The submerged coil evaporator

A single-effect submerged coil evaporator as shown in Fig. 2.8 (p. 23) and consists of a shell, a steam-heating coil, a condenser cooled by cold sea water, part of which is bled off for the evaporator feed. Provision is made for distillate removal and brine blowdown to ensure that the evaporation brine concentration does not rise unduly.

In operation, the heating steam caused evaporation to take place from the brine surface. The vapour, which is pure water, condenses on the condenser tubes giving up its latent heat of evaporation. Part of the heated coolant is bled off and used as the evaporator feed and in this way some small energy economy is achieved as the feed requires less heating before evaporation commences. However, with this arrangement the steam consumption required to produce 1 000 kg water is roughly 2.33 x 109 Joules at 100°C (or 1 000 gal water requires 107 Btu at 212°F). Thus if boiler fuel were to cost £13.5 per ton, then the actual energy cost at the heating coil (neglecting boiler capital and maintenance costs) would be 50 p/109 J (50 p/106 Btu). Thus 1 m3 distillate would cost £1.15 (1 000 gal would cost £5) with this single-effect arrangement based on energy consumption alone.

The incentives for multiple-effect operation can be clearly seen. If an evaporator could be designed with a performance ratio of 10 (i.e. 10 lb distillate per 1 000 Btu input) the energy cost per m3 would be only £0.115 (1 000 gal would be only 50 p). Multiple-effect distillation was introduced with this aim in mind. If the single-effect evaporator of Fig. 2.8 is extended as shown in Fig. 4.1 to say three effects and the vapour from the first effect is led to the heating coil of the second effect and similarly that from the second to the third, then in theory, unit mass of vapour from the first effect will produce unit mass of vapour in the second effect which in turn produces unit mass of vapour in the third effect. Thus for the consumption of unit mass of steam from the boiler, a product rate three times that amount may be produced in a triple-effect evaporator - note that there is an implied relationship between number of effects and performance ratio in multiple-effect distillation, a point we shall return to later. In practice losses are such that 2.5 kg of distillate would be produced by the consumption of 1 kg saturated steam. For a multiple-effect system to operate, the pressure (and thus the corresponding saturation temperature) in the second effect is less than that of the first one so that the latent heat of vaporisation from the first effect may be effectively transferred through the heating coil of the second and succeeding effect. The practical restrictions of multiple-effect pool boiling systems, such as the one shown in Fig.

4.1, were such that six effects with a performance ratio of 4.9 was the maximum achieved - when VTÊ was developed to its current technical proficiency this restriction was removed as discussed in Chapter 5. The major design difference between multiple-effect evaporation and multi-stage flash distillation is that the

1 st effect

1 st effect

■Saline water Vapour Distillate

Distillate

Raw water

Fig. 4.1. Multiple-effect pool boiling distillation.

■Saline water Vapour Distillate

Distillate

Raw water

Fig. 4.1. Multiple-effect pool boiling distillation.

performance ratio is dependent on the number of effects in the former, but this does not necessarily apply in the latter, i.e. in MSF the number of stages ('effect' is not used in multi-stage flash terminology) is not a direct function of the performance ratio. Because of this it is perfectly possible, and in fact quite common, to obtain performance ratios of greater than 10 in multi-stage flash plants which was not possible with multiple-effect pool boiling systems.

Multi-stage flash principles

A single-stage flash plant as shown in Fig. 2.4 (p. 19) operates as follows. Sea water is heated in the brine heater to just below the saturation temperature imax at fmax. It then enters the stage at reduced pressure P1. The reduction in pressure causes the heated feed to 'flash' or commence evaporation to obtain thermal equilibrium with stage saturation conditions dictated by Pi. The reject brine is discharged and fresh sea water used as feed in this simple system.

The vapour formed in flashing condenses on the condenser or heat recovery tubes thus heating the incoming feed, to temperature tin. The brine heater supplies the remainder of the energy required to raise the feed temperature to fmax before flashing commences. The fraction of brine which flashes in the first stage is given by

The assumption made in equation (4.1) above is that thermal equilibrium is attained in the stage - in practice this may not be so.

