Human judgment
machine thoroughness = best decision
HEAT EXCHANGER DESIGN BY COMPUTER M.
SPECIAL FEATURES OF T H I S COMPUTER PROGRAM
-A
minimum of input information i s given.
The com-
puter completes the data (by heat balances etc.1 where required. This section of the program is composed of almost 2000 machine instructions.
-It i s possible to impose very arbitrary conditions within which designs may be required. For example, tube lengths may be smaller than, larger than, or between any limits. Tube-side pass configuration may be limited t o single pass, or to an odd o r even number of passes. Design may b e restricted to a special configuration o f units in series and parallel, or all configurations may be considered.
-The
minimum price unit i s given by the program.
Each price i s cotnputed on the basis of a detailed design which takes into consideration practical details of construction.
-In addition to the minimum-price unit, the program develops alternate designs. These may have such fringe benefits as better delivery dates, and reduction in total number of units. Cheaper designs just outside the design limits of pressure drops and fouling factors can be investigated automatically. The engineer chooses between these units.
-Many built-in error-checking routines ensure that given data are consistent and adequate. Wherever possible, errors are corrected automatically and comments are made.
T. T A Y Y A B K H A N
organization, proper arrangement of the computer program-these are all important iii heat exchanger design. Through better program organization, the computer program we use optimizes more directly and exhaustively than any other we know. It handles a very wide variety of heat exchange problems. The computer provides the engineer with a range of feasible designs. Final selection can then be based on both the straightforward engineering aspects and other less tangible factors. A much larger portion of the total work should go into organizing the program than into programming the computations themselves. Program organization includes many factors. Output and input schemes should be convenient and useful. Design should be restricted to exchangers that can be manufactured. The computer should work within practical limitations of the process (such as space and piping requirements). Also, it should be possible to make major changes in calculation procedures in the future. In comparison, writing the part of the program which instructs the computer to perform the mathematics is fairly easy-even for very complex formulas. The various programs described in the literature perform practically the same engineering calculations. They differ from each other in the special restrictions that can be placed on the design, the input to the program, and the organization of the program itself. Some programs have been arranged in subroutines so that changes in computational procedures can be made readily. Some programs check input data more thoroughly than others, spotting errors in keypunching or
Proper
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OBTAIN THE DESIGN Wrm PRICEOPTIMUM CONFIGURATION FOR NUMBER OF MFfLEs. PASSES ON
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mTHE PRICE SUCH THAT THE DESIGN IS WORTH
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RECORDING? COMPARE WIW RECORDED OOOD THE T A M OF ETERS AND TU1 DEEN WAUS1 ~
:OD WE DESIGN IN THE INTERNU NOW OF ME COMPUTER. ELLMINATE 30RER DESIGNS FROM THE PREIUSLY RECORDED D U M AND APD S U ADDITK)NU "coo(y1 DESlG THERE ANY STANDUD ORSWELT CONFIGU rTloW OF WE€ BUNDLES, N DE C . UDE PASSES, LFFLES, ETC. THAT WOULD MEET D E W RESTRIG ONS FOR THE SHELL DIAMETERS AND TUBE NGTHS UNDER CONSIDERATION FROM THIS
W A K E THE PRICE OF THE SMULEST UNIT WilH IS NUMBER OF SHELLS. IS If LOWER T W THE
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RlNT OUT THE OOOD DESKiNS OBTAINED.
6 THE PROBLEM BEEN EF€Al€D MII EVERY tollU n O N OF ADJUmNG FOULING FACTORS AND
I;k mnputer conridars all cmnbinrrtionr of dl enginamkg variablar, dikiwdu hbsc not m'thin the spacial nshicfions,and tasts each of those ra&n&/orplmundlhit and f d i f gf a d w . Or& of testing 26
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
diminales many combinationr rapidly. Then the remaining cmnbinotwnr, each an optimm wirhin its class. is submitted to the mn ' mwho makes (1Jna1 choice
mishaps in card handling. An engineer can prepare the input for some programs more easily than others. 'The amount of information (such as physical properties) that the program fills in automatically differs. The layout of the output on the paper and the written titles and explanations are different. Therefore, the output from some programs is more readily understood than others. Programs have been written for different computing machines. Special requirements of the machines, such as memory limitations, have at times dictated the structure and the flexibility of the programs, Another way in which programs differ is in the degree and the type of optimization that is carried out. The number of variables over which the design is optimized varies. The detail in which the entire design is completed in the process of optimization is not the same in the various programs. For example, some programs consider mechanical features such as nozzles and pass partitions. The effect of these considerations can be important. There may be an advantage in using longer tubes and smaller shell diameters to improve the heat transfer coefficient. However, the higher velocities may require very large nozzles. This may be very expensive or impossible, and the chosen design may not be a true optimum. We found that for sales engineering, the nature of problems encountered not only justifies but necessitates the work required to organize a very flexible and thorough computer program. Detailed designing and completely automatic pricing make sense since actual quotations must be given. Customer requirements vary widely, and it must be possible to find an optimum design between very special restrictions. And an engineer must be able to use the program readily, even in the face of very special customer conditions. The program both designs and rates heat exchangers. I t is limited to shell and tube heat exchangers with cross-flow baffles. I n design problems, details of mechanical construction and pricing are built into the program, limiting it to one type of exchanger. The program described here is set up for Karbate impervious graphite heat exchangers. The principles can be applied to any other type of exchanger. Heat Transfer Calculations
The various correlations and equations for the heat transfer calculations are well known. For most calculations, we used the equations given by Kern (4). Specific heat and thermal conductivity of fluids are considered to be constant. Viscosities of the fluids, however, are assumed to be exponential functions of temperature. Values of viscosity at two temperatures
AUTHOR M . T . Tayvabkhan is an Assistant Manager of Electronic Data Processing in the Management Services department of Union Carbide Corp. He wishes to acknowledge the assistance of J . A . M r a r in setting ufi this program. Some of the ideas are based on the work of N.J.Bowlden.
