The optimization of a heat exchanger design can be viewed at three different levels: 1) the identification of a heat exchanger design that meets the process specifications (described below) at the lowest initial cost; 2) the identification of a heat exchanger design that will meet process specifications and operate most satisfactorily over the lifetime of the plant; 3) the identification of a system of heat exchangers and auxiliary components that will meet plant process specifications with minimum total cost to the process (including utilities and lost production).
The distinctions among these three levels of optimization can be best understood if we list the required and desired criteria of the ideal heat exchanger:
The exchanger must achieve the required changes in the thermal conditions of the process streams within the allowable pressure drops; this is what is meant by "meeting process specifications."
The heat exchanger construction must withstand the mechanical stresses of manufacturing, transport, installation, operation under normal and foreseeable operating conditions (including emergency shut downs) and maintenance, as well as minimizing effects of corrosion and fouling.
The heat exchanger must be maintainable with minimum downtime, including cleaning and repair or replacement of short-lived components such as gaskets and tubes.
The heat exchangers should be flexible enough to meet process specifications under reasonable changes in process conditions, such as normal fouling transients and seasonal and diurnal changes in service stream temperatures.
Subject to the above, the exchanger should cost as little as possible (installed).
The exchanger may need to meet special requirements of length, diameter, weight, or inventory standards, especially in retrofit applications.
Other requirements may apply in special situations, such as manufacturing time, or experience and/or capability of operating and maintenance personnel.
Another vital but often overlooked factor is the uncertainty associated with every step in the exchanger design (and of course characteristic to some degree of every piece of engineering equipment). Palen and Taborek (1969) showed that the best proprietary method for shell and tube exchangers available at the time could only predict overall heat transfer rate within about ±30 percent and shell side pressure drop within about ±40 percent for a large sample of carefully tested exchangers under minimum fouling conditions and using fluids with well-known properties. While there have been some improvements since, the uncertainties for heat exchangers in normal plant service are probably no better and may well be worse than these values.
The design of a heat exchanger that meets process requirements at lowest first cost (Level 1 above) explicitly satisfies criteria 1 and 5 (though transport and installation cost differences are sometimes ignored) and implicitly those aspects of criterion 2 that are governed by the ASME Unfired Pressure Vessel Code or other applicable codes. Criteria 3, 6, and 7 may be met if the purchaser has specified a priori those features which he deems important in each case; these specifications operate as initial conditions or constraints on the optimization process. Unfortunately, personnel doing the specification and bid evaluation for heat exchangers all too often lack the plant operating experience or input to include these requirements.
Optimization at this level can be handled by various case-study methods, with the objective function being the cost of the heat exchanger. A cost estimation program is required. If the vendor is doing the optimization, the cost program can be quite precise; if the customer is doing the optimization, the cost program can represent at best only an estimate of what the quoted cost will be because of variations in manufacturing capabilities (and therefore costs) among manufacturers.
Palen et al. (1974) demonstrated the use of the M. J. Box Complex Method (1965) in the optimization of shell and tube heat exchangers, using a rating program somewhat simpler than the best Stream Analysis Method available at that time. Even with the computing power available (CDC6400), the optimization program for a realistic case ran in under 10 seconds. With present computing capabilities, there is no need to use anything less than the best available rating method. It is also true that very little improvement (<1 percent) in objective function was realized in the last half of the runs, though at the end, the design was rationalized to standard dimensions (e.g., tube diameter was set to 3/4 inch, rather than 0.7 inch.). Given the irremovable uncertainties in the basic rating method, a wide range of plausible solutions would fall in the uncertainty band of the objective function.
The second level of optimization (as described in the first paragraph) requires consideration of all of the criteria listed. Concentration upon first cost as the objective function may result in selection of basic design features that preclude maximum operational efficiency (e.g., fixed tube sheet vs. removable bundle in an application where mechanical cleaning of the shell side will result in a cleaner heat exchanger and longer/higher efficiency operation between cleanings than with chemical cleaning only). Unfortunately, many of these considerations can only be expressed qualitatively and do not lend themselves to decision making solely on quantitative computation. Both lack of real-world operational experience and time pressure on the designer militate against proper weight being given to these often substantial cost factors.
Criterion 4 can only be considered in the global context of the entire process design and economic and market forecasting, requiring input from a variety of company personnel and necessarily involving high degrees of uncertainty. But it is only in these circumstances that one can move to Level 3 optimization. Examples of heat exchanger systems where very high economic value (even the technical feasibility of the process) ride on this level of optimization include crude oil preheat trains and feed-effluent heat recovery systems for chemical reactors. In another application, central station heating/cooling systems are moving towards this need.
Great progress has been made in this area, notably through the use of "Pinch Technology", now increasingly referred to as "Pinch Analysis" [Linnhoff (1994)], to synthesize heat exchanger networks and integrate them with the rest of the process system. A number of organizations offer computer programs to retrofit existing systems or to design new ones using this approach. (See also Process Integration.)
Heat recovery (or more precisely, efficient use of heat within the process, primarily by using hot process streams to heat cold process streams within the plant) originally provided the incentive for this kind of optimization, with less attention paid to capital cost. Recently, attention and capability have expanded to include capital minimization and waste stream reduction.
These are powerful computational techniques, but they still must be used with great care to consider the nonquantitative factors (e.g., maldistribution of a stream among parallel paths in an exchanger can render it incapable of meeting a very close approach temperature difference) and the uncertainties in the basic design methods and especially in future operating conditions. Some investigations have been done on the effect of uncertainties on system design using Monte Carlo methods [Al-Zakri and Bell (1981); Uddin and Bell (1988)]. Until these approaches can be fully developed and integrated into practical design guidance, large-scale systems need to incorporate redundancy and resilience: stand-by capability, trim heating and cooling, and flexible piping layouts with adequate instrumentation and control.
Ai-Zakri, A. S. and Bell, K. J. (1981) Heat transfer: estimating performance when uncertainties exist, Chem. Eng. Prog. 77, 7, 39.
Box, M. J. (1965) A new method of constrained optimization and a comparison with other methods, Computer J. 8, 42.
Linnhoff, B. (1994) Use pinch analysis to knock down capital costs and emissions, Chem. Eng, Prog. 90, No. 8, 32.
Palen, J. W. and Taborek, J. (1969) Solution of shell side flow pressure drop and heat transfer by stream analysis method, CEP Symp. Series No. 92, 65, 53.
Palen, J. W., Cham, T. P., and Taborek, J. (1974) Optimization of shell and tube heat exchangers by case study method, AIChE Symp. Series No. 138, 70.
Uddin, A. K. M. Mahbub and Bell, K. J. (1988) Effect of uncertainties upon the performance of a feed-effluent heat exchanger system, Heat Trans. Eng, 9, No. 4, 63.