8'4 PHASE CHANGE OPERATIONS

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8.4 PHASE CHANGE OPERATIONS
Phase changes such as fusion and vaporization
are usually accompanied by large changes in
internal energy and enthalpy, and heat duties in
phase change operations consequently tend to be
substantial.
8.4a Latent Heats

• Latent heat of the phase change the enthalpy
  change
• associated with the transition of a substance
  from one
• phase to another phase at constant T and P.

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• Heat of fusion (or heat of melting).
  is
• the specific enthalpy difference between the
  solid
• and liquid forms of a species at T and P.
• 2. Heat of vaporization. is the
  specific
• enthalpy difference between the liquid and
  vapor
• forms of a species at T and P.

• Tabulated values of these two latent heats, such
  as
• those in Table B.1 and on pp. 2-151 through
  2-160
• of Perrys Chemical Engineers Handbook,
  usually
• apply to a substance at its normal melting or
  boiling
• point that is, at a pressure of 1 atm. The
  quantities
• are referred to as standard heats of fusion and
• vaporization.

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• The latent heat of a phase change may vary
  consider-
• ably with the temperature at which the change
  occurs
• but hardly varies with the pressure at the
  transition
• point. For example

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Example 8.4-1 Heat of Vaporization At what rate
in kilowatts must heat be transferred to a
liquid stream of methanol at its normal boiling
point to generate 1500 g/min of saturated
methanol vapor?
From Table B.1, for CH3OH
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• Phases changes often occur at temperatures other
  than
• the temperature for which the latent heat is
  tabulated.
• When faced with this situation, you must select
  a hypo-
• thetical process path that permits the available
  data to
• be used.

EXAMPLE 8.4-2 Vaporization and Heating One
hundred g-moles per hour of liquid n-hexane at
25? and 7 bar is vaporized and heated to 300? at
constant pressure. Neglecting the effect of
pressure on enthalpy, estimate the rate at which
heat must be applied.
n-C6H14(v,300?,7bars)
n-C6H14(l,25?,7bars)
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n-C6H14(v,300?,7bars)
n-C6H14(l,25?,7bars)
True path
n-C6H14(l,25?,1.013bars)
n-C6H14(l,69?,1.013bars)
n-C6H14(v,69?,1.013bars)
n-C6H14(v,69?,7bars)
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(Table B.1 ? SG0.659 ? ?? 0.659kg/l 659kg/m3)
(Table B.2 Cp0.2163 kJ/moloC)
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(Table B.1)
(Table B.2 )
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8.4b Estimation and Correlation of Latent Heats

• A simple formula for estimating a standard heat
  of
• vaporization ( at the normal boiling
  point) is
• Troutons rule (30 accuracy)

Nonpolar liquids
Water, low MW alcohols
Tb the normal boiling point
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• Another formula that provides roughly 2
  accuracy
• is Chens equation

Tb the normal boiling point (in K) Tc the
critical temperature (in K) Pc the critical
pressure (atm)
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• may be estimated from vapor pressure data
  by
• using the Clapeyron equation

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• A useful approximation for estimating at
  T2 from
• a known value at T1 is Watsons correlation

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• A formula for approximating a standard heat of
  fusion is

(Metallic elements)
(Inorganic elements)
(Organic elements)
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8.4c Energy Balances on Processes Involving
Phase Changes
EXAMPLE 8.4-4 Partial Vaporization of a
Mixture An equimolar liquid mixture of benzene
(B) and toluene (T) at 10? is fed continuously to
a vessel in which the mixture is heated to 50?.
The liquid products is 40 mole B, and the vapor
product is 68.4 mole B. How much heat must be
transferred to the mixture per mole of feed?
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Total Mass Balance
Benzene Balance
The energy balance
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• An enthalpy table for the process appears as
  follows

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(1)
(2)
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(3)
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(4)
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5.332
6.34
37.52
42.93
Energy Balance
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8.4d Psychrometric Charts

• On a psychrometric chart (or humid chart) several
  pro-
• perties of a gas-vapor mixture are
  cross-plotted, pro-
• viding a concise compilation of a large quantity
  of
• physical property data. The most common of these
  
• charts, that for the air-water system at 1 atm,
  is used
• extensively in the analysis of humidification,
  drying,
• and air-conditioning processes.
• The ordinate of the psychrometric chart is the
  absolute
• humidity (the mass ratio of water vapor to dry
  air) of
• the humid air.

