annual review
a
ROBERT F. SWEENY ROBERT S. DAVIS CHARLES D. HENDRlX
ti
Optimi&ion dominates the limelight in the
ap-
plication of mathematics in chemical research, development, and practice
ptimimtion has again this year dominated the applica I: ons of mathematics in chemical engineering. The number of papers published on this subject has approximately doubled. Indeed, optimization has become more than a tool for better process and plant design and operation; it has assumed the character of a special field of chemical technology distinctive from the established concepts. There are specialists In optimization, just as there are specialists in distillation and reactor engineering. Today, there are half a dozen chemical engineers who are identified as optimization specialists even though their work has been applied to various unit operations or processes. There is a trend toward optimization techniques characterized by widespread applicability to many phases of chemical engineering. Probably a more important trend. is that these techniques are being developed in a general way. Chemical engineers are developing methods without reference to the established concepts except by way of example. Finally, the application of optimization in many cases is a n integration of many disciplines within chemical engineeringthe entire plant is considered. This was done intuitively in the past-there was no systematic method involved. Most other applications of mathematics (except for process control which is covered in a separate review by T. J. Williams in this issue of I&EC) are really works in the established subjects which happen to use mathematics. They are included here in tabular form to complete the record, to show trends, and as reference for workers in those fields who are looking for reports selected for their mathematical approach. General R e f e r e n c e s
In the past year there were some novel applications of mathematics. Use of Monte Carlo techniques to de72
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
scribe physical processes is a fascinating concept. It was applied (7711) to reacting and coalescing dispersed phase systems. Another up and coming technique is statistical mechanics, long used by physical chemists on the molecular scale, but rather neglected by chemical engineers for discrete macroscale systems. The technique was used to describe certain problems in particle technology (2x1, 811)’the growth and agglomeration of particles, as in crystallization. The basic problem in many applications is to find a coupled solution of related equations such as equations of motion and energy. The firs1 of a series of papers appeared (7011) which attempts to develop a variational integral to do this job better. Another brief paper (3-4) gives a method for evaluating a convolution integral. Three tutorial series of articles of interest appeared during the year. One \\‘as on matrix mathematics ( I Z A ) , another on analog simulation techniques (711)’ and a third on analog simulation of continuous reactions ( 6 A ) . A new textbook on analog computations and simulations (411) should also be of special interest to chemical engineers. An article (In) on a simple but novel method of electrical analog simulation also appeared. The method is based on the use of silver conduction paint applied to paper. A book (YA) of general interest and a Chemical Engineering Progress Symposium Series (5A) covering new mathematical applications and methods, process design optimization and simulation, and process control and dynamics appeared. Statistics
Revised editions of two well known texts were published (7B, 4B). Alder’s ( I B ) covers a wide range of topics at an elementary level, and is suitable for selfinstruction. Brownlee’s (4B) includes theory and practice, with answers to selected problems. Some chemical applications, with emphasis on measurement and sampling, were discussed (72B). The title of a new book (9B) aptly describes its contents. An unusually clear discussion of quality control for managers and engineers is available (76B). A cornprehensive review of articles describing statistical methods in chemistry appeared ( 15B). Some applications in analytical chemistry were discussed (5B). Three typical reliability problems in chemistry were described and analyzed by Smith and Dubey (78B).
Staged drug screening under some simplifying assumptions was discussed (IOB). The question of the optimum number of stages and samples per stage was explored. I n another reference a method for estimating the composition of a three-component mixture was presented (14B). One or more responses in a factorial or fractional factorial experiment are frequently lost or tainted. A method for estimating missing values was presented ( 6 B ) , and the design and analysis of experiments for studying physical mechanisms are discussed (7B). A central composite design was used to describe the physical properties of a water-soluble film ( 2 B ) . The properties of ratios of random variates is a subject of great interest and complexity. A study of the distributions of ratios of normal and uniform variates was conducted (13B). Bias in ratios is analyzed by Mandel (IZB). Analysis of variance and F-tests is insufficient for most single and double classification arrays. A shortcut method for multiple comparisons is prescribed ( 7 IB) . Curve fitting using orthogonal polynominals (8B) was found to be faster and better than using least squares. A novel use of least squares fitting was presented (3B) in which noncompatible simultaneous equations were solved by fitting possible solutions. Curve fitting with nonparametric statistics was discussed by Ratkowsky (77B). Operations Research
I n reviewing the literature this past year, one is struck by the fact that relatively few publications are encountered which give applications of operations research (OR) techniques to the chemical and petroleum industries. It is unfortunate that there are not more lucid articles being published on the application of OR in these fields. I t seems that there is a communications gap, which unfortunately is widening, between the active practitioners of O R and the management group which makes the ultimate decisions-sometimes based on O R techniques. Much more work is needed in better acquainting managers with these newer techniques. An excellent book appeared this past year in paperback form which should help to bridge this gap (42). I t was prepared by the editors of the Harvard Business Review and is highly recommended to all management personnel. It covers such areas as operations research, mathematical programming, queuing techniques, econometrics, and mathematical models in capital budgeting, marketing, and production. The presentation is very clear and advanced mathematics are not required to follow the concepts involved. A general survey of the nature of O R the form of the problems encountered and the relation of O R to other management sciences were presented ( I C ) . This text discusses the types of problems which O R can handle and gives a n idea of the organizational and administrative structure required for an OR group. The use of OR in small businesses, the facilities required, and a list of companies currently using O R techniques as well as a summary on future prospects for the field are covered. I t is highly recommended as a general guide to the field. Another introductory text also appeared (26C). For the experienced practitioner in the field, the newest volume in the series on “Progress in Operations Research” ( I IC) appeared. This is a n excellent survey
of the fields of applications of O R . I t has an extensive bibliography and is a valuable working reference. It describes the body of knowledge that applied OR workers have accumulated and gives quite a bit of information about the application of models to solve problems in business and government with sections on petroleum, chemical, and pharmaceutical applications. An interesting book (24C) appeared which covers the application of economic theory to real situations. I t uses simple mathematical models in making practical business and production decisions. I t covers the area of linear programming, pricing theory, profitability models, replacement models, and cycling models. There is also extensive material on decision making for capital invest-
TABLE I .
