallel-plate channel and for Reynolds numbers barely above

that for fully developed turbulence. LES has proven to have the same geometrical limitation

and to require very empirical supplementation.

Mass Transfer

The analogy between heat and mass transfer

The substitution of Sh and Sc for Nu and Pr  has been shown both experimentally and by

Lagrangian direct numerical simulationto be invalid.

The Lewis number

In a session in his honor at the 57th AIChEAnnual Meeting, Warren K. Lewis jokingly

complained that the dimensionless group named in his honor commemorates one of his

worst mistakes, namely the presumption that because that grouping happened to be

nearly equal to unity in some of his experiments with water vapor in air it was unity for all

conditions and systems.