found Rhades' "instant statistics" helpful and time-saving in two rocket development reports. I recommend the purchase of both: they complement one another. They are useful additions to the reference shelf of the h a d w o r k i n g undergraduate or graduate student. They are equally useful t o the haddriving recent or not-sorecent graduate who is conscious of the need for more precise expression.
JOAN WILSON Atlantic Research Corporatia Alezandria, V a .
The Optimal Design of Chemical Raactors: A Study in Dynamic Programming
Rutherfwd Aris, Univemity of Minnesota, Minneapolis. Academic Press, Inc., New York, 1961. 191 pp. Figs. and tables. 16 X 23 cm. li.
Dr. Aris summarizes his important work neatly in the opening paragraph of the preface: "This monograph, as its subtitle indicates, treats some of the significant problems of chemical reactor engineering from a unified point of view. The methods of dynamic programming have proved themselves both powerful and versatile in a number of branches of economies and engineering and it is remarkable how naturally they fit the needs of reactor design. The chemical cnginror will he interested in the method as a practical tool in the design process, and it is hoped that he will find here a sufficient variety of example to allom- him to treat any specific problem with as much realism ils he may desire. In the interest of clarity the simpler problems have been chosen for extended treatment, but in all cases the methods of solution of the more general have been shown. Mathematicians and those interested in the rapidly developing field of mathematical programming will find here an ecological study of the species whose anatomy, physiolog,y, and nattturd history have been opened up in Bellman's book ('Dynamic Programming,' Princeton 1957)." Dr. Aris shows how the chemical engineer can coordinate chemical kinetic information with ecouomio estimates in order to design chemical reactors which are optimum according to any one of the customary measures of effectivenessoperating cost, profit, yield, or reactor volume. The unifying concept of the hook is that a variety of problems intermingling rat,e processes with physical limitations can all he solved in the same way by using dynamic programming, a rather recent development in the analysis of mathematical functions. After summarieing the work of the past twenty years concerning design of chemical reactors for minimum volume or maximum yield, Dr. Aris develops the
(Continued a page A502) Vol~me39, Number 6, June 1962
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BOOK REVIEWS This is followed by an exposition of the mathematical description of chemicsl reactors and oi the measures of their cffoetiveness commonly chosen to be optimized. I n three succeeding chapters the author then discusses in some detail the optimal design oi continuous flow stirred tank reactors, multihed adiabatic reactors, and tubular reactors. Dr. Aris then turns t o stochastic problems involving uncertain events which must be treated probabilistically, such as the formulation of optimal catalyst replacement policies when the effectiveness of regeneration is not entirely predictable. The work concludes by showing how dynamic programming may he of ~ e r v i r e in finding how existing reactors should be operated and controlled optimally. Perhaps the most interesting and original feature of the book is its extensive nso of clever graphical constructions which show tho functional relationships of d,vnnmie programming more I l y t o engineers a t least, than do the customary functional equations. Another valuable contribution t o the l i t e r a t u r ~is the exposition and proof of certain general qoalitativc properties of optimal rhemical reactors such as the dependence of the shape of optimal temperature profilea on the type of reaction taking place. .Athough most of thrse properties have been dcrived previously h,v such other methods as tho calculus of variations, the usc of dynamic programming provides a certain economy of t,hought and unifies the several results. The xrit,ing is exrellent-clear, rompact, and flavored with wit and irony. Nevertheless the hook could be a hit diffirult for an mgineer not strong in mathematics. We recommend i t as an advanced reference work for design engineers, operations analysts, and research workers dealing with kinetic problems. I n conjunction with a standard text concerning kinetic expressions, the hook could be employed as a graduate text in chemical reactor design. I n fact, several of t,he examples and graphical ronstructions would not be b ~ y a n dthe compr~hension of undergraduate students if presented properly, and tearhers of plant design courses might use t,hem to introduce the important concept of dynamic programming (or serial optimization) into the undergraduate chemical engineering curriculum. DOUGLASS J. WILDE Univemily of Terns Austin
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Journd of Chemical Education