QPTlMlZATlON
Hill Climbing (Statistical Techniques)
(1E) (ZE) (3E) (4E)
(5E) (6E) (7E) (BE) (SE)
Extension of Simplex method to constraints Steepest ascent Sequential search of, constrained problems Direct search of constrained problems Multistage optimization Review of EVOP, random search, Simplex Simplex method adapts to local conditions Monte Carlo simulation of batch time variations Examples of hill climbing applications
Dynamic Programming
(1F) (ZF) (3F) (427)
Optimum design of grain drier A book on discrete dynamic programming Optimum rectification cascades Multistage processes with feedback
Maximum Principle (Variational Techniques)
(7G) Discussion of Green’s vector (ZG) Derivation of maximum principle through Green’s function (3C) Demonstrates general failure of maximum principle in discrete cases (4G) Iterative solution to constrained multistage problem (5G) Steepest ascent with use of Green’s functions (6G) A book on discrete maximum principle (7G) Discussion of discrete form of principle (8G) Discussion of discrete form of principle (9G) Unsteady state optimization by maximum principle (1OG) Control of a stirred reactor ( 1IG) Control of batch and tubular reactors (12G) Discrete form with recycle compared Miscellaneous
( 1 H ) Optimum yield of tubular reactors (ZH) Nonlinear programming ( 3 H ) Optimal policies for first-order consecutive reversible reactions ( 4 H ) Best initial compositions in gas reactions ( 5 H ) Dynamic optimization of two-stage reactor
ment and comparison of various cash flow methods. This is an excellent text on applying basic economic theory to the chemical and petroleum fields. A good text ( I 7 C ) on management decision theory also appeared. I t covers the fundamentals of engineering decisions, including managerial economics. I t covers areas of OR management science and decision theory. The use of simulation to handle O R problems was discussed (29C). I t discusses the methods used in simulation studies and shows the application of Monte Carlo techniques as well as giving computer programs for simulating queuing problems and other industrial processes. Two articles on Monte Carlo techniques appeared (73C, 28C) which should be especially helpful to the chemical engineer not familiar with the technique. The application of industrial dynamics techniques to research and development and management problems VOL. 5 7
NO. 1 2 D E C E M B E R 1 9 6 5
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Mathematical model building plays new key roles in research management in industry and government was covered (27C). This reference gives an excellent quantitative description of research and development projects and combines social, psychological, technical, and economic factors into a unified theory of research and development projects. T h e model-building, simulation techniques and systems
TABLE I I .
OTHER APPL ICAT IONS
Miscellaneous Simulation a n d Design ( 7 K ) Theory of grinding operations (2K j Stead? state ammonia synthrsis converter ( 3 K ) Analytical simulation of transients in equilibrium still ( 4 K j Adsorbers ( 5 K ) Transient behavior of ammonia synthesis (6K) Cooler-condenser with fog (analog) ( 7 K ) Multiple equilibrium sraged processes ( S K ) Batch solvent extraction (analog) (SKj Foam fractionation ( 7 0 K ) Ethylene production (analog) ( 7 1 K ) Gas recovery ( 1 2 K ) Effect of equilibrium on dynamics of distillation (13.T) Roasting oven (analog) ( 1 4 K ) 'Thermal diffusion columns (15x1 Solvent extraction (16Kj Rotas>-driers (17K) Unsteadv state complex distillation (18K) Multicomponent distillation Forced Response Testing (1L) Nonlinear frequency response in radiation (2L) Frequency response in adiabatic hiimidifier ( 3 L ) Boiling water nuclear reactor response (4L) Frequency response beat transfer in jacketed pans ( 5 L ) Frequency response of multipass heat exchanger (6L) Flow-forced heat exchanger (7L) Frequency response in heat removal from tank Residence Time Distribution (Axial Dispersion) Dispersion ii'ith time variable flow hsjmptotic solutions to fixed bed separations Dispcrsion of heat in fluid flow in porous media Distribution in multistage systems with recycle Ion exchange P e c k numbers and retardation (6M) Design model for ion exclusion column Tcith nonlinear isotherms (7Mj Distribution in cascade of vessels with recycle (8.ll) TTashing soliible material from bed of packed solids ( 9 M j Residence time probability density ( ? O M ) Film diffusion-controlled binary ion exchange (7,M) (2.11 j (3.M) (4.M) (5,M)
Reactor Stability (7.V) Tubular reactor (2.V) Basic investigation of reaction on catalyst particle (3.V) Search for better Lyapunov functions (4s) Cascaded reactors using Lj-apunov's method ( 5 5 ) Fixed catalyst bed ( 6 5 ) For the novice ( 7 5 ) Dynamics of tubular reactor with back-mixing (8~vJPolymerization in immiscible phases (9.V) Testing the linear assumption in nonlinear systems (10,Vj Tubular reactors ( 7 7 N ) Test of simplifying assumptions in packed beds ( 12'V) Stirred tank reactors Yield and molecular distribution in polymerization Interfacial reactions in laminar Aow Molecular weight distribution in polymerization Determine kinetics from D T A curves Complex reactions in liquid phase Polymerization in a CSTR Reaction a t entrance of tubular reactor Continuous polymerization models-CSTR with Mass Transfer A general modulus for effectiveness facrors Ionic penerration theory Gas absorption with two-step reactions Heat and mass transfer with reaction Reaction a t surface of nonporous catalyst Transfer from gas bubbles with reaction
74
approaches that are developed here \+ill help researchers obtain a better understanding of the optimization procedures to be used in research and development. Linear Programming. One of the basic linear programming (LP) texts has no\\- been revised in a new second edition (8C). Kew sections have been added
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(7Q) Catalyst systems
(EQ) Reaction in transfer from fluid and solid spheres (QQ) (1OQ) (71Q)
(724)
Moving beds Reaction on a rotating disk Fixed bed reactor Reaction a t surface of nonporous catalyst
Mass Transfer
