Cap 18 Evaporation

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Evaporation

Text of Cap 18 Evaporation

  • 2003 by CRC Press LLC

    625

    18

    Evaporation

    18.1 Introduction

    Evaporation is a unit operation that consists of the elimination of water ofa fluid food by means of vaporization or boiling. Several foods are obtainedas aqueous solutions and, in order to facilitate their preservation and trans-port, they are concentrated during a water elimination stage. This elimina-tion can be performed in different ways, although evaporation is one of themost used methods. The equipment used to remove this water from the foodproduct is called an evaporator.

    An evaporator consists mainly of two chambers, one for condensation andanother for evaporation. Steam condenses in the condensation chamber, giv-ing off the latent heat of condensation, which is contained in the evaporationchamber. The evaporated water leaves the evaporation chamber at boilingtemperature, obtaining at the same time a stream of concentrated solution.

    V

    while that of food is

    w

    A

    , obtaining a stream of vapor

    V

    and another of concen-trated solution (or liquid)

    w

    C

    . The removed vapor

    V

    is driven to the condenserwhere it condenses. It is important to note that many food solutions are heatsensitive and can be adversely affected if exposed to high temperatures. Forthis reason it is convenient to operate under vacuum conditions in the evapo-ration chamber, which causes the boiling temperature of the aqueous solutionto decrease, and the fluid to be affected by heat to a lesser extent. If it is desiredto operate under vacuum, a vacuum pump is needed. Also, a barometric col-umn to compensate for the pressure difference with the exterior is needed inthe condenser to condense the vapor released in the evaporation chamber.

    The capacity of the evaporator (

    V

    ) is defined as the amount of waterevaporated from the food per unit time. The consumption (

    w

    V

    ) is the amountof heating steam consumed per unit time. The economy (

    E

    ) is the amountof solvent evaporated per unit of heating steam:

    (18.1) E

    VwV

    = =

    capacity consumption

    TX69299 ch01 frame.book Page 625 Wednesday, September 4, 2002 2:13 PM

    Figure 18.1 shows a scheme of an evaporator. The mass flow of steam is w ,

  • 2003 by CRC Press LLC

    626

    Unit Operations in Food Engineering

    18.2 Heat Transfer in Evaporators

    Figure 18.2 presents a scheme of a single-effect evaporator including thedifferent variables of each stream. The condensation chamber is fed with asaturated vapor stream

    w

    V

    that has a temperature

    T

    and an enthalpy

    H

    w

    .Vapor condenses and the only heat given off is that of condensation, so astream

    w

    V

    of liquid water leaves this chamber at the condensation temper-ature

    T

    , and with enthalpy

    h

    w

    , which corresponds to the enthalpy of waterat the boiling point. The condensation heat flow

    Q

    is transferred through theexchange area of the evaporator to the food stream in the evaporation chamber.

    FIGURE 18.1

    Scheme of the installation of an evaporator.

    FIGURE 18.2

    Simple evaporator.

    Vapor

    Barometric column

    Condenser

    Evaporator

    wa

    ww

    wV

    wc

    Pt

    Vapor

    wA

    wV

    wCtA.hA

    T, H W

    wVT, h W

    Q

    t, H V

    tC, h C

    .

    TX69299 ch01 frame.book Page 626 Wednesday, September 4, 2002 2:13 PM

  • 2003 by CRC Press LLC

    Evaporation

    627

    A stream

    w

    A

    is fed into the evaporation chamber at a temperature

    t

    A

    withenthalpy

    h

    A

    . Due to the heat released by the condensed vapor (

    Q

    ), a concen-trated stream

    w

    C

    is obtained, with temperature

    t

    C

    and enthalpy

    h

    C

    . Also, avapor stream

    V

    is obtained, at a temperature

    T

    V

    and with enthalpy

    H

    V

    . Notethat the temperatures of the concentrated and vapor streams are equal andcorrespond to the boiling temperature of the concentrated solution thatleaves this chamber.

    The energy balances that should be performed are:

    Condensation chamber: (18.2)

    Evaporation chamber: (18.3)

    Exchange area: (18.4)

    where

    U

    is the overall heat transfer coefficient and

    A

    is the area of theevaporator.