are given as data to the program, and viscosities are computed as required. In calculating pressure drops and heat transfer coefficients, the program takes into consideration the effects of the fluids entering or leaving the unit, and effect of viscosity differences arising from temperature gradients in the boundary layers. Rating Heat Exchangers
In rating problems, an exchanger design is given to the program and some description of the flow stream is given. There are six crucial process variables-inlet temperature, outlet temperature, and flow rate for each of the two streams, one on the tube side and one on the shell side. If all six of these are given, the program checks consistency of the energy balance and computes the fouling factor. In case of an inadequate size exchanger, this would be a negative number. If any five are given, the sixth is determined by energy balance and a fouling factor is computed. If any four are given, the program sets up the necessary trial and error schemes of calculations and obtains a solution that satisfies simultaneously the energy balance and the heat transfer calculations. In the latter, a desired value of fouling factor is given to the program. Optimizing the Design
In design problems the required process variables are given in the input. Design restrictions such as maximum allowable velocities, maximum allowable pressure drops, and the minimum desired fouling factor are also given. The computer program then obtains the best combination of the values of the following engineering variables : -Number of streams in parallel -Number of heat exchangers in series in each stream -Diameter of the shell of each exchanger. Total number of tubes is directly related to this variable. -Length of the tubes in each exchanger -Number of passes on the tube side in each exchanger -Number of baffles in each shell -Baffle cut expressed as per cent of the cross sectional area of the shell that is available for baffled cross flow The program is capable of considering tube diameter as a variable for optimization. However, in present manufacturing practices of Karbate exchangers, a tube having a 7/a inch inside diameter and a 11/4 inch outside diameter is preferred. If a job requires more than one heat exchanger, it is assumed that they are identical in size and internal details. I t is also assumed that each parallel stream has the same number of exchangers in a series. These assumptions are consistent with common practice and make for standardization and ease of maintenance. The criterion for selection is the price of a single unit (or train of units) that meets all the special requirements and performs the necessary heat transfer job. The price depends on the entire combination of all the VOL. 5 4
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.i28
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Optimum design can be determined only by calculating a complete, detailed cost. A greatly simpltjfed case of heat exchanger design involves only two uariables-shell diameter and tube length-the least-cost combination of which is desired f o r a heat transfer job. Let there be two controlling constraints: thepressure drop in the tube side should not exceed lOp.s.i., and the minimum fouling factor designed should be 0.02. The cost is assumed to be directly proportional to the heat transfer area. Any point on the graph represents a combination of shell diameter and tube length. The only combinations that are manufactured are shown as small circles. Three sets of leuel curues haue been obtained from process engineering calculations for our example. They are families of lines denoting constant
pressure drops, constant fouling factor, and constant values of total cost. Thus the heat exchnnger represented by point A, a unit with shell diameter of 28 inches and tube length of 8 feet, would produe a pressure drop of 7p.s.i., would give a designed fouling factor oJ0.029,and wouldcost about 82oOO. All combinations of shell diameter and tube lengths represented by the colored region above the curve BCD would satisfy the pressure drop and fouling factor conditions. Point C exactly meets the conditions and it is the point of lowest cost. At this point, shell diameter is 16.8 inches, and tube length is 9 feet, neither of which are dimensions of practical manufacture. Designs represented by points E or F can be manufactured, but, the cheapest is at F, euen though E is closer to C.