(1Rj Similarity for nonlinear diffusion ( 2 R ) Multicomponent diffusion (3R) Diffusion ivirh moving boundary (4R) Diffusion with moving boundary (5R) Diffusion with moving boundary (6R) Mass or hear transfer from oscillating cylinder (7R) Transfer during short exposures ( S R ) Transfer around revolving body (OR) Interaction of diffusion and surface process in absorption (10R) M a s s and hear transfer in multiparticle systems ( 7 1 X ) Trrnsfer in flowing films (1ZRj Reverse osmosis (13R) Diffusion a t moving surface (74R) Diffusion a t moving surface (75R) hlulticomponent mass transfer (76R) Multicomponent mass transfer (17R) Multicomponent mass transfer (18R) Zone melting H e a t Transfer (IS) (2s) (38') (4s) (5s) (6s)
(7s)
(ESj (9s) (10s) (17s) (72s)
Similarity transform of three-dimensional eqrrationa to O.D.E.'s Heat and mas? transfer with flow Multilayered bodies Konhomogeneous medium Monte Carlo solution for radiation Cnsteady state transfer to shear OMBook-especially good section on transient nonlinear transfer Use of computers Laminar and turbulent flow between plates Transfer to spinning plate in space Condensation on fins Transfer to non-Newtonian flow a t conduit inlet
Fluid Flow
(IT) (2T) (3T) (4T) (ST) (6T) (7T)
Power law fluids Falling film Damped oscillating manometers Ozone flame Isotropic turbulent mixer Liquid film flow Rotameter dynamics (8T) Applications of Galerkin's method ( S T ) Flow past a sphere ( I O T ) Power law fluids ( I 7 Tj Heat transfer to a steady Coutte floxv (12Tj Miscible displacement from porous medium ( 1 3 T ) Laminar wall jet ( 1 4 T ) Applications of Galerkin's method (7573 Steady flow of pseudoplastic fluids ( ? 6 T ) Drag out of liquids on flat plates Fluidization Stokes flow past arbitrary particle Stokes flow past arbitrary particle Stokes flow past arbitrary particle Stokes flow past arbitrary particle Stokes flow past arbirrary particle Flow around spheres Inclined settling of suspensions Hydrodynamic stability of beds Homogeneous fluidization Effect of solid thermal properties on heat transfer in beds Dispersed two-phase flow
on sensitivity analysis, integer programming, and the decomposition algorithm. A separate section on LP applications is given along with a listing of the various LP codes available on different computers in the United States and Europe. It has an extensive list of references. An excellent paperbound text has appeared on linear programming applications (7%). I t also is a good survey of theory and is highly recommended for managers. An excellent discussion of the use of sensitivity analysis in LP problems was presented (32C). Sensitivity analysis gives a better insight into linear programming and shows how the optimum solution changes with changes in factors such as input data. The article uses crude-oil refining as an example for use of sensitivity analysis. This technique is very useful in doing LP on smaller computers since the problem can be solved on a large computer and then variations in input data and how they affect the optimum solution can be studied on smaller computers. This technique can be the basis for a n on-line computer program which would constantly recalculate the optimum LP solution for changes in the process variables. This is a n extremely useful technique and a very lucid article on the subject. An unusual application of linear programming appeared (3C) in which LP was used to carry out economic planning for an underdeveloped country. An LP model was used to select projects for a national development program with the constraints of the model covering the whole economy. It made use of sensitivity analysis in order to find the optimum development program for long range planning in an underdeveloped country. Another application of LP was given in a n article (27C) which the novice should find helpful. PERT a n d C.P.M. Several texts and articles appeared on PERT and C.P.M. This area has been one of the most profitable applications for operations research techniques. An excellent text (ZOC) on the use of critical path methods in construction management appeared. I t teaches C.P.M. and P E R T and gives excellent insights into the construction industry. I t discusses cost control, allocation of resources, and the applications of computers. I t is highly recommended for anyone who wants to be familiar with the use of these techniques in the construction industry. T N Oother introductory texts on critical path methods also appeared (52, 7SC). A programmed instruction manual for PERT cost was also presented (72C). The use of PERT and C.P.M. for planning and scheduling work that involves a high degree of uncertainty is covered (2C). A mathematical analysis of the standard P E R T assumptions, which shows the errors involved in them and gives suggested methods for improving the P E R T technique, appeared (23C). A method of modifying C.P.M. and PERT to handle large projects with limited resources was presented (37C). I t shows that the critical sequence in the limited resource case is analogous to the critical path in the unlimited resource case. Computational Techniques. A test on computing methods in optimization problems appeared (20). This test is the published proceedings of a conference on optimization held a t U.C.L.A. from January 30 to 31, 1964. Among the subjects of interest covered in the O R area are dynamic optimization and dynamic programming. An excellent review is given of optimization techniques along with many illustrative examples and computer programs for certain cases. A new procedure
for mixed integer programming appeared (QC). I t gives an interesting application of integer programming to refining problems. The use of analog computers in O R for simulating management control systems and as hill climbing devices to solve both linear and nonlinear programming problems was covered (75C). A discussion of inequalities for stochastic nonlinear programming problems appeared (22C). Marketing a n d Sales Forecasting. Some interesting applications of O R to the areas of marketing and sales forecasting appeared this past year. An excellent article on the use of dynamic simulation in market planning appeared (702). This article presents the use of computer models of industrial marketing systems to help set sales goals for present operations and to plan future investments. I t gives an example of the application of O R techniques to the fertilizer industry. The use of cumulative sum techniques from process control as applied to sales forecasting was discussed (6C). This technique was used to detect changing patterns of customer demand and also to detect when the forecasting system