Now the single-stage flash plant in Fig. 2.4 (p. 19) can be extended to n stages as shown in simplified form in Fig. 4.2. The pressures in each stage are successively reduced until vapour volume, equilibrium and heat rejection considerations fix the minimum temperature of the last (nth) stage. For most purposes Tn is c. 38 43.5°C (100°F). Thus to increase the fraction of flashed vapour imax must be increased. However, imax is prescribed by CaS04 formation and is for most plants 122°C (250°F) and 93°C (200°F) for acid or polyphosphate-dosed plants, respectively.

As discussed in Chapter 2 the fraction of the brine stream which can be flashed is restricted to 0.1 to 0.15, i.e. to produce the desired rate of distillate requires a minimum brine circulation rate in the range 10-6.6 times the product rate. Thus a

A/WAr

A/WAr

Brine heater fmax

Evaporator

Raw water

Fig. 4.2. Multi-stage flash distillation.

Brine heater fmax

Evaporator

Raw water

Fig. 4.2. Multi-stage flash distillation.

flash plant requires substantially larger brine flow rates than an equivalent multiple-effect plant. Not only that, other things being equal the mean temperature difference available for overall heat transfer in a flash stage is lower than the corresponding temperature difference in a submerged coil evaporator. In the flash evaporator the heat recovery raises the temperature of the brine in the condenser tubes which means a temperature rise in the circulating brine which in turns means a reduced temperature difference for heat transfer.

In the submerged coil evaporator the boiling brine temperature is a constant in each effect and so is the steam temperature; thus the temperature differences for heat transfer is constant. The superior thermodynamics of flash plants (over those of multiple-effect pool boiling distillation) could only be realised when the technology became available to allow the economic insertion of a large number of stage walls in the plant. A multiple-effect plant with 6 effects will have a performance ratio slightly less than 5, whereas a flash plant can have a performance ratio of 5 and use 12 or more stages. The thermodynamic characteristics of the multi-stage flash plant are illustrated by the following analysis based on a two-stage

Brine out

Fig. 4.3. Schematic two-stage flash evaporator.

Brine out

Fig. 4.3. Schematic two-stage flash evaporator.

flash plant, shown in Fig. 4.3, with the flash chambers schematically separated from the respective condensing sections.

For a given stage vapour temperature T\ in flash chamber 1, the approach temperature of the brine leaving the condenser or heat recovery portion of stage 1 can be changed by varying the stage heat transfer surface. Increasing the surface reduces the terminal temperature difference (Tl - /¡n) by increasing f;n the brine temperature at inlet to the brine heater. Thus there will be an increase in the performance ratio proportional to

'max 'in where (rmax - fdis) scales the total product output, and (rmax - tm) scales the thermal energy input to the brine heater.

A plot of temperature versus heat transfer surface areas can be drawn for the two-stage plant as shown in Fig. 4.4. The straight sloping line gives the profile for the feed in the brine heater and heat recovery sections. The stepped line gives the temperature profile for the flashing brine stream. The effect of varying heat transfer surface is shown. For a reduced heat transfer surface, temperature fin is reduced and therefore there is a decrease in the performance ratio as scaled by equation (4.2). Note that even using an infinitely large heat transfer surface in each stage, the performance ratio cannot be increased above a certain maximum value which in the limit approaches the number of heat recovery stages. Thus for the two-stage flash plant in Fig. 4.3 the maximum theoretically attainable performance ratio is 2.

As long as the same design methods were considered and the same number of stages used as in multiple effect pool boiling, then the submerged coil units were superior. The flash evaporator rose to prominence when shell designs evolved that

Heat recovery section

Heat input section

1st flash chamber

2nd flash chamber

Heat input section

1st flash chamber

2nd flash chamber f,

Total heat transfer surface

Fig. 4.4. Schematic temperature diagram for two-stage flash evaporator.

