Transport Phenomena and Unit Operations: A Combined Approach - Softcover

Griskey, Richard G.

Softcover

ISBN 10: 0471998141 ISBN 13: 9780471998143

Publisher: Wiley-Interscience, 2006

Synopsis

The subject of transport phenomena has long been thoroughly and expertly addressed on the graduate and theoretical levels. Now Transport Phenomena and Unit Operations: A Combined Approach endeavors not only to introduce the fundamentals of the discipline to a broader, undergraduate-level audience but also to apply itself to the concerns of practicing engineers as they design, analyze, and construct industrial equipment.

Richard Griskey's innovative text combines the often separated but intimately related disciplines of transport phenomena and unit operations into one cohesive treatment. While the latter was an academic precursor to the former, undergraduate students are often exposed to one at the expense of the other. Transport Phenomena and Unit Operations bridges the gap between theory and practice, with a focus on advancing the concept of the engineer as practitioner. Chapters in this comprehensive volume include:

• Transport Processes and Coefficients
• Frictional Flow in Conduits
• Free and Forced Convective Heat Transfer
• Heat Exchangers
• Mass Transfer; Molecular Diffusion
• Equilibrium Staged Operations
• Mechanical Separations

Each chapter contains a set of comprehensive problem sets with real-world quantitative data, affording students the opportunity to test their knowledge in practical situations. Transport Phenomena and Unit Operations is an ideal text for undergraduate engineering students as well as for engineering professionals.

About this title

About the Author

Richard G. Griskey, PhD, PE, is Institute Professor Emeritus at the Stevens Institute of Technology in Hoboken, New Jersey.

From the Back Cover

The subject of transport phenomena has long been thoroughly and expertly addressed on the graduate and theoretical levels. Now, Transport Phenomena and Unit Operations: A Combined Approach endeavors not only to introduce the fundamentals of the discipline to a broader, undergraduate-level audience but also to apply itself to the concerns of practicing engineers as they design, analyze, and construct industrial equipment.

Richard Griskey's innovative text combines the often separated but intimately related disciplines of transport phenomena and unit operations into one cohesive treatment. While the latter was an academic precursor to the former, undergraduate students are often exposed to one at the expense of the other. Transport Phenomena and Unit Operations bridges the gap between theory and practice, with a focus on advancing the concept of the engineer as practitioner. Chapters in this comprehensive volume include:

• Transport Processes and Coefficients
• Frictional Flow in Conduits
• Free and Forced Convective Heat Transfer
• Heat Exchangers
• Mass Transfer; Molecular Diffusion
• Equilibrium Staged Operations
• Mechanical Separations

Each chapter contains a set of comprehensive problem sets with real-world quantitative data, affording students the opportunity to test their knowledge in practical situations. Transport Phenomena and Unit Operations is an ideal text for undergraduate engineering students as well as for engineering professionals.

From the Inside Flap

The subject of transport phenomena has long been thoroughly and expertly addressed on the graduate and theoretical levels. Now, Transport Phenomena and Unit Operations: A Combined Approach endeavors not only to introduce the fundamentals of the discipline to a broader, undergraduate-level audience but also to apply itself to the concerns of practicing engineers as they design, analyze, and construct industrial equipment.

Richard Griskey's innovative text combines the often separated but intimately related disciplines of transport phenomena and unit operations into one cohesive treatment. While the latter was an academic precursor to the former, undergraduate students are often exposed to one at the expense of the other. Transport Phenomena and Unit Operations bridges the gap between theory and practice, with a focus on advancing the concept of the engineer as practitioner. Chapters in this comprehensive volume include:

• Transport Processes and Coefficients
• Frictional Flow in Conduits
• Free and Forced Convective Heat Transfer
• Heat Exchangers
• Mass Transfer; Molecular Diffusion
• Equilibrium Staged Operations
• Mechanical Separations

Each chapter contains a set of comprehensive problem sets with real-world quantitative data, affording students the opportunity to test their knowledge in practical situations. Transport Phenomena and Unit Operations is an ideal text for undergraduate engineering students as well as for engineering professionals.

Excerpt. © Reprinted by permission. All rights reserved.