being used was no longer adequate. An interesting application of O R in advertising appeared (7C) which covered the use of linear programming in media selection as applied to magazine advertising buying. Production Planning. The application of linear programming to production planning was discussed ( 7 4 3 . A multi period model was used because of the seasonal nature of the parameters. The article discusses model formulation in detail. An application of L P to planning transistor production appeared (25C). Model formulation and data collection operation and results are described. The use of O R techniques to determine the optimum size for plant capacity for both a minimum cost and competitive effect or survival viewpoint was considered (302). One article studies the criteria to be used for various industries, including petroleum. I t concludes that the survival concept in determining optimal plant capacity was best for the various companies and industries considered. T h e use of O R and computers by British Petroleum in production control, plant construction, transportation planning, and resource allocation was covered ( 19C). Optimization
The high interest in this subject is illustrated by the publication of a list of over 100 projects on process optimizations in schools and government installations in the United Kingdom alone (40). Two publications brought together papers of the various categories within the general subject ( 2 D , 3 D ) . A very good review article appeared ( 8 0 )which covered the classic Euler approach; methods based on Fibonacci search; use of Lagrange multipliers; linear, nonlinear, and dynamic programming techniques. A method new and perhaps very
Robert F. Sweeny is Assistant Professor at the Chemical Engineering Department of Villanova Univtrsity; Robert S. Davis is Executive Vice President of Chem Systems, Znc.; Charles D . Hendrix is Engineer and Statistician, Union Carbide Chemicals Co. AUTHORS
VOL. 5 7
NO. 1 2
DECEMBER 1965
75
.
important to chemical engineering, called geometric programming, was briefly introduced. According to this technique. instead of directly finding the optimal values of the independent variables, the optimal distribution of the terms in the objective function is determined. The optimal independent variables can then be found by “back-calculation.” Three important papers appeared (ID,6D, 7 0 ) which describe what might be called optimization policy. This is the dissection of large multipart systems into the best combinations of parts, then the systematic optimization of parts, and then the whole. Another possibly important article described a “learning machine” and its use (5D).This is a special conditional probability computer which optimizes a process by observing the process in operation. Table I lists other articles and books on optimization. -Most of these are applications of established methods, clarifications, and variations. Other Applications
The problem of process heat and material balances in a complex plant is much more complicated than most people would expect. A book ( I J ) which is related to the subject appeared and two articles also (2J, 3 J ) on the fundamentals. Another article ( 4 J )described a computer program for the calculations. Table I1 lists and classifies the other applications which appeared during the past year. Most of these are applications of established methods of analysis to new problems.
Operations Research (1C) Ackoff, R . L., Rivett, P..“Manager’s Guide t o Operations Research,” Wiley, New York, N. Y., 1963. ( 2 C ) Baker, B. iY., Eris, R . L., “Introduction :o Pert-CPSI,” Irwin, Homewood) Ill., 1964. (3C) Bhende, V. P., M a n a g e m e n t Science 10 (4), 7 9 6 (1964). (4C) Bwisk, E. C., Chapman, J. F., ‘.New Decision Making Tools For Managers,” Mentor, New York, K,Y..1965. (5C) Collins, F. T . , “h-etwork Planning a n d Critical Path Scheduling,” Know-How Publications, Berkeley, Calif., 1964. (6‘2) Davies, 0. L., Harrison. P. J., Operations Res. 12 (2), 235 (1964). (7C) Engel, J. F . . h‘arshaw. M. R., J . A d i . Res. 4 (3), 42 (1964). (BC) Gass, S. I., “Linear Programming Methods and Applications,” 2nd ed., McGraw-Hill, N e w York. 1964. (9‘2) Healy, W. C., Jr., Operations Res. 12 ( l ) , 122 (1964;. (10‘2) Hegeman, G. B., Chem. Eng. .\rei~s43 ( l ) , 64 (1965). (11C) Hertz, D. B.. Eddison, R. T., “Progress in Operations Research,” Vol. 11, LYiley, New York, N.Y.,1164. (12C) I. T. T., “Pert Cost--.\ Programmed Instruction Manual,” Federal Electric Corp., Paramus. N. J., 1961. (13C) Jackson, K. E.. Klomparens, A . J., W‘estbrook, G. T., Ciirm. Bng. Progr. 61 (1). 83 (1965). (14C) Jones, W.G.. Rope, C. % Oprratiotral I., Res. Quart. (L’.K,) 15 (4), 293 (1964). (15C) Longley, D., Electr. E y r . (C-. K.) 36 (4361, 378 (1964). (16C) hlartino, R . L.. “Finding the Critical Path,” American Management Assoc., New York, N. Y., 1964. (17C) Morris, rV, T.: “Analysis of Managcment Decisions,” Irwin. Ilomewood, Ill., 1964. (18C) Naylor, T . H., Byrne, E , T., “Linear Programming,” lVadsli.orth, Belmont, Calif., 1963. (l9C) Newly, W .J., .Tern Scimlirt (C.X.) 22 (3941, 602 (1964). (20‘2) O’Brien, J. J., “CPhI in Construction Management.” McGraw-Hill, Ncw York, K. Y., 1965. (21C) Roberts, E. E., “Dynamics of Research and Development,” Harpcr and Row, New York, N.Y.,1964. (22C) Rosen, J. B., Mangasarian, 0 . L., Operntions Res. 12 [ i ) ,143 (1964). (23C) Ryavec, C. A , , MacCrimmon, K. R., Zbid.,p. 16. (24C), S;pweyer, H. E.,“Analytic Models f o r Managerial and Engineering Economics, Reinhold, New York, N. Y., 1964. (25C) Smirh, S. B.. Operations Res. 13 (1). 132 (1965). (26C) Stoller, D. S., “Operations Research-Process and Strategy,” U. of Calif. Press, Berkeley. Calif., 1965. (27C) Tayyabkhan, bf.T., Richardson, T. C.. Ciiem. Eng. Progr. 60 (9), 58 (1964). (28C) Ibid., 61 ( I ) , 78 (1965). (29C) Tocher, K. D.. “Art of Simulation,” Van Nostrand, Princeton, 1963. (30C) U’eiss, L. LV., J.ofPo/. E m . 72 ( 3 ) , 246 (1964). (31C) TViest, 3. D., Operalions Res. 12 (3), 395 (1964). (32C) \Vilde, D. J., Beightler, C. S., Hydrocarbon Process. Pelroi. Rejner 44 (Z), 111 (1965). Optimization
BI BLl OG RAPHY G e n e r a l References (14) Albright, M. .A,. H]diocarbox Process. Petrol. ReJner 43 (7), 135 (1964). (2h)H u l b u r t , H. hi., K a t z , S.: Chem. En!. Sci. 19, 555 (1964). (3A) Jain, S. C., Chandra, I., Bri!. Ckem. E n g . 9 (12), 827 (1964).
