Heat exchangers heating curves

Figure 3.26 compares the Nyquist plots for four different cases. The jacket-cooled Nyquist plot is much closer to the critical (—1,0) point. As more area is used in the external heat exchanger, the curves move deeper into the third quadrant, indicating the potential for improved closedloop control. However, the point where they cross the negative real axis moves further to the left. The ultimate gains for the three areas with the external heat exchanger are = 39.8/24.9/15.1 (dimensionless) for areas of 45.2/58.1/ 100 m2. These results are counter-intuitive since we would expect the controllability to improve with increasing area. 

The output includes material and heat balances, exchanger heat curves with various physical properties, compressor performance calculations and any additional output desired through the use of fortran subroutines. These models were used to predict the plant sensitivity. 

The differential heat curves for pyridine adsorption at 473 K on Na,H-Y zeolites with various Na contents (84%, 68%, and 39% levels of proton exchange, respectively) were studied by Chen et al. [55]. Increasing the pro-... 

Another defect of the cell model that we have already mentioned is the neglect of correlations. This appears very clearly in the limit of high densities and low temperatures. In this case we may use a harmonic oscillator cell potential. All molecules perform independent harmonic oscillations in their cells and the result is a specific heat curve of the Einstein type with an exponential decrease for T- 0 instead of a specific heat curve of the Debye type with a characteristic 7 law. Furthermore quantum statistical effects (exchange effects) cannot be introduced in a one-partide model. For this reason the cell model cannot be applied to problems in which such exchange effects play a dominant role (e.g. the X point of liquid He ). However, multiple cell occupations do take account of these correlations and exchange effects. IDgher multiple cell occupations prodde a continuous transition from a one-particle model to the correct 2V-partide model. 

Figure 7.9 The Xp parameter avoids steep slopes on the Fp curves, whereas minimum Fp does not. (Reprinted from Ahmad, Linnhoff, and Smith, Cost Optimum Heat Exchanger Networks II. Targets and Design for Detailed Capital Cost Models, Computers Chem, Engg., 7 751, 1990 with permission from Elsevier Science, Ltd.)...

However, the concentration of impurity in the recycle is varied as shown in Fig. 8.5, so each component cost shows a family of curves when plotted against reactor conversion. Reactor cost (capital only) increases as before with increasing conversion (see Fig. 8.5a). Separation and recycle costs decrease as before (see Fig. 8.56). Figure 8.5c shows the cost of the heat exchanger network and utilities to again decrease with increasing conversion. In Fig. 8.5d, the purge... 

Once the distillation is integrated, then driving forces between the composite curves become smaller. This in turn means the capital/energy tradeofiF for the heat exchanger network should be adjusted accordingly. 

Having decided that no exchanger should have a temperature difference smaller than ATmi, two rules were deduced. If the energy target set by the composite curves (or the problem table algorithm) is to be achieved, there must be no heat transfer across the pinch by... 

Figure B.l shows a pair of composite curves divided into vertical enthalpy intervals. Also shown in Fig. B.l is a heat exchanger network for one of the enthalpy intervals which will satisfy all the heating and cooling requirements. The network shown in Fig. B.l for the enthalpy interval is in grid diagram form. The network arrangement in Fig. B.l has been placed such that each match experiences the ATlm of the interval. The network also uses the minimum number of matches (S - 1). Such a network can be developed for any interval, providing each match within the interval (1) satisfies completely the enthalpy change of a strearh in the interval and (2) achieves the same ratio of CP values as exists between the composite curves (by stream splitting if necessary).

The uppermost curve shows the response from the detector mounted on the heat exchanger... 

If U varies along the tube length or the stream temperature profile is not a smooth curve, then divide the entire tube length into a number of small heat-exchange elements, apply steps (2) through (8) to each element, and sum up the resulting area requitements as follows ... 

Fig. 4. Heat-exchanger effectiveness where numbers on the curves represent the ratio flow (b) counterflow (c) parallel...

A low temperature of approach for the network reduces utihties but raises heat-transfer area requirements. Research has shown that for most of the pubhshed problems, utility costs are normally more important than annualized capital costs. For this reason, AI is chosen eady in the network design as part of the first tier of the solution. The temperature of approach, AI, for the network is not necessarily the same as the minimum temperature of approach, AT that should be used for individual exchangers. This difference is significant for industrial problems in which multiple shells may be necessary to exchange the heat requited for a given match (5). The economic choice for AT depends on whether the process environment is heater- or refrigeration-dependent and on the shape of the composite curves, ie, whether approximately parallel or severely pinched. In cmde-oil units, the range of AI is usually 10—20°C. By definition, AT A AT. The best relative value of these temperature differences depends on the particular problem under study. 

Fig. 5. Simple heat-exchange network where stream C is heated, and streams A and B are cooled (a) schematic (b) temperature—cumulative duty curve...

Optimum Pressure Drop. For most heat exchangers there is an optimum pressure drop. This results from the balance of capital costs against the pumping (or compression) costs. A common prejudice is that the power costs are trivial compared to the capital costs. The total cost curve is fairly flat within 50% of the optimum (see Fig. lb), but the incremental costs of power are roughly one third of those for capital on an aimualized basis. This simple relationship can be extremely useful in quick design checks. 

The shape of the coohng and warming curves in coiled-tube heat exchangers is affected by the pressure drop in both the tube and shell-sides of the heat exchanger. This is particularly important for two-phase flows of multicomponent systems. For example, an increase in pressure drop on the shellside causes boiling to occur at a higher temperature, while an increase in pressure drop on the tubeside will cause condensation to occur at a lower temperature. The net result is both a decrease in the effective temperature difference between the two streams and a requirement for additional heat transfer area to compensate for these losses. 

Equipment Constraints These are the physical constraints for individual pieces of eqiiipment within a unit. Examples of these are flooding and weeping limits in distillation towers, specific pump curves, neat exchanger areas and configurations, and reactor volume limits. Equipment constraints may be imposed when the operation of two pieces of equipment within the unit work together to maintain safety, efficiency, or quahty. An example of this is the temperature constraint imposed on reactors beyond which heat removal is less than heat generation, leading to the potential of a runaway. While this temperature could be interpreted as a process constraint, it is due to the equipment limitations that the temperature is set. 

Fig. 20-11 Potential-time curves of an enamelled container with built-in stainless steel heat exchanger as a function of equalizing resistance, R. Curve 1 container potential in the region of the heat exchanger. Curve 2 heat exchanger potential in the voltage cone of defects in the enamelling. Curve 3 heat exchanger potential outside the voltage cone of the defects.

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