variables mentioned above. All must be considered, since unusual situations may arise. For example, in comparing two exchangers with the same number of tubes, a unit with longer tubes may be cheaper than a unit with shorter tubes. The exchanger with longer tubes may require fewer passes and fewer cross baffles on the shell side. The savings made in reduced costs of consmcdng pass partitions and baffles may more than balance the added cost of longer tubes. Consequently, it is necessary to cany out complete process calculations on all feasible designs before final selection can be made.
is the discrete nature of the values that the variables can assume. For example, tubes and shells are manufactured in only certain definite sizes. Therefore a complete search of all manufactured combinations is p o s s i b l e and in fact is necessary if the best solution is to be found. However, the design variables are considered to be continuous in the calculations of heat transfer and fluid flow used to determine pressure drops and fouling factors. Consequently, a design taking maximum advantage of the available pressure drops, with minimum heat transfer area, would often have fractional values of the design variables. For actual use, practical values clok to such a design would be chosen. Where there are many variables, there may be many combinations near this design. Some sort of a procedure searching all possible combinationsbecomes necessary.
Practical Desian
An interesting feature of the problem of equipment design optimization, common to many practical problems, 28
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Such a situation is shown in the figure on page 28, where a detailed cost must be worked out to decide between the feasible designs E and F. I t is worth noting that in this example, the problem arises in spite of a very simple cost function. I n general, the actual cost function is quite arbitrary and irregular. This, compounded with the greater number of variables in a n actual problem, forces one to make a fairly complete search of all exchangers which meet the design restrictions. There are further possibilities. Referring to the graph, designs represented by points G, H, and J all cost less than the chosen designs E and F. Design J meets the fouling factor criterion, but the pressure drop is a trifle too large. Design H has the lowest cost and would be accepted if the fouling factor restriction could be relaxed. Such designs should be investigated, since in practice these limitations often have additional latitudes. This is performed by the program by automatically changing the limits and rerunning the optimization. The amounts by which each limit should be changed is indicated by a n engineer and fed to the computer. The exchanger of lowest price may not always be the hest choice. Compared to a train of two or three small off-the-shelf units, a somewhat more expensive single custom built unit may be preferred, since the number of exchangers affects piping and instrumentation costs. I n the interest of standardization and more rapid delivery, units assembled from parts carried on the shelf may be preferred to a custom-built unit, if additional cost is minor. The computer program considers these two extra benefits by making economic choices according to the following rules. The factors of 70 and 15% are arbitrarily chosen to ensure that no advantageous design is rejected : -Of any two designs, the cheaper design is selected if the number of shells is the same for both designs, and if both of the exchangers are either standard units or specially designed units. -If two designs have the same number of shells but one consists of standard units and the other consists of specially designed units, the computer will let the engineer make the decision if cost of the standard unit is between 100 and 115y0 of the cost of the custom unit. -If two designs have a n unequal number of shells, since fewer shells are preferred, the computer will again pass the decision to the engineer if the design with the greater number of shells is between 70 and lOOyo of the cost of the unit with the smaller number.
The analytical and programming time required is roughly estimated as one and a half man years from conception through numerical analysis and programming to a n operational system. As a n indication of the versatility of the program, it is interesting to note that no program changes have been made during the last year of use. Most design problems require 30 to 60 seconds of 7090 computer time. Rating problems require only 2 to 10 seconds. Designs involving large amounts of heat duty generally have many feasible combinations of engineering variables and they require more computer time than those involving small heat duty. Unusually small design problems have been done in 5 to 10 seconds of computer time. Unusually large problems have required as much as 10 minutes.
Computer Oriented Information
REFERENCES
The program is written in FORTRAN language for an IBM 7090 computer. There about 2500 FORTRAN statements in the program broken up into 50 subroutines. They have generated about 15,000 IBM 7090 instructions. Additional storage locations are taken up in the memory for such data as standard tables of manufacturing practices and constants for computing prices.
(1) Githens, R. E., Jr., Chem. Eng. 65, No. 5, 143 (1958). (2) Higgins, E. J., Kellet, J. W., Ung, L. T., IND.ENG.CHEM. 50, 712 (1958). (3) Houtby, D. K., Chem. Proc. Eng. and Atomic World 42, 442 (1961). (4) . , Kern, D. Q., - “Process Heat Transfer,” McGraw-Hill, New York, 1950. (5) Peiser, A. M., ReJning Engr. 29, No. 11 (1957). (6) Taborek, J. J., Chem. Eng. Progr. 55, No. 10, 45 (1959).
Output information
Five different types of output are produced by the program : -Comments arising from checking input data, such as : “Error in identification spotted a t card 9. Skip to next problem.” “Given temperatures inconsistent.”