(4A) Jennes?, R . R., “Analog Computation and Simulation: T h e Laboratory Approach, Allyn & Bacon, Inc.. Boston, Mass., 1964. (5A) Krone, L. H., Williams: T. J., Chem. Eng. Progr. Sjfnp. SeriesSo. 55 61, (1965). (6A) M a t t h e w , T., Chem. Eng. 71 (16), 93 (1964). (7.A) Ibid., 72 (l), 79 (1965). (8A) Randolph, A. D.: Con. J . Chem. Eng. 42, 280 ( 1 9 6 4 ) . (9A) Rosenbrock, H. H., Storey, C., “Computational hiethods in Chemical Engineering.” Pergamon Press, London, 1964. (l0A) Slattery, J. C., Chem. Eng. Sci. 19, 801 (1964). (11.4) Spielman, L. A,, Levenspiel. 0.:Ibid., 20, 247 (1965). (12A) T a o , L. C.:Chem. E7tg. 72 (5), 77 (1965). Statistics ( l a ) Alder, H. L., Roessler, E. D., “Introduction t o Probability a n d Statistics,” 3rd ed., Freeman, San Francisco, Calif.: 1964. (2B) Bentz, A. P., R o t h , R . W’,, J . S p p l . PolymerScr. 9, 1095 (1965). (3B) Bright, J. W., Dankins, G. S., INO.ENG.CHEM. FUNDAMENTALS 4, 93 (1965). (4B) Bfownlee, K . A,, “Statistical Theory a n d Methodology in Science a n d Engineering,” 2nd ed., Wiley, New York, N. Y., 1965. (5B) Calder. A. B., A n a / . Chem. 36 (9), 25.4 (1964). (6B) Draper, N.R.. Stoneman, D. M., Bmrnetrics 20 (3). 443 (1964). (7B) Hunter, W. G., Box, G. E . P., Technometrm 7 ( I ) , 23 (1965). (8B) Ingels, R . M.. Chem. Eng. 7 1 (22). 133 (1964). ( 9 B ) Johnson, N.L.. Leone, F. C.. “Statistics a n d Experimental Design in Engineering a n d t h e Physical Sciences,’‘ Wiley, New York? N. Y,, 1964. (1OB) King, E. P., Biometrika 51, 1 (1964). (11B) Kurtz, T. E., Link, R . F., Tukey. J. IV,,Wallace, D. L., Technometrics 6 (2), 95 (1965). (12R) Mandel, J., “Statistical Analysis of Experimental Data,” Interscience, Kew York, N. Y.,1964. (13B) Marsaglia, G., Am. Slat. Assoi.. J . 60 (309) 193 (March 1965). (14B) Myers, R . H., Technometrics 6 , 343 (1964). (15B) Nelson, B. N., A n d . Chem. 3 6 (5), 344R (19G4). (16B) Peach. P., “Quality Control for hlanagement,” Prentice-Hall, Englewood Cliffs, N . J., 1964. (17B) Ratkowsky, D . A,, Brit. C h m . Eng. 9 ( 8 ) , 527 (1964). (18B) Smith, H., Dubey, S. D., I d . Quai. Cont. 21 (2), 64 (1964)
76
INDUSTRIAL AND ENGINEERING CHEMISTRY
f l D ) Aris, R., Nemhauser, G. L., Vrilde. D. J.,B.Z.Ch.E. J. 10, 913 (1964). ( 2 0 ) Balakrishnan, A. V.,Neustadt, L. \V,, “Computing Methods in Optimization Prob!ems,” 327 pp., Academic Press, New York, K , Y . , 1964. (3D) Blakemore, 3. W., Davis: S. H., Jr., eds., Chem. Eng. Progr. Sjmp. Series .Yo. 50 60 (1964). (4D) The Chemical En5ineer (188), CE 112-117, (SIay 1965). (5D) Tinker, E. B., Nikiforuk, P.iY., Can. J . Chem. EnE. 42, 126-131 (1964). (6D) Van Cauwenberghe, A. R., Bri!. Chem. Enp. 9 (12), 833-839 (1964). (7D) Wilde, D. J., CEP 61, 3-0.3: 86-93 (1965). (89) Wilde, D. J., I r u . ENG.CHEM. 57, Bo. 8 : 18-31 (1965). Hill Climbing (Statistical Techniques) (1E) Box, hi. J., CompulerJ. 8 (11, 42 (1965). (2E) Brauder, J. F. R., Cannon, E. J., Dagnall, B. D., Brit. phem. Eng. 9 ( l l ) , 745 (1964). (3E) Glass, H., Cooper, L.: J . ACM 12 (I), 71 (1765). (4E) Klingman, IV. R., Himmelblau, D. hl., Zbid., 1 1 (4), 400 (1964). FUNDAMENTALS 3 , 3 7 3 (1964). (5E) Lee, E. S., IND.ENG.CHCM. (6E) Lowe, C. TV., Trans. Ins!. Chem. Engrs. 