Transport Phenomena and Unit Operations

A Combined ApproachBy Richard A. Griskey

Wiley-Interscience

Copyright © 2006 Richard A. Griskey
All right reserved.
ISBN: 9780471998143

Chapter One

TRANSPORT PROCESSES AND TRANSPORT COEFFICIENTS

INTRODUCTION

The profession of chemical engineering was created to fill a pressing need. In the latter part of the nineteenth century the rapidly increasing growth complexity and size of the world's chemical industries outstripped the abilities of chemists alone to meet their ever-increasing demands. It became apparent that an engineer working closely in concert with the chemist could be the key to the problem. This engineer was destined to be a chemical engineer.

From the earliest days of the profession, chemical engineering education has been characterized by an exceptionally strong grounding in both chemistry and chemical engineering. Over the years the approach to the latter has gradually evolved; at first, the chemical engineering program was built around the concept of studying individual processes (i.e., manufacture of sulfuric acid, soap, caustic, etc.). This approach, unit processes, was a good starting point and helped to get chemical engineering off to a running start.

After some time it became apparent to chemical engineering educators that the unit processes had many operations in common (heat transfer, distillation, filtration, etc). This led to the concept of thoroughly grounding the chemical engineer in these specific operations and the introduction of the unit operations approach. Once again, this innovation served the profession well, giving its practitioners the understanding to cope with the ever-increasing complexities of the chemical and petroleum process industries.

As the educational process matured, gaining sophistication and insight, it became evident that the unit operations in themselves were mainly composed of a smaller subset of transport processes (momentum, energy, and mass transfer). This realization generated the transport phenomena approach-an approach that owes much to the classic chemical engineering text of Bird, Stewart, and Lightfoot.

There is no doubt that modern chemical engineering in indebted to the transport phenomena approach. However, at the same time there is still much that is important and useful in the unit operations approach. Finally, there is another totally different need that confronts chemical engineering education-namely, the need for today's undergraduates to have the ability to translate their formal education to engineering practice.

This text is designed to build on all of the foregoing. Its purpose is to thoroughly ground the student in basic principles (the transport processes); then to move from theoretical to semiempirical and empirical approaches (carefully and clearly indicating the rationale for these approaches); next, to synthesize an orderly approach to certain of the unit operations; and, finally, to move in the important direction of engineering practice by dealing with the analysis and design of equipment and processes.

THE PHENOMENOLOGICAL APPROACH; FLUXES, DRIVING FORCES, SYSTEMS COEFFICIENTS

In nature, the trained observer perceives that changes occur in response to imbalances or driving forces. For example, heat (energy in motion) flows from one point to another under the influence of a temperature difference. This, of course, is one of the basics of the engineering science of thermodynamics.

Likewise, we see other examples in such diverse cases as the flow of (respectively) mass, momentum, electrons, and neutrons.

Hence, simplistically we can say that a flux (see Figure 1-1) occurs when there is a driving force. Furthermore, the flux is related to a gradient by some characteristic of the system itself-the system or transport coefficient.

(1-1) Flux = Flow quantity/(Time)(Area) = (Transport coefficient)(Gradient)

The gradient for the case of temperature for one-dimensional (or directional) flow of heat is expressed as

(1-2) Temperature gradient = dT/dY

The flux equations can be derived by considering simple one-dimensional models. Consider, for example, the case of energy or heat transfer in a slab (originally at a constant temperature, [T.sub.1]) shown in Figure 1-2. Here, one of the opposite faces of the slab suddenly has its temperature increased to [T.sub.2]. The result is that heat flows from the higher to the lower temperature region. Over a period of time the temperature profile in the solid slab will change until the linear (steady-state) profile is reached (see Figure 1-2). At this point the rate of heat flow Q per unit area A will be a function of the system's transport coefficient (k, thermal conductivity) and the driving force (temperature difference) divided by distance. Hence

(1-3) Q/A = k ([T.sub.1] - [T.sub.2]) (X - O) (1-3)

If the above equation is put into differential form, the result is

(1-4) [q.sub.x] = -k dT/dx

This result applies to gases and liquids as well as solids. It is the one-dimensional form of Fourier's Law which also has y and z components

(1-5) [q.sub.Y] = -k dT/dy

(1-6) [q.sub.z] = -k dT/dz

Thus heat flux is a vector. Units of the heat flux (depending on the system chosen) are BTU/hr [ft.sup.2], calories/sec [cm.sup.2], and W/[m.sup.2].

