TRANSPORT PHENOMENA AND UNIT OPERATIONS TRANSPORT PHENOMENA AND UNIT OPERATIONS A COMBINED APPROACH Richard G. Griskey A JOHN WILEY & SONS, INC., PUBLICATION This book is printed on acid-free paper Copyright 0 2002 by John Wiley and Sons, Inc , New York All rights reserved Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recordlng, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. 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Library of Congress Cataloging-in-Publication Data: ISBN 0-47 1-43819-7 Printed in the United States of America. 109 8 76 54 3 2 * To Engineering, the silent profession that produces progress CONTENTS Preface Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Transport Processes and Transport Coefficients Fluid Flow Basic Equations Frictional Flow in Conduits Complex Flows Heat Transfer; Conduction Free and Forced Convective Heat Transfer Complex Heat Transfer Heat Exchangers Radiation Heat Transfer Chapter 10 Mass Transfer; Molecular Diffusion Chapter 11 Convective Mass Transfer Coefficients Chapter 12 Equilibrium Staged Operations ix 1 23 55 83 106 127 157 179 208 228 249 274 vii viii CONTENTS Chapter 13 Additional Staged Operations Chapter 14 Mechanical Separations Appendix A Appendix B Appendix C Appendix References Index 321 367 410 416 437 440 443 PREFACE The question of “why another textbook,” especially in the areas of transport processes and unit operations, is a reasonable one. To develop an answer, let us digress for a moment to consider Chemical Engi- neering from a historical perspective. In its earliest days, Chemical Engineering was really an applied or industrial chemistry. As such, it was based on the study of definitive processes (the Unit Process approach). Later it became apparent to the profession’s pioneers that regardless of process, certain aspects such as fluid flow, heat transfer, mixing, and separation technology were common to many, if not virtually all, processes. This perception led to the development of the Unit Operations approach, which essentially replaced the Unit Processes-based curriculum. While the Unit Operations were based on first principles, they represented nonetheless a semiempirical approach to the subject areas covered. A series of events then resulted in another evolutionary response, namely, the concept of the Transport Phenomena that truly represented Engineering Sciences. No one or nothing lives in isolation. Probably nowhere is this as true as in all forms of education. Massive changes in the preparation and sophistication of students - as, for example in mathematics -provided an enthusiastic and skilled audience. Another sometimes neglected aspect was the movement of chemistry into new areas and approaches. As a particular example, consider Physical Chem- istry, which not only moved from a macroscopic to a microscopic approach but also effectively abandoned many areas in the process. ix X PREFACE Furthermore, other disciplines of engineering were moving as well in the direction of Engineering Science and toward a more fundamental approach. These and other factors combined to make the next movement a reality. The trigger was the classic text, Transport Phenomena, authored by Bird, Stewart, and Lightfoot. The book changed forever the landscape of Chemical Engineering. At this point it might seem that the issue was settled and that Transport Phenomena would predominate. Alas, we find that Machiavelli’s observation that “Things are not what they seem” is operable even in terms of Chemical Engineering curricula. The Transport Phenomena approach is clearly an essential course for grad- uate students. However, in the undergraduate curriculum there was a definite division with many departments keeping the Unit Operations approach. Even where the Transport Phenomena was used at the undergraduate level there were segments of the Unit Operations (particularly stagewise operations) that were still used. Experience with Transport Phenomena at the undergraduate level also seemed to produce a wide variety of responses from enthusiasm to lethargy on the part of faculty. Some institutions even taught both Transport Phenomena and much of the Unit Operations (often in courses not bearing that name). Hence, there is a definite dichotomy in the teaching of these subjects to under- graduates. The purpose of this text is hopefully to resolve this dilemma by the mechanism of a seamless and smooth combination of Transport Phenomena and Unit Operations. The simplest statement of purpose is to move from the fundamental approach through the semiempirical and empirical approaches that are frequently needed by a practicing professional Chemical Engineer. This is done with a minimum of derivation but nonetheless no lack of vigor. Numerous worked examples are presented throughout the text. A particularly important feature of this book is the inclusion of comprehensive problem sets at the end of each chapter. In all, over 570 such problems are presented that hopefully afford the student the opportunity to put theory into practice. A course using this text can take two basically different approaches. Both start with Chapter 1, which covers the transport processes and