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CHAPTER 14
Evaporation
14.1. INTRODUCTION
Evaporation, a widely used method for the concentration of aqueous solutions, involves the
removal of water from a solution by boiling the liquor in a suitable vessel, an evaporator,
and withdrawing the vapour. If the solution contains dissolved solids, the resulting strong
liquor may become saturated so that crystals are deposited. Liquors which are to be
evaporated may be classified as follows:
(a) Those which can be heated to high temperatures without decomposition, and those
that can be heated only to a temperature of about 330 K.
(b) Those which yield solids on concentration, in which case crystal size and shape
may be important, and those which do not.
(c) Those which, at a given pressure, boil at about the same temperature as water, and
those which have a much higher boiling point.
Evaporation is achieved by adding heat to the solution to vaporise the solvent. The heat
is supplied principally to provide the latent heat of vaporisation, and, by adopting methods
for recovery of heat from the vapour, it has been possible to achieve great economy in heat
utilisation. Whilst the normal heating medium is generally low pressure exhaust steam
from turbines, special heat transfer fluids or flue gases are also used.
The design of an evaporation unit requires the practical application of data on heat
transfer to boiling liquids, together with a realisation of what happens to the liquid during
concentration. In addition to the three main features outlined above, liquors which have
an inverse solubility curve and which are therefore likely to deposit scale on the heating
surface merit special attention.
14.2. HEAT TRANSFER IN EVAPORATORS
14.2.1. Heat transfer coefficients
The rate equation for heat transfer takes the form:
Q = U AT ( 14. 1 )
where: Q is the heat transferred per unit time,
U is the overall coefficient of heat transfer,
A is the heat transfer surface, and
T is the temperature difference between the two streams.
772 CHEMICAL ENGINEERING
In applying this equation to evaporators, there may be some difficulty in deciding the
correct value for the temperature difference because of what is known as the boiling point
rise (BPR). If water is boiled in an evaporator under a given pressure, then the temperature
of the liquor may be determined from steam tables and the temperature difference is readily
calculated. At the same pressure, a solution has a boiling point greater than that of water,
and the difference between its boiling point and that of water is the BPR. For example,
at atmospheric pressure (101.3 kN/m^2 ), a 25 per cent solution of sodium chloride boils at
381 K and shows a BPR of 8 deg K. If steam at 389 K were used to concentrate the salt
solution, the overall temperature difference would not be ( 389 − 373 ) = 16 deg K, but
( 389 − 381 ) = 8 deg K. Such solutions usually require more heat to vaporise unit mass
of water, so that the reduction in capacity of a unit may be considerable. The value of the
BPR cannot be calculated from physical data of the liquor, though D¨uhring’s rule is often
used to find the change in BPR with pressure. If the boiling point of the solution is plotted
against that of water at the same pressure, then a straight line is obtained, as shown for
sodium chloride in Figure 14.1. Thus, if the pressure is fixed, the boiling point of water
is found from steam tables, and the boiling point of the solution from Figure 14.1. The
boiling point rise is much greater with strong electrolytes, such as salt and caustic soda.