42, T334 (1964). (?E) Nelder, J. A., M e a d , R., Computer J . 7 (41, 308 (1965). (8E) Smith, K, H., R u d d , D . F., Chem. Eng. Sci. 19, 403 (1964). (9E) Storey, C., Trans. Inst. Citem. Engr. 42, T345 (1964). Dynamic Programming (1F) Ahn. Y . K., Chen. H. C., Fan, L. T., ‘Ivan, C. G., Con. J.Chem. Enx. 42, 117 (1 964). (2F) Aris, R . , “Discrete Dynamic Programming,” Blaisdell Publishing Co., N e w York, h-. Y., 1964. (3F) Petyluk, F. B., Platonov, V. hi., Girsanov, 1. V., rnlern, Chem. Ertg. 5 , 309 (1965). (4F) Van Canwenberghe, A. R . , Chem. Eng. Sci. 19, 514 (1964). Maximum Principle (Variational Techniques) Denn, M.h l . , IND.ENG.CHEM.FUXDAMENTALS 4, 231 (1965). Denn, 41. M., ?iris, R., A.I.Ch.E. J . 11, 367 (1965). Denn, M,hi., h i s , R., Chem. Eng. Sci. 20, 373 (1965). Denn, 41. M., Ark, R., IND.ENG.CHEM.FUXO.AM€NTALS 4, 7 (1965). Zbid., p. 213. Fan, L . T., \Van& C. S.; “Discrete Maximum Principle,” IViIey, New Ynrk, N. Y . , 1964.
(IG) (2G) (3G) (4G) (5G) (6G)
Kilkson, A., Ibid., 3, 381 (1964). Reed, R. L., Weber, L., Gottfried, B. S., Ibid., 4, 38 (1965). Setty,H. S. N., Berona, N., Prengle, H. W., Ibid., 3,294 (1964). Smith, N. H., Sather, G. A., Chem. Eng. Sci. 20, 15 (1965). Ulrichson, D. L., Schmitz, R . A., IND.ENO.CHEM.FUNDAMENTALS 4 , 2 (1965). Zeman, R . J., Amundson, N. R., Chem. Eng. Sci. 20, 331 (1965).
(7G) Fan, L. T., Wang, C. S., Horn, F., Jackson, R., Denn, M . M., IND.ENG. CHEM. FUNDAMENTALS 4,239 (1965). (8G) Horn, F., Jackson, R., Ibid., p. 110. (9G) Jackson, R., Chcm. Eng. Sa’.20, 405 (1965). (10G) Siebenthal, C. D., Aris, R., Zbid., 19, 729 (1964). (11G) Zbid., p. 747. 3, 384 (1%) Zahradnik, R . L., Archer, D. H., IND.ENG. CHEM. FUNDAMENTALS (1964).
(3P) (4P) (5P) (6P) (7P) (8P)
Miscellaneous
(1Q) Bischoff, K. B., A.Z.Ch.E. J . 11, 351 (1965). ( 2 4 ) Brian, P. L. T., Baddour, R . F., Matiatos, D. C., Zbid., 10,727 (1964). ( 3 4 ) Brian, P. L. T., Beaverstock, M . C., Chem. Eng. Sci. 20,47 (1965). 3, 339 (1964). ( 4 4 ) Brian, P. L. T., Bodman, S., IND.END. CHEM.FUNDAMENTALS (5Q) Friedly, J. C., Petersen, E. E., Chem. Eng. Sci. 19, 783 (1964). (6Q) Gal-Or, B., Resnick, W., Zbid., p . 653. ( 7 4 ) Gunn, D . J., Thomas, W. J., Zbid., 20, 89 (1965). ( 8 4 ) Johnson, A. I., Akehata, T., Can. J. Chem. Eng. 43 (l), 10 (1965). (9Q) Leung, P. K., Quon, D., Ibid., p. 45. (lOQ) . Litt, . M., Serad, G., Chem. Enx. Sci. 19.. 867 (1964). . ( l l Q ) Murphree, E. V., Voorhies, A., Mayer, F. X., IND.END. CHEM.PROCESS. DESIONDEVELOP. 3, 381 (1964). ( 1 2 4 ) Petersen, E. E., Friedly, J . C., DeVogelaere, R. J., Chem. Eng. Sci. 19, 683 (1 964).
(1H) Adler, J., Vortmeyer, D., Chrm. Eng. Sci. 19, 413 (1964). DESIGNDEVELOP. (2H) DiBella, C. W., Stevens, W. F., IND.ENG.CHEM.PROCESS 4, 16 (1965). (3H) Mah, R. S. H., Aris, R., Chem. Eng. Sci. 19, 541 (1964). (4H) Pings, C. J., A.Z.Ch.E. J. 10, 934 (1964). (5H) Thibodeau, R . D., Stevens, FV. F., Ibid,, p. 944. Process H e a t a n d Material Balances (1 J) Nagiev, M . F., “Theory of Recycle Processes in Chemical Engineering,” Macmillan, New York, 1964. (25) Naphtali, L. M., Chrm. Eng. Progr. 60 (9), 70 (1964). (35) Norman, R. L., A.Z.Ch.E. J . 11, 450 (1965). (4J) Sargent, R. VI. H., Westerberg, A. W., Trans. Znsl. Chem. Engrs. 42, T190 (1964).
