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transfer units (HTU = temperature rise of the process fluid divided by the mean temperature difference). As indicated, whenever unequal passes are used, the correction factor calls for a considerable increase in area. This is particularly important when unequal flow conditions are handled. If high and low flow rates are to be handled, the necessary velocities must be maintained with the low fluid flow rate by using an increased number of passes. Although the plate unit is most efficient when the flow ratio between two fluids is in the range of 0.7-1.4, other ratios can be handled with unequal passes. This is done, however, at the expense of the LMTD factor.

The issue of how to specify a fouling resistance for a plate heat exchanger is difficult to resolve. Manufacturers generally specify 5% excess HTU for low fouling duties, 10% for moderate fouling, and 15-20% excess for high fouling. The allowed excess surface almost always is sufficient even though in many cases, it represents a low absolute value of fouling in terms of (Btu/h • ft2 • °F)_1. If a high fouling resistance is specified, extra plates have to be added, usually in parallel. This results in lower velocities, more extreme temperatures during startup, and the probability of higher fouling rates. Because of the narrow plate gaps and, in particular, because of the small entrance and exit flow areas, fouling in a plate usually causes more problems by the increase in pressure drop and/or the lowering of flow rates than by causing large reductions in heat-transfer performance. Increasing the number of plates does not increase the gap or throat area, and a plate unit sometimes can foul more quickly when oversurfaced.

The customer who does not have considerable experience with both the process and the plate heat exchanger should allow the equipment manufacturer to advise on fouling and the minimum velocity at which the exchanger should operate.

Laminar Flow

The other area suitable for the plate heat exchanger is that of laminar flow heat transfer. It has been pointed out already that the Paraflow can save surface by handling fairly viscous fluids in turbulent flow because the critical Rey nolds number is low. Once the viscosity exceeds 20-50 cP, however, most plate heat exchanger designs fall into the viscous flow range. Considering only Newtonian fluids since most chemical duties fall into this category, in laminar ducted flow the flow can be said to be one of three types: (1) fully developed velocity and temperature profiles (ie, the limiting Nusselt case), (2) fully developed velocity profile with developing temperature profile (ie, the thermal entrance region), or (3) the simultaneous development of the velocity and temperature profiles.

The first type is of interest only when considering fluids of low Prandtl number, and this seldom exists with normal plate heat-exchanger applications. The third is relevant only for fluids such as gases that have a Prandtl number of about 1. Therefore, consider type 2.

As a rough guide for plate heat exchangers, the ratio of the hydrodynamic entrance length to the corresponding thermal entrance length is given by

Plate the heat transfer for laminar flow follows the

Dittus—Boelter equation in this form: Nu _

where L is the nominal plate length, c is the constant for each plate (usually in the range 1.86-4.50), and x is the exponent varying from 0.1 to 0.2 depending on plate type. For pressure loss, the friction factor can be taken as f = a/Re where a is a constant characteristic of the plate.

It can be seen that for heat transfer, the plate heat exchanger is ideal because the value of d is small and the film coefficients are proportional to d~2m. Unfortunately, however, the pressure loss is proportional to d~* and the pressure drop is sacrificed to achieve the heat transfer.

From these correlations, it is possible to calculate the film heat-transfer coefficient and the pressure loss for laminar flow. This coefficient combined with the metal coeffi cient and the calculated coefficient for the service fluid together with the fouling resistance then are used to produce the overall coefficient. As with turbulent flow, an allowance has to be made to use the LMTD to allow for either end effect correction for small plate packs and/or concurrency caused by having concurrent flow in some passages. This is particularly important for laminar flow since these exchangers usually have more than one pass.

Beyond Liquid-Liquid

Over many years, APV has built up considerable experience in the design and use of Paraflow plate heat exchangers for process applications that fall outside the normal turbulent flow that is common in chemical operations. The Paraflow, for example, can be used in laminar flow duties, for the evaporation of fluids with relatively high viscosities, for cooling various gases, and for condensing applications where pressure drop parameters are not overly restrictive.

Condensing

One of the most important heat-transfer processes if possible, is the condensation of vapors—a duty that often is carried out on the shell side of a tubular exchanger but is entirely feasible in the plate-type unit. Generally speaking, the determining factor is pressure drop.

For those condensing duties where permissible pressure loss is less than one pound per square inch, there is no doubt but that the tubular unit is most efficient. Under such pressure drop conditions, only a portion of the length of a Paraflow plate would be used and substantial surface area would be wasted. However, when less restrictive pressure drops are available the plate heat exchanger becomes an excellent condenser since very high heat-transfer coefficients are obtained and the condensation can be carried out in a single pass across the plate.

The pressure drop of condensing steam in the passages of plate heat exchangers has been investigated experimen

Steam condensation rate (Ib/h per passage)

Figure 18. Steam-side pressure drop for R5.

Steam condensation rate (Ib/h per passage)

Figure 18. Steam-side pressure drop for R5.

tally for a series of different Paraflow plates. As indicated in Figure 18, which provides data for a typical unit, the drop obtained is plotted against steam flow rate per passage for a number of inlet steam pressures.

It is interesting to note that for a set steam flow rate and a given duty, the steam pressure drop is higher when the liquid and steam are in countercurrent rather than cocurrent flow. This is due to differences in temperature profile.

Figure 19 shows that for equal duties and flows, the temperature difference for countercurrent flow is lower at the steam inlet than at the outlet with most of the steam condensation taking place in the lower half of the plate. The reverse holds true for cocurrent flow. In this case, most of the steam condenses in the top half of the plate, the mean vapor velocity is lower, and a reduction in pressure drop of 10-40% occurs. This difference in pressure drop becomes lower for duties where the final approach temperature between the steam and process fluid becomes larger.

The pressure drop of condensing steam therefore is a function of steam flow rate, pressure, and temperature difference. Since the steam pressure drop affects the saturation temperature of the steam, the mean temperature difference in turn becomes a function of steam pressure drop. This is particularly important when vacuum steam is being used since small changes in steam pressure can give significant changes in the temperature at which the steam condenses.

By using an APV computer program and a Martinelli— Lockhart-type approach to the problem, it has been possible to correlate the pressure loss to a high degree of accuracy. Figure 20 cites a typical performance of a steam heated Series R4 Paraflow. From this experimental run during which the exchanger was equipped with only a small number of plates, it can be seen that for a 4-5-psi pressure drop and above, the plate is completely used. Below that figure, however, there is insufficient pressure drop available to fully use the entire plate and part of the surface therefore is flooded to reduce the pressure loss. At only one psi allowable pressure drop, only 60% of the plate is used for heat transfer, which is not particularly economic.

Figure 19. Temperature profile during condensation of steam.

Available pressure loss, psi

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