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• The abscissa the dry-bulb temperature is the
• temperature that would be determined by any of
  the
• devices discussed in chap3.
• Curves showing the relative humidity
  
• of humid air also appear on the chart. The
  curve for
• 100 relative humidity is referred to as the
  saturation
• curve.
• Dew point, Tdp the temperature at which humid
  air
• becomes saturated if it is cooled at constant
  pressure.
• T29oC, 20 relative humidity
• ? temperature decreases, relative humidity
  increases
• Tdp4oC.

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• The other temperature plotted on the chart is the
  
• wet-bulb temperature. When the gas is saturated,
• TdbTwb the lower the humidity, the greater the
• difference between the two temperatures.
• T29oC, relative humidity20? Twb15oC
• T30oC, relative humidity30? Twb?
• T30oC, relative humidity60? Twb?
• T34oC, Twb25oC, relative humidity?
• Lines that give the humid volume of air are also
• shown on the chart. Notice that the units of
• are (m3 wet air/kg dry air).
• T40oC, relative humidity20 ?

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• The specific enthalpy of the air, relative to
  liquid water
• at 0? and 1 atm and dry air at 1 atm and 0? is
  shown.
• The value of this quantity for saturated air can
  be read
• by extending the constant wet-bulb temperature
  line to
• the diagonal scale above the saturation curve.
  To cal-
• culate for unsaturated air, read the
  value for sa-
• turated air and add the enthalpy deviation
  obtained
• from the curves for this quantity shown on the
  chart.

T35oC, 10 relative humidity
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EXAMPLE 8.4-5 The Psychrometric Chart Use the
psychrometric chart to estimate (1) the absolute
humidity, wet-bulb temperature, humid volume,
dew point, and specific enthalpy of humid air at
41? and 10 relative humidity, and (2) the
amount of water vapor in 150m3 of air at these
conditions.
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(1) Reading from the chart
(2)
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8.4e Adiabatic Cooling

• Adiabatic cooling a warm gas is brought into
  contact
• with a cold liquid (causing the gas to cool and
  some of
• the liquid to evaporate). No heat is transferred
  between
• the gas-liquid system and its surroundings.
• Spray cooling, spray humidification Liquid
  water
• is sprayed into a relatively dry warm air
  stream. Some
• of the water evaporates and the temperature
  of the
• air and of the unevaporated liquid both
  decrease. If
• the object is to cool the water or the air,
  the operation
• is called spray cooling if the point is to
  increase the
• moisture content of the air, the operation is
  spray
• humidification.

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2. Spray dehumidification Warm humid air is
dehu- midification by spraying cold water
into it. Provided that the liquid temperature
is low enough, the air is cooled below its
dew point, causing some of the water vapor
in it to condense. 3. Drying Hot air is blown
over wet solids for example, over a wet
cake deposited in a filter or cen- trifuge.
The water evaporates, leaving a dry solid
product. Drying is the last step in the
production of most crystalline products and
powders, including many pharmaceuticals and
food products.
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• 4. Spray drying A suspension of small solid
  particles
• in water is sprayed as a fine mist into a
  stream of hot
• air. The water evaporates, larger solid
  particles
• settled out of the air and are removed by a
  conveyer.
• Dried milk is produced in this manner
• Writing material and energy balances on an
  adiabatic
• cooling operation is a straightforward but
  cumbersome
• procedure. Air undergoing adiabatic cooling
  through
• contact with liquid water moves along a constant
  
• wet-bulb temperature line on the psychrometric
  chart
• from its initial condition to the 100 relative
  humidity
• curve. Further cooling of the air below its
  saturation
• temperature leads to condensation and hence
  dehu-
• midification.

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EXAMPLE 8.4-7 Adiabatic Humidification A stream
of air at 30? and 10 relative humidity is hu-
midified in an adiabatic spray tower operating at
P?1 atm. The emerging air is to have a relative
humidity of 40.

• Determine the absolute humidity and the adiabatic
• saturation temperature of the entering air.
• 2. Use the psychrometric chart to calculate (i)
  the rate at
• which water must be added to humidify 1000
  kg/h of the
• entering air, and (ii) the temperature of the
  exiting air.