Reaction with Mass Transfer
Mass Transfer M i l c e l h n e o u l Simulation a n d Design (1K) Austin, L. G., Klimpel, R. R., I N D . ENG. CHEM.FUNDAMENTALS 56 ( l l ) , 18 (1964). (2K) Baddour, R . F., Brian, P. L. T., Logeais, B. A., Eymery, J. P., Chem. Eng. Sci. 20,281 (1965). (3K) Balasubramanian, S. N , , Narsimhan, G., Brit. Chem. Eng. 10 (S), 310 (1965). (4K) Bowen, J. H., Trans. Znst. Chem. Engrs. 42, T259 (1964). (5K) Brian, P. L. T., Baddour, R . F., Eymery, J. P., Chem. Eng. Sci. 20, 297 (1965). (6K) Coughanowr, D. R., Steusholt, E. O., IND. END. CHEM. PROCESS DESIGN DEVELOP.3, 369 (1964). (7K) Friday, J. R., Smith, B. D., A.Z.Ch.E. J . 10, 698 (1964). (8K) Jeffreys, G. V.,Jenson, V. G., Brit. Cbm. Eng. 10 (S), 304 (1965). (9K) Leonard, R . A., Lemlich, R., A.I.Ch.E. J . 11, 18 (1965). (10K) Lichtenstein, I., Chem. Eng. Progr. 60 (12), 64 (1964). (11K) Lindahl, H , A., Ibid., 61 (4), 77 (1965). (12K) Mohr, C. M., A.Z.Ch.E. J . 11, 253 (1965). (13K) Ridgion, J. M., Willmott,A. J., Thewlis, J. H., COmflUter J . 7 (3), 188 (1964). (14K) Ruppel, T. C., Coull, J., IND.ENC.CHEM.FUNDAMENTALS 3,368 (1964). (15K) Sharp, B. M., Smutz, M., I N D .ENG. CHEM.PROCESS DESIGNDEVELOP.4, 49 (1965). (16K) Sharples, K., Glikin, P. G., Warne, R., 7rans. Inst. Chem. Eng. 42, T275 (1964). (17K) Waggoner, R. C., Holland, C. D., A.I.Ch.E. J. 11, 112 (1965). (18K) Zykov, D. D., Maikov, V. P., Nikitin, V. A,, Trebin, A. G., Znlern. Chem. Eng., 4, 492 (1964). Forced Response Testing (1L) (2L) (3L) (4L) (5L) (6L) (7L)
Blum, E. H., A.I.Ch.E. J . 11, 532 (1965). Bruley, D. F., Prados, J. W., Zbid., IO, 612 (1964). Hudson, J. L., Atit, K. M., Bankoff, S. G., Chem. Eng. Sci. 19, 387 (1964). Stainthorp, F. P., Axon, A. G., Zbid., 20, 1 (1965). Zbrd., p. 107. Stermole, F. J., Larson, M. A,, A.Z.Ch.E. J . 10, 688 (1964). 4,155 (1965). Weber, T. W., Harriott, P., IND.ENG.CHEM.FUNDAMENTALS
Residence Time Distribution (Axial Dispersion) ( I M ) Bischoff, K. B., Chem. Erg. Sci. 19, 989 (1964). (2M) Cooney, D. O., Lightfoot, E. N., IND. ENG. CHEM.FUNDAMENTALS 4, 233 (1 965). j3M) Green, D. W., Perry, R . H., Babcock, R. E., A.Z.Ch.E. J . 10,645 (1964). (4M) H a d d a d , A,, Wolf, D., Resnick, W., Can. J . Chem. Eng. 42, 216 (1964). (5M) Hashimoto, I., Deshpande, K. B., Thomas, H . C., IND.ENG. CHEM.FUNDAMENTALS 3, 213 (1964). (6M) Johnson, H. A., M’heelock, T. D., Zbid., p. 201. (7M) Retallick, W. B., Zbid., 4, 88 (1965). (8M) Sherman, W. R., A.Z.Ch.E. J . 10, 8 5 5 (1964). ( 9 M ) Sinclair, C. G., McNaughton, K. J., Chem. Eng. Sci. 20,261 (1965). (10M)Smith, T. G., Dranotl, J. S., TND. END.CHEM.FUNDAMENTALS 3, 195 (1964). Reactor Stability
(1N) Amundson, N . R., Can. J. Chem. Enp. 43 (2), 49 (1965). (2N) Amundson, N. R., Raymond, L. R., A.I.Ch.E. J . 11, 339 (1965). (3N) Berger, J. S., Perlmutter, D. D., Chem. Eng. Sci. 20, 147 (1965). (4N) Berger, J. S., Perlmutter, D . D., 4, 90 (1965). (5N) Beskov, V. S., Kuzin, V. P., Slinko, M . G., Intern. Chem. Eng. 5,201 (1965). (6N) Dassqu, W. J., Wolfgang, G . H., Hydrocarbon Process Petrol. Refiner 43 ( 1 2 ) , 76 (1964). (7N) Gall, C. E., Aris, R., Con. J . Cbem. Eng. 43 ( l ) , 16 (1965). (8N) Goldstein, R . P., Amundson, N. R., Chem. Eng. Sci. 20, 195 (1965). (9N)Gura, I. A,, Perlmutter, D. D., A.1.Ch.E. J . 11,474 (1965). (10N) Lee, R., Amundson, N. R., Can. J . Chem. Eng. 42 (4), 173 (1964). (11N) McGuire, M . L., Lapidus, L., A.Z.Ch.E. J . 11, 85 (1965). (12N) Regenass, W., Aris, R., Chem. Eng. Sci. 20, 60 (2965). Kinetics (1P) Biesenberger, J. A,, A.Z.Ch.E. J. 11, 369 (1965). 4, 150 (ZP) Cowherd, C., Hoelscher, H. E., IND. END. CHEM. FUNDAMENTALS (1 965).