    18.2.1 Enthalpies of Vapors and Liquids

    In the notation used here, the enthalpies per unit mass of vapor streams willbe designated by

    H

    , and those of liquid by

    h

    .The enthalpy per unit mass of vapor at a temperature

    T

    can be expressedas the summation of the enthalpy at saturation (

    H

    sat

    ) plus the integral betweenthe boiling temperature

    T

    b

    and the enthalpy at

    T

    of the specific heat times

    dT

    :

    (18.5)

    The term

    H

    SAT

    is the enthalpy of the vapor at its condensation temperature.The specific heat of the water vapor (

    C

    P

    )

    V

    depends on the pressure, althoughits value is close to 2.1 kJ/(kg C).

    Since enthalpy is a function, the state of the enthalpy of a liquid shouldbe expressed as a function of a reference temperature. If this temperature is

    t

    *

    and the liquid is at a temperature

    t

    , it is obtained that:

    (18.6)

    Tables used for the calculation of these enthalpies can be found in theliterature. Generally, the reference temperature is the freezing temperatureof water (0C).

    w H w h Q V w V w

    = +

    w h Q w h V HA A C C V + = +

    Q U A T U A T t = = ( )

    H H C dTSAT P VTe

    T

    = + ( )

    h C dT C t tP P*

    t*

    t

    = = ( )

    TX69299 ch01 frame.book Page 627 Wednesday, September 4, 2002 2:13 PM

  • 2003 by CRC Press LLC

    628

    Unit Operations in Food Engineering

    The enthalpy of the liquid at its boiling temperature is called

    h

    SAT

    . Thelatent heat of condensation or evaporation (

    ) will be the difference betweenthe saturation enthalpies of the vapor and the liquid, since the evaporationand condensation temperatures are the same.

    (18.7)

    The numerical values of the enthalpies of saturated vapor and of the liquidcan be obtained from saturated water vapor tables, and the latent heat ofcondensation can be calculated. However, this value can be obtained in anapproximate way from the equation of Regnault as follows:

    (18.8)

    where

    T

    is in C.The enthalpies of the liquid streams, food (

    h

    A

    ) and concentrated (

    h

    C

    ), thatappear in Equation 18.3 are expressed as:

    (18.9)

    (18.10)

    The enthalpy of the vapor in Equation 18.3 will be different if the solutionbeing concentrated presents or does not present a boiling point rise. In caseof no increase in the boiling point of the concentrated solution, the enthalpyof the vapor will be the sum of the saturated liquid plus the latent heat:

    (18.11)

    where

    t

    b

    is the boiling temperature of the solution.In case of an increase in the boiling point, the boiling temperature of the

    solution (

    t

    e

    ) will be greater than that of pure water (

    t

    ), so the vapor enthalpywill be:

    (18.12)

    In order to simplify the calculations, the reference temperature usuallyselected is the boiling point of pure water,

    t

    * =

    t

    b

    , which makes the enthalpyof the vapor leaving the evaporation chamber coincide with the latent heat

    = H hSAT SAT

    = 2538 2 91. T kJ kg

    h C dT C t tA P A P A A*

    t

    tA

    *

    = ( ) = ( ) ( ) h C dT C t tC P C P C C

    *

    t*

    tC

    = ( ) = ( ) ( )

    H C t tV SAT P b

    *( ) = ( )+

    H C t t C t tV P b

    *P V b

    = ( ) ( ) ( )+ +

    TX69299 ch01 frame.book Page 628 Wednesday, September 4, 2002 2:13 PM

  • 2003 by CRC Press LLC

    Evaporation

    629

    of condensation if there is no increase in the boiling point. Also, the enthalpyof the concentrated stream will be annulled, since

    t

    C

    =

    t

    b

    =

    t

    .

    18.2.2 Boiling Point Rise

    Water boils at a fixed temperature whenever the pressure remains constant.If the pressure varies, the boiling point varies too. For aqueous solutions,the boiling temperature depends not only on pressure, but also on theamount of solute contained, in such a way that the presence of the solutecauses the boiling temperature to increase. The determination of the boilingpoint rise presented by food solutions is very important for the calculationof evaporators. For this reason, expressions and means to calculate theincrease in boiling temperature will be given next.

    For diluted solutions that comply with the law of Raoult, the boiling pointincrement can be calculated by the expression:

    (18.13)

    where

    M

    S

    is the molecular weight of the solute,

    X

    is the ratio of kg solute/kgsolvent, and

    Ke

    is the so-called boiling constant of the solvent.For aqueous solutions the following equation can be used:

    (18.14)

    where

    C

    is the molal concentration of the solute.A general expression that allows the calculation of the boiling point rise

    considering an ideal solution is the equation:

    (18.15)

    If the solutions are diluted, the following equation can be used:

    (18.16)

    In these two last equations,

    X

    w