coefficients. Next, the areas of fluid flow, heat transfer, and mass transfer can be each considered in turn (i.e., Chapter 1, 2, 3, . . ., 13, 14). The other approach would be to follow as a possible sequence 1, 2, 5, 10, 3, 6, 11, 4, 7, 8, 9, 12, 13, 14. This would combine groupings of similar material in the three major areas (fluid flow, heat transfer, mass transfer) finishing with Chapters 12, 13, and 14 in the area of separations. The foregoing is in the nature of a suggestion. There obviously can be many varied approaches. In fact, the text’s combination of rigor and flexibility would give a faculty member the ability to develop a different and challenging course. PREFACE xi It is also hoped that the text will appeal to practicing professionals of many disciplines as a useful reference text. In this instance the many worked examples, along with the comprehensive compilation of data in the Appendixes, should prove helpful. Richard G. Griskey Summit, NJ 1 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, filtra- tion, 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 trans- fer). This realization generated the transport phenomena approach - an approach 1 Transport Phenomena and Unit Operations: A Combined Approach Richard G. Griskey Copyright 0 2002 John Wiley & Sons, Inc. ISBN: 0-471-43819-7 [...]... can be partially explained by seeing that liquids are much more dense than gases Additionally, theoretical and experimental work for gases is far more voluminous than for liquids In any case the net result is that approaches to transport coefficient behavior in liquid systems are mainly empirical in nature An approach used for liquid viscosities is based on an application of the Eyring (9,10) activated... them the scale-up process would be almost impossible Additionally, these groups are the way that we make use of semiempirical or empirical approaches to the transport processes As we will see later, the theoretical/analytical approach cannot always be used, especially in complex situations For such cases, dimensionless groups enable us to gain insights and to analyze and design systems and processes... 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 ft2, g mole/sec cm2, and kg mole/sec m2 THE TRANSPORT COEFFICIENTS We have seen that the transport processes (momentum, heat, and mass) each involve... diameters, compare them, and evaluate 1-14 Compute a value for DAB for a system of argon (A) and oxygen (B) at 294°K and atmospheric pressure 1-15 The diffusivity for carbon dioxide and air at 293°K and atmospheric pressure is 1.51 x lop5 m2/sec Estimate the value at 1500°K using equations (1-12) and (1-16) 1-16 A dilute solution of methanol in water has a diffusivity of 1.28 x m2/sec at 15°C Estimate... Slattery and Bird (8) This, however, should be used only with great caution because it is based on very limited data (8) Example 1-3 Compare estimates of the viscosity of CO2 at 114.6 atm and 40.3"C using 1 Figure 1-6 and an experimental viscosity value of 1800 x lo-' pascal-sec for COz at 45.3 atm and 40.3"C 2 The Chapman-Enskog relation and Figure 1-6 From Table A- 3-3 of Appendix A, T, = 304.2"K and. .. 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 6 TRANSPORT PROCESSES AND TRANSPORT COEFFICIENTS This approach gives the following expression for viscosity, thermal conductivity, and diffusivity: (1-10) where K is the Boltzmann constant (1-1 1) where the gas... collision diameter (a characteristic diameter) and t a characteristic energy of interaction (see Table A- 3-3 in Appendix for values of CJ 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 p = 2.6693...2 TRANSPORT PROCESSES AND TRANSPORT COEFFICIENTS that owes much to the classic chemical engineering text of Bird, Stewart, and Lightfoot ( I ) 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... x of pascals-' What is its thermal conductivity? 1-12 What is the thermal conductivity of a mixture of methane (mole fraction of 0.486) and propane at atmospheric pressure and 1OO"C? 1-13 Argon at 27°C and atmospheric pressure has values of viscosity and thermal conductivity of 2.27 x lop5 pascal-sec and 1.761 x Joules/(sec m OK) from each property respectively Calculate molecular diameters and collision... lo-' pascal-sec pmix = 1714 x lo-' pascal-sec 16 TRANSPORT PROCESSES AND TRANSPORT COEFFICIENTS Actual experimental value of the mixture viscosity is 1793 x lop8 pascal-sec The percent errors are 2.51 and 4.41%, respectively, for cases 1 and 2 TRANSPORT COEFFICIENTS IN LIQUID AND SOLID SYSTEMS In general, the understanding of the behavior of transport coefficients in gases is far greater than that for . TRANSPORT PHENOMENA AND UNIT OPERATIONS TRANSPORT PHENOMENA AND UNIT OPERATIONS A COMBINED APPROACH Richard G. Griskey A JOHN WILEY & SONS, INC., PUBLICATION This. were mainly composed of a smaller subset of transport processes (momentum, energy, and mass trans- fer). This realization generated the transport phenomena approach - an approach 1 Transport. Engineering Science and toward a more fundamental approach. These and other factors combined to make the next movement a reality. The trigger was the classic text, Transport Phenomena, authored by