Figure 14.1. Boiling point of solutions of sodium chloride as a function of the boiling point of water. D¨uhring lines
Overall heat transfer coefficients for any form of evaporator depend on the value of
the film coefficients on the heating side and for the liquor, together with allowances
for scale deposits and the tube wall. For condensing steam, which is a common heating
medium, film coefficients are approximately 6 kW/m^2 K. There is no entirely satisfactory
774 CHEMICAL ENGINEERING
the nucleate boiling mechanism will partially collapse and portions of the surface will
be exposed to vapour blanketing. In the region of transition boiling CD the average heat
transfer coefficient, and frequently the heat flux, will decrease with increasing temperature
difference, due to the increasing proportion of the surface exposed to vapour. This self-
compensating behaviour is not exhibited if heat flux rather than temperature difference is
the controlling parameter. In this case an attempt to increase the heat flux beyond point C
will cause the nucleate boiling regime to collapse completely, exposing the whole surface
to a vapour film. The inferior heat transfer characteristics of the vapour mean that the
surface temperature must rise to E in order to dissipate the heat. In many instances this
temperature exceeds the melting point of the surface and results can be disastrous. For
obvious reasons the point C is generally known as burnout , although the terms departure
from nucleate boiling (DNB point) and maximum heat flux are in common usage. In the
design of evaporators, a method of predicting the heat transfer coefficient in nucleate
boiling h b, and the maximum heat flux which might be expected before h b begins to
decrease, is of extreme importance. The complexity of the nucleate boiling process has
been the subject of many studies. In a review of the available correlations for nucleate
boiling, W ESTWATER(^1 )^ has presented some fourteen equations. P ALEN and T ABOREK(^2 )
reduced this list to seven and tested these against selected experimental data(^3 ,^4 ). As
a result of this study two equations, those due to MCN ELLY(^5 )^ and G ILMOUR(^6 ), were
selected as the most accurate. Although the modified form of the Gilmour equation is
somewhat more accurate, the relative simplicity of the McNelly equation is attractive and
this equation is given in dimensionless form as:
[
h b d
k
]
[
Cp μ L
k
] 0. 69 [
qd
λμ L
] 0. 69 [
P d
] 0. 31 [
ρ L
ρ v
] 0. 31
The inclusion of the characteristic dimension d is necessary dimensionally, though its
value does not affect the result obtained for h b.
This equation predicts the heat transfer coefficient for a single isolated tube and is not
applicable to tube bundles, for which P ALEN and T ABOREK(^2 )^ showed that the use of this
equation would have resulted in 50–250 per cent underdesign in a number of specific
cases. The reason for this discrepancy may be explained as follows. In the case of a
tube bundle, only the lowest tube in each vertical row is completely irrigated by the
liquid with higher tubes being exposed to liquid–vapour mixtures. This partial vapour
blanketing results in a lower average heat transfer coefficient for tube bundles than the
value given by equation 14.2. In order to calculate these average values of h for a tube
bundle, equations of the form h = Cs h b have been suggested(^2 )^ where the surface factor
Cs is less than 1 and is, as might be expected, a function of the number of tubes in a
vertical row, the pitch of the tubes, and the basic value of h b. The factor Cs can only
be determined by statistical analysis of experimental data and further work is necessary
before it can be predicted from a physical model for the process.
The single tube values for h b have been correlated by equation 14.2, which applies to the
true nucleate boiling regime and takes no account of the factors which eventually lead to
the maximum heat flux being approached. As discussed in Volume 1, Chapter 9, equations
for maximum flux , often a limiting factor in evaporation processes, have been tested by
P ALEN and T ABOREK(^2 ), though the simplified equation of ZUBER(^7 )^ is recommended. This
EVAPORATION 775
takes the form:
qmax =
λρ v
[
σg(ρ L − ρ v )
ρ v^2
] 1 / 4 [
ρ L + ρ v
ρ L
] 1 / 2
where: qmax is the maximum heat flux,
λ is the latent heat of vaporisation,
ρ L is the density of liquid,
ρ v is the density of vapour,
σ is the interfacial tension, and
g is the acceleration due to gravity.
14.2.3. Forced convection boiling
The performance of evaporators operating with forced convection depends very much
on what happens when a liquid is vaporised during flow through a vertical tube. If the
liquid enters the tube below its boiling point, then the first section operates as a normal
heater and the heat transfer rates are determined by the well-established equations for
single phase flow. When the liquid temperature reaches the boiling point corresponding
to the local pressure, boiling commences. At this stage the vapour bubbles are dispersed
in the continuous liquid phase although progressive vaporisation of the liquid gives rise
to a number of characteristic flow patterns which are shown in Figure 14.3. Over the
initial boiling section convective heat transfer occurs with vapour bubbles dispersed in
the liquid. Higher up, the tube bubbles become more numerous and elongated, and bubble
coalescence occurs and eventually the bubbles form slugs which later collapse to give an
annular flow regime in which vapour forms the central core with a thin film of liquid
carried up the wall. In the final stage, dispersed flow with liquid entrainment in the vapour
core occurs. In general, the conditions existing in the tube are those of annular flow. With
further evaporation, the rising liquid film becomes progressively thinner and this thinning,
together with the increasing vapour core velocity, eventually causes breakdown of the
liquid film, leading to dry wall conditions.