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• Solution We assume that the heat required to
  raise the
• temperature of the liquid in the spray tower is
  negligible
• compared with the heat of vaporization of water,
  so that
• the air follows an adiabatic saturation curve
  (constant
• wet-bulb temperature line) on the psychrometric
  chart.
• Air at 30oC, 10 relative humidity
• ? from Figure 8.4-1

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2. The state of the outlet air must lie on the
Twb13.2oC line. From the intersection of this
line with the curve for hr40, the absolute
humidity of the exit gas is deter- mined to be
0.0063kg H2O/kg DA. The inlet (and outlet) flow
rate of dry air is
The amount of water that must be evaporated may
be calculated as the difference between the
outlet and inlet water flow rates in the air
stream.
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From the psychrometric chart, the temperature of
the exiting air is 21.2oC.
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8.5 MIXING AND SOLUTION

• When two different liquids are mixed or when a
  gas
• or solid is dissolved in a liquid, bonds are
  broken be-
• tween neighboring molecules and possibly
  between
• atoms of the feed materials, and new bonds are
• formed between neighboring molecules or ions in
  the
• product solution. If less energy is required to
  break
• the bonds in the feed materials than is released
  when
• the solution bonds form, a net release of energy
  
• results. Unless this energy is transferred from
  the so-
• lution to its surroundings as heat, it goes into
  raising
• the solution temperature.

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• Suppose you mix 1 mole of pure liquid sulfuric
  acid with
• water at a specified T and P and then cool the
  mixture
• at constant P to bring it back to the initial T.
  The energy
• balance for this constant pressure process is

heat of solution the difference
between the enthalpy of the solution at the
specified T and P and the total enthalpy of the
pure solute and solvent at the same T and P.

• For an ideal mixture

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8.5a Heats of Solution and Mixing

• heat of solution -- the change in
  enthalpy for
• a process in which 1 mole of a solute (gas or
  solid) is
• dissolved in r moles of a liquid solvent at
  constant T.
• (Table B.11)
• as r?? , heat of solution at
  infinite dilution.
• In general, the enthalpy of a solution
  containing r moles
• H2O/mole solute is for reference states of pure
  solute
• and solvent at 25? and 1 atm.

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• For reference states of pure solvent and an
  infinitely
• dilute solution at 25? and 1 atm.

Note that these enthalpies are expressed per mole
of solute, not per mole of solution.
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8.5b Balances on Dissolution and Mixing Processes

• When setting up an energy balance on a process
  that
• involves forming, concentrating, or diluting a
  solution for
• which the heat of solution or mixing cannot be
  neglected,
• prepare an inlet-outlet enthalpy table
  considering the so-
• lution as a single substance and the pure
  components
• at 25? as reference states.
• To calculate the enthalpy of the solution at a
  temperature
• T?25?, first calculate its enthalpy at 25? from
  tabulated
• heat of solution data, then add the enthalpy
  change for
• the heating or cooling of the solution from 25?
  to T. The
• enthalpy change for the latter step should be
  calculated
• from tabulated solution heat capacities if they
  are avail-
• able otherwise, use the average heat capacity
  deter-
• mined for liquid mixtures or the heat capacity
  of the pure
• solvent for dilute solutions.

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EXAMPLE 8.5-1 Production of Hydrochloric
Acid Hydrochloric acid is produced by absorbing
gaseous HCl (hydrogen chloride) in water.
Calculate the heat that must be transferred to
or from an absorption unit if HCl(g) at 100?
and H2O(l) at 25? are fed to produce 1000kg/h
of 20.0 wt HCl(aq) at 40?.
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Soln
The molar amounts of the components are
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HCl(g,100oC) H2O(l,25oC)
HCl(aq,40oC)
Table B.2
Table B.11
HCl(g,25oC) H2O(l,25oC)
HCl(aq,25oC)
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? from Table B.2
For the production solution,
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From Table B.11
From Perrys Chemical Engineers Handbook
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Energy Balance
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8.5c Enthalpy-Concentration Charts
Single Liquid Phase
Energy balance calculations on liquid-phase
systems involving mixtures can be cumbersome
when heats of mixing are significant. The
calculations can be simplified for binary
(two-component) systems by using an
enthalpy-concentration chart. The reference
conditions for the H-x chart for aqueous
solutions of sulfuric acid are pure liquid H2SO4
at 77oF and liquid water at 32oF.
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Enthalpy - Concentration chart
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EXAMPLE 8.5-2 Concentration of an Aqueous H2SO4
Solution A 5.0 wt H2SO4 solution at 60oF is to
be concentrated to 40.0 wt by evaporation of
water. The concentrated solution and water vapor
emerge from the evaporator at 180oF and 1 atm.
Calculate the rate at which heat must be
transferred to the evaporator to process 1000
lbm/h of the feed solution.
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Soln
H2SO4 balance
Total mass balance
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From enthalpy-concentration chart
From steam table
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• Adiabatic mixing process (??H0) are particularly
  simple
• to analyze when chart is available.

