Heat transfer surface and performance ratio

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The schematic arrangement in Fig. 2.4 shows the principle of flash distillation. Concentrated sea water or brine is heated to just below its boiling point at pressure jPmax and temperature imax in the brine heater. The brine then flows to the flash chamber which is at pressure Pl which is less than Pmax. The pressure reduction causes flashing or instantaneous evaporation to take place until the brine is in thermodynamic equilibrium with the vapour conditions at Pt 7\ (where t denotes brine temperature, and T denotes vapour temperatures, ib, is the re-cycle brine temperature at stage 1 inlet, t-m is the re-cycle brine temperature at stage 1 exit i.e. the brine heater inlet temperature).

The flashing vapour is condensed and gives up its latent heat to the inlet sea water in the condenser tubes. The latent heat of evaporation is thus recovered and

Heat transfer surface and performance ratio 19

re-used. As the flash chamber runs at steady state the evaporation rate is constant and heat flux Qx to the condenser tubes is constant, Now, as we have seen the stage heat transfer coefficient U is a constant, then if a low energy input into the brine heater is desired fin must be as near as practicably possible to imax, so that the

Brine heater Evaporator

Fig. 2.4. Flash distillation (brine heater and first stage).

Brine heater Evaporator

Fig. 2.4. Flash distillation (brine heater and first stage).

heating steam has to provide a small temperature difference (imax — fjn) only. In order to do this, the brine inlet temperature to the feed heater must approach the vapour temperature Tx in the first flash chamber. Inserting some typical values on these temperatures we have, using the vapour temperature Tl as datum, that the inlet temperature difference between brine and vapour, i.e. (7^ - fbi) can be 4.16°C (7.5°F) and the terminal or minimum temperature difference between brine and vapour, i.e. (7\ — ijn) is 2.78°C (5°F), i.e. the brine temperature in the condenser tubes has increased by 1.39°C (2.5°F) from the recovery of the latent heat of condensation of the vapour.

The logarithmic mean temperature difference for a condenser is calculated as follows (see Kern [2] for details).

Ariog= tin~tbi - 138

What this means is shown in the temperature plot of Fig. 2.5. The varying temperature difference may now be replaced by the logarithmic mean temperature difference of 3.4°C. These figures apply to an MSF plant with a performance ratio of 11 and a flash range of 55.5°C (100°F), i.e. the brine flashes over this total temperature range in 40 stages each with a 1.39°C (2.5°F) temperature drop. Performance ratio is defined as the number of pounds of distillate produced per pound of steam used in the brine heater, i.e. pounds distillate produced per 1 000 Btu steam consumed (kg product per 2.33 Xl06 J steam consumed to keep comparison identical with the literature, where L is commonly taken as 1 000 Btu/lb.)

Comparable figures for a plant with a performance ratio of 5.5 are

with corresponding logarithmic mean temperature difference of 6.2°C (11.2°F). Thus the plant with the lower performance ratio will have a 45 per cent reduction in heat transfer area compared with the high performance ratio plant (given that all other factors are the same for both plants). This illustrates the relationship between energy costs and capital costs. A high performance ratio plant would be specified for a location where fuel is expensive whereas the low performance ratio plant would be used where fuel is very cheap, e.g. in Kuwait.

Distance

Fig. 2.5. Typical temperature profiles for brine and vapour streams in a heat recovery stage of an MSF plant (symbols used refer to first stage of the plant).

Distance

Fig. 2.5. Typical temperature profiles for brine and vapour streams in a heat recovery stage of an MSF plant (symbols used refer to first stage of the plant).

Many other factors interplay in distillation plant heat transfer considerations especially in those plants where a high performance ratio is required and low mean effective temperature differences are employed. The major source of temperature reduction or thermal energy degradation, as this is what a temperature reduction implies, are boiling point elevation and pressure drop losses respectively.

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