Let us consider another situation: a liquid at rest between two plates (Figure 1-3). At a given time the bottom plate moves with a velocity V. This causes the fluid in its vicinity to also move. After a period of time with unsteady flow we attain a linear velocity profile that is associated with steady-state flow. At steady state a constant force F is needed. In this situation

(1-7) F/A = -5 O - V/Y - O

where 5 is the fluid's viscosity (i.e., transport coefficient).

Hence the F/A term is the flux of momentum (because force = d(momentum)/dt. If we use the differential form (converting F/A to a shear stress [tau]), then we obtain

(1-8) [[tau].sub.yx] = -5 d[V.sub.X]/dy

Units of [[tau].sub.yx] are poundals/[ft.sup.2], dynes/[cm.sup.2], and Newtons/[m.sup.2].

This expression is known as Newton's Law of Viscosity. Note that the shear stress is subscripted with two letters. The reason for this is that momentum transfer is not a vector (three components) but rather a tensor (nine components).

As such, momentum transport, except for special cases, differs considerably from heat transfer.

Finally, for the case of mass transfer because of concentration differences we cite Fick's First Law for a binary system:

(1-9) [J.sub.A.sub.y] = -[D.sub.AB] dCA/dy

where [J.sub.A.sub.y] is the molar flux of component A in the y direction. [D.sub.AB], the diffusivity of A in B (the other component), is the applicable transport coefficient.

As with Fourier's Law, Fick's First Law has three components and is a vector. Because of this there are many analogies between heat and mass transfer as we will see later in the text. Units of the molar flux are lb moles/hr [ft.sup.2], g mole/sec [cm.sup.2], and kg mole/sec [m.sup.2].

THE TRANSPORT COEFFICIENTS

We have seen that the transport processes (momentum, heat, and mass) each involve a property of the system (viscosity, thermal conductivity, diffusivity). These properties are called the transport coefficients. As system properties they are functions of temperature and pressure.

Expressions for the behavior of these properties in low-density gases can be derived by using two approaches:

1. The kinetic theory of gases

2. Use of molecular interactions (Chapman-Enskog theory).

In the first case the molecules are rigid, nonattracting, and spherical. They have

1. A mass m and a diameter d

2. A concentration n (molecules/unit volume)

3. A distance of separation that is many times d.

This approach gives the following expression for viscosity, thermal conductivity, and diffusivity:

(1-10) 5 = 2/3[[pi].sup.3/2] [square root of (mKT)]/[d.sup.2]

where K is the Boltzmann constant.

(1-11) k = 1/[d.sup.2] [square root of ([K.sup.3]T)]/[[pi].sup.3]m

where the gas is monatomic.

(1-12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The subscripts A and B refer to gas A and gas B.

If molecular interactions are considered (i.e., the molecules can both attract and repel) a different set of relations are derived. This approach involves relating the force of interaction, F, to the potential energy [phi]. The latter quantity is represented by the Lennard-Jones potential (see Figure 1-4)

(1-13) [phi](r) = 4[epsilon] [[([sigma]/r).sup.12] - [([sigma]/r).sup.6]]

where [sigma] is the collision diameter (a characteristic diameter) and [epsilon] a characteristic energy of interaction (see Table A-3-3 in Appendix for values of [sigma] and e).

The Lennard-Jones potential predicts weak molecular attraction at great distances and ultimately strong repulsion as the molecules draw closer.

Resulting equations for viscosity, thermal conductivity, and diffusivity using the Lennard-Jones potential are

(1-14) 5 = 2.6693 W [10.sup.-6] [square root of (MT)/[[sigma].sup.2][OMEGA]5

where 5 is in units of kg/m sec or pascal-seconds, T is in :K, [sigma] is in E, the [OMEGA]5 is a function of KT/e (see Appendix), and M is molecular weight.

(1-15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where k is in W/m :K, [sigma] is in E, and [[OMEGA].sub.k] = [OMEGA]5. The expression is for a monatomic gas.

(1-16) [D.sub.AB] = 1.8583 W [10.sup.-7] [square root of [T.sup.3](1/M.sub.A + 1/M.sub.B)/P][sigma].sup.2.sub.AB][[OMEGA].sub.DAB]

where [D.sub.AB] is units of [m.sup.2]/sec P is in atmospheres, [[sigma].sub.AB] = 1/2([[sigma].sub.A] + [[sigma].sub.B]), [[epsilon].sub.AB] = [[epsilon].sub.A][[epsilon].sub.B], and [[OMEGA].sub.DAB] is a function of KT/[[epsilon].sub.AB] (see Appendix B, Table A-3-4).