(1R) Ames, W. F., IND.ENG. CHEM.FUNDAMENTALS 4, 72 (1965). (2R) Cullinan, H . T., Jr., Zbid., p. 133. (3R) Griffen, J. R., Coughanowr, D. R., A.I.Ch.E. J . 11, 133 (1965). (4R) Zbid., p. 151. (5R) Ibid., p. 246. (6R) Jameson, G. J., Chem. Eng. Sci. 19, 793 (1964). (7R) King, J. C., IND. END. CHEM.FUNDAMENTALS 4, 125 (1965). (8R) Lochiel, A. C., Calderbank, P. H., Chem. Eng. Sci. 19, 471 (1964). (9R) Masamune, S., Smith, J. M., A.Z.Ch.E. J . 11, 34 (1965). (1OR) Pfefler, R., Happel, J., Zbid., 10, 605 (1964). (11R) Rukenstein, E., Intern. Chem. Eng. 5, 88 (1965). (12R) Sherwood, T. K., Brian, P . L. T., Fisher, R . E., Dresner, L., I N D . E N D . CHEM.FUNDAMENTALS 4, 113 (1965). (13R) Slattery, J. C., Chem. Eng. Sci. 19, 379 (1964). (14R) Zbid., p. 453. 3, 224 (1964). (15R) Stewart, W. E,, Prober, R., IND.ENG. CHEM.FUNDAMENTALS (16R) Toor, H. L., A.I.Ch.E. J . 10, 448 (1964). (17R) Zbid., p. 460. (18R) Wilcox, W. R., IND.ENG. CHEM.FUNDAMENTALS 3, 235 (1964). H e a t Transfer (IS) Berkovskii, B. M., Intern. Chem. Eng. 4, 499 (1964). (25) Bisnovatyi-Kogan, G. S., Zbid., p. 705. (3s) Bulavin, P. E., Kashcheev, V. M., Zbid., 5 , 112 (1965). (4s) Heaps, H . S., Srivastava, R. D., Can. J . Chem. Eng. 42, 120 (1964). (5s) Howell, J. R., Perlmutter, M., A.Z.Ch.E. J . 10, 562 (1964). (6s) Hudson, J. L., Bankoff, S . G., Chem. Eng. Sci. 19, 591 (1964). (7s) Irvine, T. F., Hartnett, J. P., eds., “Advances in H e a t Transfer,” Vol. I, Academic Press, New York, N. Y., 1964. (8s) Katz, D. L., Briggs, D. E., Chem. Eng. Progr. 61 ( l ) , 91 (1965). (9s) Lee, S. M., Gill, W. N., A.I.Ch.E. J . 10, 896 (1964). (10s) Lemlich, R., Steinkamp, J. S., Zbid., p. 445. (11s) O’Brien, N . G., Turner; R. L., Zbzd., 11, 546 (1965). (12s) Pawlek, R., Tien, C., Can. J . Chem. Eng. 42, 222 (1964). Fluid Flow (1T) Acrivos, A,, Shah, M. J., Petersen, E. E., Chem. Eng. Sci. 20, 101 (1965). (2T) Atkinson, B., McKee, R . L., Zbid., 19, 457 (1964). (3T) Biery, J. C., A.I.Ch.E. J. 10, 551 (1964). (4T) Campbell, E. S., Chem. Eng. Sci. 20, 311 (1965). (5T) Coorsin, S., A.Z.Ch.E. J . 10, 870 (1964). (6T) Davis, E. J., Chem. Eng. Sci. 20, 265 (1965). (7T) Dijstelbergen, H . H., Zbid., 19, 853 (1964). (ET) Finlayson, B. A,, Scriven, L. E., Chem. Eng. Sci. 20, 395-404 (1965). (9T) Flunerfelt, R. W., Slattery, J. C., Chem. Eng. Sci. 20, 157-163 (1965). (10T) Gutfinger, C., Shinnar, R., A.Z.Ch.E. J. 10, 631-639 (1964). (11T) Hudson, J. L., Bankoff, S. G., Chem. Eng. Sci. 20, 415 (1965). (12T) Schowalter, W. R., A.Z.Ch.E. J . 11, 99 (1965). (13T) Schwarz, W. H., O’Nan, M., Chem. Eng. Sci. 20, 365 (1965). (14T) Snyder, L. J., Spriggs, T. W., Stewart, W. E., A.2.Ch.E. J. 10, 535 (1964). (15T) Wheeler, J. A,, Wissler, E. H., Ibid., 11, 207 (1965). (16T) White, D. A,, Tallmadge, J. A., Chem. Eng. Sci. 20, 33 (1965). Fluidization Acrivos, A,, Taylor, T. D., Chem. Eng.Sci. 19,445 (1964). Brenner. H., Zbid., p. 519. Ibid., p. 599. Ibid., p. 631. Zbid., p. 703. Kaufman, R. N., Intern. Chem. Eng. 5, 8 (1965). Oliver, D. R., Jenson, V. G., Can. J. Chem. Eng. 42, 191 (1964). (8U)Pigford, R . L., Baron, T., IND.END.CHEM.FUNDAMENTALS 4, 81 (1965). (9U) Ruckenstein, E., Zbid., 3, 260 (1964). (1OU) Ziegler, E. N., Bikoppel, L., Brazelton, W . T., Ibid., p. 324. (11U) Zuber, N., Chem. Eng. Sci. 19, 897 (1964). (1U) (PU) (3U) (4U) (5U) (6U) (7U)
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