For boiling in a tube, there is therefore a contribution from nucleate boiling arising
from bubble formation, together with forced convection boiling due to the high velocity
liquid–vapour mixture. Such a system is inherently complex since certain parameters
influence these two basic processes in different ways.
D ENGLER and A DDOMS(^8 )^ measured heat transfer to water boiling in a 6 m tube and found
that the heat flux increased steadily up the tube as the percentage of vapour increased,
as shown in Figure 14.4. Where convection was predominant, the data were correlated
using the ratio of the observed two-phase heat transfer coefficient (h tp ) to that which
would be obtained had the same total mass flow been all liquid (h L ) as the ordinate. As
discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt ,
the parameter for two-phase turbulent flow developed by L OCKHART and MARTINELLI(^9 ).
The liquid coefficient h L is given by:
h L = 0. 023
[
k
dt
] [
4 W
πdt μ L
] 0. 8 [
Cp μ L
k
] 0. 4
EVAPORATION 777
1 /Xtt is strongly dependent on the mass fraction of vapour y. The density and viscosity
terms give a quantitative correction for the effect of pressure in the absence of nucleate
boiling.
Eighty-five per cent of the purely convective data for two-phase flow were correlated
to within 20 per cent by the expression:
h tp
h L
[
Xtt
] 0. 5
where 0. 25 <
Xtt
Similar results for a range of organic liquids are reported by G UERRIERI and TALTY(^10 ),
though, in this work, h L is based on the point mass flowrate of the unvaporised part of
the stream, that is, W is replaced by W ( 1 − y) in equation 14.4.
One unusual characteristic of equation 14.2 is the dependence of h b on the heat flux q.
The calculation of h b presents no difficulty in situations where the controlling parameter is
the heat flux, as is the case with electrical heating. If a value of q is selected, this together
with a knowledge of operating conditions and the physical properties of the boiling liquid
permits the direct calculation of h b. The surface temperature of the heater may now
be calculated from q and h b and the process is described completely. Considering the
evaluation of a process involving heat transfer from steam condensing at temperature T c to
a liquid boiling at temperature T b, assuming that the condensing coefficient is constant and
specified as h c, and also that the thermal resistance of the intervening wall is negligible,
an initial estimate of the wall temperature T w may be made. The heat flux q for the
condensing film may now be calculated since q = h c (T c − T w ), and the value of h b may
then be determined from equation 14.2 using this value for the heat flux. A heat balance
across the wall tests the accuracy of the estimated value of T w since h c (T c − T w ) must
equal h b (T w − T b ), assuming the intervening wall to be plane. If the error in this heat
balance is unacceptable, further values of T w must be assumed until the heat balance falls
within specified limits of accuracy.
A more refined design procedure would include the estimation of the steam-side coeffi-
cient h c by one of the methods discussed in Volume 1, Chapter 9. Whilst such iterative
procedures are laborious when carried out by hand, they are ideally handled by computers
which enable a rapid evaluation to any degree of accuracy to be easily achieved.
14.2.4. Vacuum operation
With a number of heat sensitive liquids it is necessary to work at low temperatures, and
this is effected by boiling under a vacuum, as indeed is the case in the last unit of a multi-
effect system. Operation under a vacuum increases the temperature difference between
the steam and boiling liquid as shown in Table 14.1 and therefore tends to increase the
heat flux. At the same time, the reduced boiling point usually results in a more viscous
material and a lower film heat transfer coefficient.