Example 1-1 The viscosity of isobutane at 23C and atmospheric pressure is 7.6 W [10.sup.-6] pascal-sec. Compare this value to that calculated by the Chapman-Enskog approach.

From Table A-3-3 of Appendix A we have

[sigma] = 5.341 E, [epsilon]/K = 313 K

Then, KT/[epsilon] = 296.16/313 = 0.946 and from Table A-3-4 of Appendix B we Obtain

[OMEGA]5 = 1.634

5 = 2.6693 W [10.sup.-6] [square root of (MT)]/[[sigma].sup.2][OMEGA]5

5 = 2.6693 W [10.sup.-6] [square root of ((58.12)(296.16)]/[(5.341).sup.2](1.634)

5 = 7.51 W [10.sup-6] pascal-sec

% error = [(7.6 ? 7.51)/7.6] W 100 = 1.18%

Example 1-2 Calculate the diffusivity for the methane-ethane system at 104:F and 14.7 psia.

T = 104 + 460/1.8 :K = 313:K

Let methane be A and let ethane be B. Then,

(1/[M.sub.A] + 1/[M.sub.B]) = (1/16.04 + 1/30.07) = 0.0956

From Table A in the Appendix we have [MATHEMATICAL NOT REPRODUCBLE IN ASCII.]

From Table A-3-4 in Appendix we have [OMEGA]DAB = 1.125

[MATHEMATICAL NOT REPRODUCBLE IN ASCII.]

The actual value is 1.84 W [10.sup.-5] [m.sup.2]/sec. Percent error is 9.7 percent.

TRANSPORT COEFFICIENT BEHAVIOR FOR HIGH DENSITY GASES AND MIXTURES OF GASES

If gaseous systems have high densities, both the kinetic theory of gases and the Chapman-Enskog theory fail to properly describe the transport coefficients' behavior. Furthermore, the previously derived expression for viscosity and thermal conductivity apply only to pure gases and not to gas mixtures. The typical approach for such situations is to use the theory of corresponding states as a method of dealing with the problem.

Figures 1-5, 1-6, 1-7, and 1-8 give correlation for viscosity and the thermal conductivity of monatomic gases. One set (Figures 1-5 and 1-7) are plots of the reduced viscosity (5/[5.sub.c], where 5c is the viscosity at the critical point) or reduced thermal conductivity (k/kc) versus (T/[T.sub.c]), reduced temperature, and (p/[p.sub.c]) reduced pressure. The other set are plots of viscosity and thermal conductivity divided by the values ([5.sub.0], [k.sub.0]) at atmospheric pressure and the same temperature.

Values of [5.sub.c] can be estimated from the empirical relations

(1-17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

[5.sub.c] = 7.70 [M.sup.1/2][P.sup.2/3.sub.c]/([T.sub.c).sup.1/6] (1-18)

where [5.sub.c] is in micropoises, [T.sub.c] is in :K, [P.sub.c] in atmospheres, and [??] is in [cm.sup.3]/g mole.

The viscosity and thermal conductivity behavior of mixtures of gases at low densities is described semiempirically by the relations derived by Wilke (6) for viscosity and by Mason and Saxena (7) for thermal conductivity:

(1-19) [MATHEMATICAL NOT REPRODUCBLE IN ASCII.]

(1-20) [MATHEMATICAL NOT REPRODUCBLE IN ASCII.]

(1-21) [MATHEMATICAL NOT REPRODUCBLE IN ASCII.] The [[PHI].sub.ij] 's in equation (1-21) are given by equation (1-20). The y's refer to the mole fractions of the components.

For mixtures of dense gases the pseudocritical method is recommended. Here the critical properties for the mixture are given by

(1-22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(1-23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(1-24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [y.sub.i] is a mole fraction; P[c.sub.i], 5[c.sub.i], and 5[c.sub.i] are pure component values. These values are then used to determine the P'R and T'R values needed to obtain (5/[5.sub.i]) from Figure 1-5.

The same approach can be used for the thermal conductivity with Figure 1-7 if [k.sub.c] data are available or by using a [k.sup.0] value determined from equation (1-15).

Continues...

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Edition details

• Publisher: Wiley-Interscience
• Publication date: 2006
• Language: English
• ISBN 10: 0471998141
• ISBN 13: 9780471998143
• Binding: Paperback
• Edition number: 1
• Number of pages: 463