Total heat transfer surface

Fig. 4.4. Schematic temperature diagram for two-stage flash evaporator.

enabled much larger number of stages to be economically built than the submerged coil evaporator design. Thus an MSF plant with a performance ratio of 10 can be expected to have at least 20 stages (this is the basis of an MSF patent by Silver, [4] in that the number of stages is greater than twice the performance ratio). In practice a plant with a performance of 10 may have up to 30 to 35 heat recovery stages plus an additional 3 or 4 for heat rejection.

Stage number effect

Infinite number of stages

The effect of number of stages, is best analysed by considering the theoretical limit of an infinite number. Figure 4.5 shows a flow sheet with an infinite number of stages and brine recirculation employed as is customary for the evaporator feed. The corresponding temperature distribution for this arrangement is shown in Fig. 4.6. The heat rejection is a separate design entity and is obtained by circulating a separate cooling water supply through the last few stages, condenser tubes. The reject section tube surface area is dictated by the sea-water inlet temperature and flow rate as discussed in heat exchanger design in Chapter 2.

The feed M{ enters the bottom chamber and after blowdown Md takes place at temperature ijis t0 maintain a constant concentration on the plant the recirculated brine Mr is returned at stage j + 1 where the brine temperature ti+ ! is apposite for heat transfer purposes. The important temperature profiles in Fig. 4.6 are the heavy black lines, the lower for the feed progression through the heat recovery stages and the upper for the flashing brine in both recovery and rejection stages.

Heat in

Heat input section

Heat recovery section

Condenser; heat rejection section (j stages)

fin

Vapour

Flash chambers

Recirculated brine

-1 Mr ldis

Blow down

Condensate returned to boilers

Feed

Fig. 4.5. Schematic diagram of a flash evaporator with an infinite number of stages.

Now, the brine and distillate are both allowed to flash in cascading down the stages and as the combined heat capacity of the flashing brine plus distillate streams equals that of the recirculating brine then the temperature rise of the recirculating brine equals the temperature drop of the flashing stream.

Fig. 4.6. Schematic temperature diagram for a flash evaporator with an infinite number of stages.

The performance ratio R is then given by lb prod _ GOmax - ¿dis) 1 000

The brine circulation ratio r is given by _MT_ L

and the total distillate made may be calculated in kg (lb) with appropriate units used in (4.5) and (4.6)

Now the designer can choose R independent of the number of stages. In doing so the heat transfer surface in the heat recovery sections changes thus:

(where (imax - tm) is the mean effective temperature difference for an infinite number of stages), i.e.

i.e. for a given set of conditions the recovery stage heat transfer surface area is directly proportional to the performance ratio — this is the same type of relationship as that for multiple effect evaporators with the significant difference that the number of stages can vary.

However, in all known plants the number of stages is strictly limited and the effect of a finite number is to reduce the mean effective temperature difference available for the maximum of (imax - rin) and thus a larger stage heat recovery surface is required to obtain the same performance ratio — the stepped line in Fig. 4.6 shows the effect of a finite number of stages.

Finite number of stages

The effect of a finite number of stages on the stage heat transfer surface is important and therefore a simplified derivation of the standard relationship for surface area in terms of performance ratio, number of stages and operating temperature range quoted in most technical papers is worthwhile:

For a finite number of stages the temperature difference (?max - iin) depends on the minimum temperature difference Afm in each of the stages of the heat recovery sections and on the total number of stages («), i.e. the temperature difference ('max _ 'in) has the following components: (neglecting boiling point elevation)

flash range

where it is assumed that there is an equal stage temperature drop.

The logarithmic mean temperature difference in each stage is now given by (from the relationships developed in Chapter 2) — where Atm is the minimum stage temperature difference and (rmax — tm) the greatest.

log ('max - 'in)/A'm . , 'max — 'dis from (4.4) (imax - iin) =

from (4.9) Atm = After rearrangement,

Now the area required per unit mass of distillate made per unit time is (e.g. ft2/lb/h or m2/kg/h)

This neglects the effects of boiling-point elevation but does show the interrelationships of the design variables. Thus the effect of a finite number of stages may be readily obtained. One point to note is that to design a plant for a very high performance ratio can lead to high costs and an optimum has to be struck between capital and energy components.

