Number of Heat Exchange Units

In this context, the points correspond to process and utility streams, and the lines to heat exchange matches between the heat sources and heat sinks. 

From graph theory, the main result needed in the present context is that the number of independent loops for a graph is given by1  

S = number of streams including utilities (points in graph theory) 

Equation 17.2 put in words states that the minimum number of units required is one less than the number of streams (including utility streams). 

This is a useful result since, if the network is assumed to be loop-free and has a single component, the minimum number of units can be predicted simply by knowing the number of streams. If the problem does not have a pinch, then Equation 17.2 predicts the minimum number of units. If the problem has a pinch, then Equation 17.2 is applied on each side of the pinch separately2  

To understand the minimum number of matches or units in a heat exchanger network, some basic results oigraph theory can be used. A graph is any collection of points in which some pairs of points are 

A path is a sequence of distinct lines which are connected to each other. For example, in Fig. 7.1a, AECGD is a path. A graph forms a single component if any two points are joined by a path. Thus Fig. 7.16 has two components and Fig. 7.1a has only one. 

A loop is a path which begins and ends at the same point, such as CGDHC in Fig. 7.1a. If two loops have a line in common, they can be linked to form a third loop by deleting the common line. In Fig. 7.1a, for example, BGCEB and CGDHC can be linked to give BGDHCEB. In this case, this last loop is said to be dependent on the other two. 

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Step (i) was proved in Appendix A of Floudas et al. (1986), and hence the minimum number of matches predicted by the MILP transshipment model can always be represented with an equal number of heat exchanger units in a feasible HEN network. 

MEUmax maximum number of heat-exchange units... 

The temperature-interval method can also be used to produce grand composite curves, which show the variation of heat supply and demand in a system. These diagrams enable engineers to minimize the expensive utilities, network area, and number of heat exchanger units. 

LMTD = log mean temperature difference, °F M = mass flow rate, Ib/hr Ntu = number of heat transfer units, dimensionless N = number tubes/row in direction of air flow n = number tubes/row, per ft of exchanger width, 1 /ft Q = total exchanger heat load (duty), Btu/hr R = = heat capacity ratio, dimensionless... 

The hydrogenated gaseous stream enters the cold section, where it is passed through a number of heat exchangers and separators. A portion of the liquid stream from unit 10 is used as the recycle stream. Hydrogen is separated as a gaseous stream in unit 12. 

Each stream superstructure has one input, one output, a number of heat exchangers equal to the matches that involve the particular stream, and all possible connections from the input to the units, between each pair of units, and from the units to the output. To illustrate such a representation, we will consider the following example that has... 

A number of heat-exchanger surfaces do not fall into the categories discussed in the foregoing sections. Most notable are the compact exchangers which achieve a very high surface area per unit volume. These exchangers are most... 

The term Exc is the exergy consumed by the overall processes. We may combine the pinch analysis with the exergy analysis to reduce the number of unit operations and thermodynamic parameters, leading to an optimum operation. The minimum number of heat exchangers needed is obtained by... 

The number of heat transfer units Na on any given side of the heat exchanger is... 

The ineffectiveness of a heat exchanger and the associated heat flow to the cold end as given by equation (12) are normally associated with the complete heat exchanger. The number of heat transfer units for the complete heat exchanger is given by... 

Solutions for the heat-transfer problem, which arises in the use of packed beds as direct-contact recuperative heat exchangers, were presented by Furnas in 1930. The parameter Njj is the number of heat-transfer units. For heat transfer, the dimensionless time t is the heat capacity of the gas times the amount of gas that has passed through the bed divided by the total bed capacity. For Nu = co, the breakthrough curve of T /Tq vs. t would be a vertical line at t = 1.0, just as for mass transfer. The defining equations are... 

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