For a standard evaporator using steam at 135 kN/m^2 and 380 K with a total heat
content of 2685 kJ/kg, evaporating a liquor such as water, the capacity under vacuum
is ( 101. 3 / 13. 5 ) = 7 .5 times great than that at atmospheric pressure. The advantage in
capacity for the same unit is therefore considerable, though there is no real change in the
consumption of steam in the unit. In practice, the advantages are not as great as this since
778 CHEMICAL ENGINEERING
Table 14.1. Advantages of vacuum operation Atmospheric pressure Vacuum Operation (101.3 kN/m 2 ) (13.5 kN/m 2 ) Boiling point 373 K 325 K Temperature drop to liquor 7 deg K 55 deg K Heat lost in condensate 419 kJ/kg 216 kJ/kg Heat used 2266 kJ/kg 2469 kJ/kg
operation at a lower boiling point reduces the value of the heat transfer coefficient and
additional energy is required to achieve and maintain the vacuum.
14.3. SINGLE-EFFECT EVAPORATORS
Single-effect evaporators are used when the throughput is low, when a cheap supply of
steam is available, when expensive materials of construction must be used as is the case
with corrosive feedstocks and when the vapour is so contaminated so that it cannot be
reused. Single effect units may be operated in batch, semi-batch or continuous batch modes
or continuously. In strict terms, batch units require that filling, evaporating and emptying
are consecutive steps. Such a method of operation is rarely used since it requires that
the vessel is large enough to hold the entire charge of feed and that the heating element
is low enough to ensure that it is not uncovered when the volume is reduced to that
of the product. Semi-batch is the more usual mode of operation in which feed is added
continuously in order to maintain a constant level until the entire charge reaches the
required product density. Batch-operated evaporators often have a continuous feed and,
over at least part of the cycle, a continuous discharge. Often a feed drawn from a storage
tank is returned until the entire contents of the tank reach the desired concentration. The
final evaporation is then achieved by batch operation. In essence, continuous evaporators
have a continuous feed and discharge and concentrations of both feed and discharge
remain constant.
The heat requirements of single-effect continuous evaporators may be obtained from
mass and energy balances. If enthalpy data or heat capacity and heat of solution data are
not available, heat requirements may be taken as the sum of the heat needed to raise the
feed from feed to product temperature and the heat required to evaporate the water. The
latent heat of water is taken at the vapour head pressure instead of the product temper-
ature in order to compensate, at least to some extent, for the heat of solution. If sufficient
vapour pressure data are available for the liquor, methods are available for calculating the
true latent heat from the slope of the D¨uhring line and detailed by O THMER(^11 ). The heat
requirements in batch operation are generally similar to those in continuous evaporation.
Whilst the temperature and sometimes the pressure of the vapour will change during the
course of the cycle which results in changes in enthalpy, since the enthalpy of water
vapour changes only slightly with temperature, the differences between continuous and
batch heat requirements are almost negligible for all practical purposes. The variation of
the fluid properties, such as viscosity and boiling point rise, have a much greater effect
on heat transfer, although these can only be estimated by a step-wise calculation. In
780 CHEMICAL ENGINEERING
The enthalpy of the condensed steam leaving at 352.7 K = 4. 18 ( 352. 7 − 273 ) = 333 .2 kJ/kg
The heat transferred from 1 kg steam = ( 2530 − 333. 2 ) = 2196 .8 kJ/kg
and hence: Steam required = ( 14 , 202 / 2196. 8 ) = 6 .47 kg/s
As the preheating of the solution and the sub-cooling of the condensate represent but a small proportion of the heat load, the temperature driving force may be taken as the difference between the temperatures of the condensing steam and the evaporating water, or:
T = ( 394 − 325 ) = 69 deg K
Thus: Heat transfer area, A = Q/U T (equation 14.1)
= 14 , 202 /( 3 × 69 ) = 68 .6 m 2
14.4. MULTIPLE-EFFECT EVAPORATORS
The single effect evaporator uses rather more than 1 kg of steam to evaporate 1 kg of
water. Three methods have been introduced which enable the performance to be improved,
either by direct reduction in the steam consumption, or by improved energy efficiency of
the whole unit. These are:
(a) Multiple effect operation
(b) Recompression of the vapour rising from the evaporator
(c) Evaporation at low temperatures using a heat pump cycle.