Some of the parameters in equation (4.12) are fixed at the outset, i.e. U will be circa 2 830 W/m2 °C (450-500 Btu/ft2/h °F), and the flash range (imax - rdis) will be fixed by the method of scale control employed. Figure 4.7 shows a plot of equation (4.12) for L = 2.33 x 106 5/kg(l 000 Btu/lb), {7=2 830 W/m2 °C (500 Btu/h/ft2 °F) and (rmax - fdis) = 55° and 83°C (100° and 150°F) respectively. The effect of increasing the flash range results in a substantial reduction in heat transfer surface.

Number of stages (n)

Fig. 4.7. Heat recovery surface area as functions of performance ratio, number of stages and flash range.

Number of stages (n)

Fig. 4.7. Heat recovery surface area as functions of performance ratio, number of stages and flash range.

The designer then has to determine the evaporator performance ratio and the number of stages to be employed. Relationships such as equation (4.12) are useful in preliminary assessment of heat transfer surface in terms of the proposed number of stages. Other factors will enter that are not amenable to mathematical relationships, e.g. if the heat recovery tube lengths exceed a certain size a very sharp cost increase results; this may restrict n. As in all things the art of design is not a cut-and-dried process and allowances have to be made for losses which arise in practice.

Losses - necessary and otherwise

There are a variety of losses in an MSF plant that cannot be entirely eliminated. As discussed in Chapter 2 a drop in logarithmic mean temperature difference for heat exchange usually results.

The principal losses in this class are boiling point elevation and pressure drop loss. The sum total of these effects alone is estimated at 1.39°C (2.5°F) temperature reduction which has major implications for the heat transfer area required per stage. The effect is particularly marked in high performance ratio plants where logarithmic mean temperature differences are of order 3.9°C (7°F).

Other losses include poor venting resulting in vapour blanketing of the heat exchange surfaces which lowers the effective heat transfer coefficient and results in a reduced performance ratio. Tube fouling also falls into this class and can also significantly affect performance ratio. The significance of a lowered design performance ratio is not negligible, e.g. a 4 546 m3/day (1 m.g.d.) plant designed for a performance ratio of 8 which in practice turns out to be 7 will incur an excess steam consumption of 0.816 kg (1.8 x 106 lb) steam per day. The cost of this excess steam consumption based on a fuel oil cost of £13.5 per ton is an extra £900 per day.

Equilibration

So far the condensation heat recovery process has been considered as the principal factor in plant design. However, distillation is a two-stage process involving both evaporation and condensation. The evaporation or flashing process characteristics can also have marked effects on plant performance ratio.

The governing characteristic of the flashing process is the achievement of complete equilibration. It is a subject which has received scant attention in the technical press as the design measures taken are kept within the individual manufacturer's ambience.

Basically, equilibration is the thermal equilibrium of the flashing brine stream with its surroundings in the flash chamber. Thus, if a stream of flashing liquid is at temperature fin at entry to the flash chamber where the pressure is Ps, the flashing stream will eventually come to equilibrium at temperature t's where t's = T^ + ABPe corresponding to Ps. The attainment of equilibrium is not instantaneous and it is not unusual for the brine stream to leave the stage at an intermediate temperature t where t's < t < tin. The equilibration achieved is characterised by a parameter termed the fraction of equilibration ( j3). where

The flashing process is principally one of bubble growth within the mass of the liquid and has been analysed by Porteous and Muncaster. [5] The temperature of the vapour in the bubble (except in the early nucleation stage) may be taken as constant at the saturation value Ts. The driving temperature difference for evaporation across an element of surface may therefore be taken as (i - Ts) whether the element represents part of a plane or dispersed interface. Thus we may write for the rate of change of t with time (0):

dt -hSdd (t - Ts) c h is a suitably defined overall heat transfer coefficient assumed constant throughout the process.

Let û = mean bulk fluid velocity (constant)

L = flash chamber length dL

therefore dd=Y (4.15)

Substituting (4.13) and (4.15) into (4.14) yields for ts « t's dB hS

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