Total mass balance
A balance
?
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Energy Balance Adiabatic mixing process (??H0)
The slope of the line segment from (xA1,H1) to
(xA3,H3) the slope of the segment from (xA3,H3)
to (xA2,H2) and the segments have a point in
common, the three points must lie on a straight
line.
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? Three points must lie on a straight line.
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• EXAMPLE 8.5-3 Adiabatic Mixing
• Pure water at 60oF is mixed with 100 g of an
  aqueous
• 80 wt H2SO4 solution, also at 60oF. The mixing
  vessel
• is insulated well enough to be considered
  adiabatic.
• If 250 g H2O is mixed with the acid, what will be
  the
• final solution temperature be?
• 2. What is the maximum attainable solution
  temperature
• and how much water must be added to achieve it?

Soln
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A straight line between points at (x0,
T60oF) and (x0.8, T60oF) goes through the
point (x0.23, T??100oF)
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The line between points (x0, T60oF) and (x0.8,
T60oF) passes through a temperature maximum at
roughly (x0.58, T??150oF)
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• Use Figure 8.5-1 to answer the following
  questions.
• What is the specific enthalpy of 80wt H2SO4(aq,
• 110oF) relative to pure H2SO4 at 77oF and
  pure
• water at 32oF?
• 2. Pure water at 32oF is used to dilute a 90 wt
  H2SO4
• solution (aq, 32oF). Estimate the maximum
  tem-
• perature the product solution can achieve and
  the
• concentration of sulfuric acid (wt) in this
  solution.

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8.5d Using Enthalpy-Concentration Charts for
Vapor-Liquid Equilibrium Calculations
Enthalpy-concentration diagrams are particularly
useful for two-component systems in which vapor
and liquid phases are in equilibrium. The Gibbs
phase rule speci- fies that such a system has
(22-2)2 degrees of free- dom if as before we
fix the system pressure, then specifying only
one more intensive variable the system
temperature, or the mass or mole fraction of
either component in either phasefixes the value
of all other intensive variables of both phases.
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EXAMPLE 8.5-4 Use of Enthalpy-Concentration
Chart for a Two-Phase System An aqueous ammonia
solution is in equilibrium with the vapor in a
closed system at 160oF and 1 atm. The liquid
phase accounts for 95 of the total mass of the
system contents. Determine the weight percent of
NH3 in each phase and the enthalpy of the system
per unit mass of the system contents.
Soln The mass fractions of NH3 and specific
enthalpies of each phase may be read from the
intersections of the 160oF tie line with the
vapor and liquid equilibrium curves.
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V
Liquid Phase
L
Vapor Phase
Assume 1 lbm total mass ?0.95lbm liquid, 0.05 lbm
vapor
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• Lever Rule

V
L
Total mass balance
NH3 mass balance
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EXAMPLE 8.5-5 Equilibrium Flash Vaporization At
30 wt NH3 solution at 100 psia is fed at a rate
of 100 lbm/h to a tank in which the pressure is
1 atm. The enthalpy of the feed solution
relative to the re- ference conditions used to
construct Figure 8.5-2 is 100 Btu/lbm. The vapor
composition is to be 89 wt NH3. Determine the
temperature of the stream leaving the tank, the
mass fraction of NH3 in the liquid product, the
flow rates of the liquid and vapor product
streams, and the rate at which heat must be
transferred to the vaporizer.
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Soln
From Figure 8.5-2
?
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From lever rule
?
Energy Balance