The first of these is considered in this section and (b) and (c) are considered in Section 14.5.
14.4.1. General principles
If an evaporator, fed with steam at 399 K with a total heat of 2714 kJ/kg, is evaporating
water at 373 K, then each kilogram of water vapour produced will have a total heat
content of 2675 kJ. If this heat is allowed to go to waste, by condensing it in a tubular
condenser or by direct contact in a jet condenser for example, such a system makes very
poor use of steam. The vapour produced is, however, suitable for passing to the calandria
of a similar unit, provided the boiling temperature in the second unit is reduced so that
an adequate temperature difference is maintained. This, as discussed in Section 14.2.4,
can be effected by applying a vacuum to the second effect in order to reduce the boiling
point of the liquor. This is the principle reached in the multiple effect systems which were
introduced by Rillieux in about 1830.
For three evaporators arranged as shown in Figure 14.5, in which the temperatures and
pressures are T 1 , T 2 , T 3 , and P 1 , P 2 , P 3 , respectively, in each unit, if the liquor has no
EVAPORATION 781
Figure 14.5. Forward-feed arrangement for a triple-effect evaporator
boiling point rise, then the heat transmitted per unit time across each effect is:
Effect 1 Q 1 = U 1 A 1 T 1 , where T 1 = (T 0 − T 1 ),
Effect 2 Q 2 = U 2 A 2 T 2 , where T 2 = (T 1 − T 2 ),
Effect 3 Q 3 = U 3 A 3 T 3 , where T 3 = (T 2 − T 3 ).
Neglecting the heat required to heat the feed from Tf to T 1 , the heat Q 1 transferred
across where A 1 appears as latent heat in the vapour D 1 and is used as steam in the
second effect, and:
Q 1 = Q 2 = Q 3
So that: U 1 A 1 T 1 = U 2 A 2 T 2 = U 3 A 3 T 3 ( 14. 7 )
If, as is commonly the case, the individual effects are identical, A 1 = A 2 = A 3 , and:
U 1 T 1 = U 2 T 2 = U 3 T 3 ( 14. 8 )
On this analysis, the difference in temperature across each effect is inversely propor-
tional to the heat transfer coefficient. This represents a simplification, however, since:
(a) the heat required to heat the feed from Tf to T 1 has been neglected, and
(b) the liquor passing from stages 1© to 2© carries heat into the second effect, and this
is responsible for some evaporation. This is also the case in the third effect.
The latent heat required to evaporate 1 kg of water in © 1 , is approximately equal to
the heat obtained in condensing 1 kg of steam at T 0.
EVAPORATION 783
Solution 1
A precise theoretical solution is neither necessary nor possible, since during the operation of the evaporator, variations of the liquor levels, for example, will alter the heat transfer coefficients and hence the temperature distribution. It is necessary to assume values of heat transfer coefficients, although, as noted previously, these will only be approximate and will be based on practical experience with similar liquors in similar types of evaporators. Temperature of dry saturated steam at 205 kN/m^2 = 394 K. At a pressure of 13 kN/m^2 (0.13 bar), the boiling point of water is 325 K, so that the total temperature difference &T = ( 394 − 325 ) = 69 deg K.
First Approximation.
Assuming that: U 1 T 1 = U 2 T 2 = U 3 T 3 (equation 14.8)
then substituting the values of U 1 , U 2 and U 3 and &T = 69 deg K gives:
T 1 = 13 deg K, T 2 = 20 deg K, T 3 = 36 deg K
Since the feed is cold, it will be necessary to have a greater value of T 1 than given by this analysis. It will be assumed that T 1 = 18 deg K, T 2 = 17 deg K, T 3 = 34 deg K. If the latent heats are given by λ 0 , λ 1 , λ 2 and λ 3 , then from the Steam Tables in the Appendix:
For steam to 1: T 0 = 394 K and λ 0 = 2200 kJ/kg For steam to 2: T 1 = 376 K and λ 1 = 2249 kJ/kg For steam to 3: T 2 = 359 K and λ 2 = 2293 kJ/kg T 3 = 325 K and λ 3 = 2377 kJ/kg
Assuming that the condensate leaves at the steam temperature, then heat balances across each effect may be made as follows:
Effect 1:
D 0 λ 0 = G (^) F Cp (T 1 − Tf ) + D 1 λ 1 , or 2200 D 0 = 4 × 4. 18 ( 376 − 294 ) + 2249 D 1
Effect 2:
D 1 λ 1 + (G (^) F − D 1 )Cp (T 1 − T 2 ) = D 2 λ 2 , or 2249 D 1 + ( 4 − D 1 ) 4. 18 ( 376 − 359 ) = 2293 D 2
Effect 3:
D 2 λ 2 + (G (^) F − D 1 − D 2 )Cp (T 2 − T 3 ) = D 3 λ 3 ,
or 2293 D 2 + ( 4 − D 1 − D 2 ) 4. 18 ( 359 − 325 ) = 2377 D 3
where G (^) F is the mass flowrate of liquor fed to the system, and Cp is the specific heat capacity of the liquid, which is assumed to be constant. A material balance over the evaporator is:
Solids Liquor Total (kg/s) (kg/s) (kg/s)
Feed 0.4 3.6 4. Product 0.4 0.4 0.
Evaporation 3.2 3.
784 CHEMICAL ENGINEERING
Making use of the previous equations and the fact that (D 1 + D 2 + D 3 ) = 3 .2 kg/s, the evaporation in each unit is, D 1 ≈ 0 .991, D 2 ≈ 1 .065, D 3 ≈ 1 .144, D 0 ≈ 1 .635 kg/s. The area of the surface of each calandria necessary to transmit the necessary heat under the given temperature difference may then be obtained as:
A 1 =
D 0 λ 0 U 1 T 1
( 1. 635 × 2200 )
( 3. 1 × 18 )
= 64 .5 m 2
A 2 =
D 1 λ 1 U 2 T 2
( 0. 991 × 2249 )
( 2. 0 × 17 )
= 65 .6 m 2
A 3 =
D 2 λ 2 U 3 T 3
( 1. 085 × 2293 )
( 1. 1 × 34 )
= 65 .3 m 2
These three calculated areas are approximately equal, so that the temperature differences assumed may be taken as nearly correct. In practice, T 1 would have to be a little larger since A 1 is the smallest area. It may be noted that, on the basis of these calculations, the economy is given by e = ( 3. 2 / 1. 635 ) = 2. 0. Thus, a triple effect unit working under these conditions gives a reduction
in steam utilisation compared with a single effect, though not as large an economy as might be expected.
A simplified method of solving problems of multiple effect evaporation, suggested by
S TORROW(^13 ), is particularly useful for systems with a large number of effects because it
obviates the necessity for solving many simultaneous equations. Essentially the method
depends on obtaining only an approximate value for those heat quantities which are a
small proportion of the whole. Example 14.2A is now solved by this method.
Solution 2
From Figure 14.5 it may be seen that for a feed G (^) F to the first effect, vapour D 1 and liquor (G (^) F − D 1 ) are fed forward to the second effect. In the first effect, steam is condensed partly in order to raise the feed to its boiling point and partly to effect evaporation. In the second effect, further vapour is produced mainly as a result of condensation of the vapour from the first effect and to a smaller extent by flash vaporisation of the concentrated liquor which is fed forward. As the amount of vapour produced by the latter means is generally only comparatively small, this may be estimated only approximately. Similarly, the vapour produced by flash evaporation in the third effect will be a small proportion of the total and only an approximate evaluation is required.
Vapour production by flash vaporisation — approximate evaluation
If the heat transferred in each effect is the same, then:
U 1 T 1 = U 2 T 2 = U 3 T 3 (equation 14.8)
or: 3. 1 T 1 = 2. 0 T 2 = 1. 1 T 3
Steam temperature = 394 K. Temperature in condenser = 325 K.
Thus: &T = ( 394 − 325 ) = 69 deg K
Solving: T 1 = 13 deg K T 2 = 20 deg K T 3 = 36 deg K
These values of T will be valid provided the feed is approximately at its boiling point.
786 CHEMICAL ENGINEERING
and: Q 1 = 2209 + 4. 0 × 4. 18 ( 394 − T 1 − 294 )
= ( 3881 − 16. 72 T 1 ) kW
Applying the heat transfer equations, then:
3881 − 16. 72 T 1 = 3. 1 AT 1 , or AT 1 = ( 1252 − 5. 4 T 1 ) m 2 K
2209 = 2. 0 AT 2 , or AT 2 = 1105 m^2 K
2430 = 1. 1 AT 3 , or AT 3 = 2209 m^2 K
Further: T 1 + T 2 + T 3 = 69 deg K
Values of T 1 , T 2 , T 3 are now chosen by trial and error to give equal values of A in each effect, as follows:
T 1 A 1 T 2 A 2 T 3 A 3
(deg K) (m^2 ) (deg K) (m^2 ) (deg K) (m^2 )
18 64.2 18 61.4 33 66. 19 60.5 17 65.0 33 66. 18 64.2 17.5 63.1 33.5 65. 18 64.2 17 65.0 34 64.
The areas, as calculated in the last line, are approximately equal, so that the assumed temperature differences are acceptable and:
Steam consumption = (Q 1 / 2289 ) = ( 3580 / 2289 ) = 1 .56 kg/s
Economy = ( 3. 2 / 1. 56 ) ≈ 2. 0 kg/kg
The calculation of areas in multiple-effect systems is relatively straightforward for one
or two configurations, although it becomes tedious in the extreme where a wide range
of operating conditions is to be investigated. Fortunately the calculations involved lend
themselves admirably to processing by computer, and in this respect reference should be
made to work such as that by STEWART and B EVERIDGE(^14 ).
14.4.3. Comparison of forward and backward feeds
In the unit considered in Example 14.2A, the weak liquor is fed to effect 1© and flows on
to 2© and then to 3©. The steam is also fed to 1©, and the process is known as forward-
feed since the feed is to the same unit as the steam and travels down the unit in the same
direction as the steam or vapour. It is possible, however, to introduce the weak liquor to
effect © 3 and cause it to travel from © 3 to © 2 to © 1 , whilst the steam and vapour still
travel in the direction of © 1 to © 2 to © 3. This system, shown in Figure 14.6, is known
as backward-feed. A further arrangement for the feed is known as parallel-feed, which is
shown in Figure 14.7. In this case, the liquor is fed to each of the three effects in parallel
although the steam is fed only to the first effect. This arrangement is commonly used in
the concentration of salt solutions, where the deposition of crystals makes it difficult to use
EVAPORATION 787
the standard forward-feed arrangement. The effect of backward-feed on the temperature
distribution, the areas of surface required, and the economy of the unit is of importance,
and Example 14.2A is now considered for this flow arrangement.
Figure 14.6. Backward-feed arrangement for a triple-effect evaporator
Figure 14.7. Parallel-feed arrangement for a triple-effect evaporator
Example 14.2B (Backward-Feed)
Since the dilute liquor is now at the lowest temperature and the concentrated liquor at the highest,
the heat transfer coefficients will not be the same as in the case of forward-feed. In effect © 1 , the
liquor is now much more concentrated than in the former case, and hence U 1 will not be as large as before. Again, on the same argument, U 3 will be larger than before. Although it is unlikely to be exactly the same, U 2 will be taken as being unaltered by the arrangement. Taking values of U 1 = 2 .5, U 2 = 2 .0 and U 3 = 1 .6 kW/m^2 K, the temperature distribution may be determined in the same manner as for forward feed, by taking heat balances across each unit.
Solution 1
In this case, it is more difficult to make a reasonable first estimate of the temperature differences because the liquid temperature is increasing as it passes from effect to effect ( 3 → 2 → 1 ) and
EVAPORATION 789
With backward-feed, as shown in Figure 14.6, the liquid has to be raised to its boiling point as it enters each effect. The heat required to raise the feed to the second effect to its boiling point is:
= 4. 18 ( 4. 0 − 1. 07 )( 350 − 325 )
= 306 .2 kW
The heat required to raise the feed to the first effect to its boiling point is:
= 4. 18 ( 4. 0 − 2 × 1. 07 )( 374 − 350 )
= 186 .6 kW
Assuming a constant value of 2289 kJ/kg for the latent heat in all the stages, the relation between the heat transferred in each effect and in the condenser is:
Q 1 − 186. 6 = Q 2 = (Q 3 + 306. 2 ) = (Qc + 306. 2 + 4 × 4. 18 ( 325 − 294 ))
= Qc + 824. 5 Total evaporation = (Q 2 + Q 3 + Qc )/ 2289 = 3 .2 kg/s
and: Q 2 + (Q 2 − 306. 2 ) + (Q 2 − 824. 5 ) = 7325 kW
Thus: Q 2 = 2819 = AT 2 × 2 .0 kW
Q 3 = 2512 = AT 3 × 1 .6 kW
and: Q 1 = 3006 = AT 1 × 2 .5 kW
or: AT 1 = 1202 m^2 K
AT 2 = 1410 m^2 K
AT 3 = 1570 m^2 K
and: T 1 + T 2 + T 3 = 69 deg K
Thus: T 1 A 1 T 2 A 2 T 3 A 3 (deg K) (m^2 ) (deg K) (m^2 ) (deg K) (m^2 ) 20 60.1 24 58.9 25 62.
The areas are approximately equal and the assumed values of T are therefore acceptable.
Economy =
= 2. 4 kg/kg
On the basis of heat transfer area and thermal considerations, a comparison of the two methods of feed is:
Forward Backward
Total steam used D 0 (kg) 1.635 1. Economy (kg/kg) 2.0 2. Condenser load D 3 (kg) 1.44 0. Heat transfer surface per effect A (m^2 ) 65.1 61.
790 CHEMICAL ENGINEERING
For the conditions of Example 14.2, the backward feed system shows a reduction in steam consumption, an improved economy, a reduction in condenser load, and a small reduction in heat transfer area.
Effect of feed system on economy
In the case of forward feed systems, all the liquor has to be heated from Tf to T 1 by
steam although, in the case of backward feed, the heating of the feed in the last effect
is done with steam that has already evaporated (N − 1 ) times its own mass of water,
assuming ideal conditions. The feed temperature must therefore be regarded as a major
feature in this class of problem. W EBRE(^15 )^ has examined the effect of feed temperature
on the economy and the evaporation in each effect, for the case of a liquor fed at the rate
of 12.5 kg/s to a triple-effect evaporator in which a concentrated product was obtained at
a flowrate of 8.75 kg/s. Neglecting boiling-point rise and working with a fixed vacuum
on the third effect, the curves shown in Figures 14.8 and 14.9 for the three methods of
forward, backward and parallel feed were prepared.
Figure 14.8. Effect of feed temperature on the operation of a triple effect evaporator (a) Forward feed (b) Backward feed
Figure 14.8a illustrates the drop in steam consumption as the feed temperature is
increased with forward feed. It may be seen that, for these conditions, D 1 falls, D 2
remains constant and D 3 rises with increase in the feed temperature Tf. With backward
feed shown in Figure 14.8b, the fall in steam consumption is not so marked and it may be
seen that, whereas D 1 and D 2 fall, the load on the condenser D 3 increases. The results are
conveniently interpreted in Figure 14.9, which shows that the economy increases with Tf
for a forward-feed system to a marked extent, whilst the corresponding increase with the
backward-feed system is relatively small. At low values of Tf , the backward feed gives
the higher economy. At some intermediate value, the two systems give the same value
of economy, whilst for high values of Tf the forward-feed system is more economical
in steam.
These results, whilst showing the influence of Tf on the economy, should not be
interpreted too rigidly, since the values for the coefficients for the two systems and
