Energy Conservation in EthanolWater Distillation Column with Vapour Recompression Heat Pump
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Conference Paper: Investigation of heat loss in ethanolwater distillation column with direct vapour recompression heat pump
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ABSTRACT: Vapour recompression system has been used to enhance reduction in energy consumption and improvement in energy effectiveness of distillation columns. However, the effects of certain parameters have not been taken into consideration. One of such parameters is the column heat loss which has either been assumed to be a certain percent of reboiler heat transfer or negligible. The purpose of this study was to evaluate the heat loss from an ethanolwater vapour recompression distillation column with pressure increase across the compressor (VRCAS) and compare the results obtained and its effect on some parameters in similar system (VRCCS) where the column heat loss has been assumed or neglected. Results show that the heat loss evaluated was higher when compared with that obtained for the column VRCCS. The results also showed that increase in heat loss could have significant effect on the total energy consumption, reboiler heat transfer, the number of trays and energy effectiveness of the column.International Conference on Thermal Engineering (World Academy of Science, Engineering & Technology, WASET), Amsterdam, The Netherlands; 09/2010
Page 1
2
Energy Conservation in
EthanolWater Distillation Column
with Vapour Recompression Heat Pump
Christopher Enweremadu
University of South Africa, Florida Campus
South Africa
1. Introduction
Ethanol or ethyl alcohol CH3CH2OH, a colorless liquid with characteristic odor and taste;
commonly called grain alcohol has been described as one of the most exotic synthetic
oxygencontaining organic chemicals because of its unique combination of properties as a
solvent, a germicide, a beverage, an antifreeze, a fuel, a depressant, and especially because
of its versatility as a chemical intermediate for other organic chemicals. Ethanol could be
derived from any material containing simple or complex sugars. The sugarcontaining
material is fermented after which the liquid mixture of ethanol and water is separated into
their components using distillation.
Distillation is the most widely used separation operation in chemical and petrochemical
industries accounting for around 2540% of the energy usage. One disadvantage of
distillation process is the large energy requirement. Distillation consumes a great deal of
energy for providing heat to change liquid to vapour and condense the vapour back to
liquid at the condenser. Distillation is carried out in distillation columns which are used for
about 95% of liquid separations and the energy use from this process accounts for an
estimated 3% of the world energy consumption (Hewitt et al, 1999). It has been estimated
that the energy use in distillation is in excess. With rising energy awareness and growing
environmental concerns there is a need to reduce the energy use in industry. The potential
for energy savings therefore exists and design and operation of energy efficient distillation
systems will have a substantial effect on the overall plant energy consumption and
operating costs.
The economic competitiveness of ethanol has been heightened by concerns over prices and
availability of crude oil as well as greenhouse gas emissions which have stimulated interest
in alternatives to crude oil to provide for automotive power and also by the use of
bioethanol in the production of hydrogen for fuel cells. Therefore, there is the need to
explore ways of producing ethanol at competitive costs by the use of energy efficient
processes. To cope with the high energy demand and improve the benefits from the process,
the concept of polygeneration and hydrothermal treatment especially when dealing with
small scale ethanol plants is fast gaining interest. However, the analysis of the bioethanol
process shows that distillation is still the most widely used.
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Distillation – Advances from Modeling to Applications
36
Over the years, there have been many searches for lower energy alternatives or improved
efficiencies in distillation columns. One such search led to the use of heat pumps, the idea
which was introduced in the 1950s. Also, Jorapur and Rajvanshi (1991) have used solar
energy for alcohol distillation and concluded that it was not economically viable. Heat
pumping, however, has been known as an economical energy integration technology for
reduction in consumption of primary energy and to minimize negative impact of large
cooling and heating demands to the environment. One of the heat pump cycles which have
been widely studied is the recompression of the vapours where the reboiler is heated by
adding a compressor to the column to recover some of the heat lost in the distillate.
Most studies have concluded that heat pumping is an effective means of saving energy and
reducing column size without estimating the actual energy consumption and the parameters
that are likely to have significant effect on energy consumption. Estimating the actual
energy consumption is an important aspect towards the determination of the viability of the
system in ethanol–water separation.
The purpose of this chapter was to study how previously neglected and/or assumed values
of different parameters (the pressure increase across the compressor was ignored, column
heat loss was assumed to be 10% of the reboiler heat transfer rate, and the overall heat
transfer coefficient was determined without considering it as an explicit function of
dimensionless numbers, and its dependence on fluid viscosity and thermal conductivity
neglected) affect the process efficiency, energy consumption and the column size of a
vapour recompression heat pump.
2. Energy requirements in ethanol distillation
Ethanol distillation, like any other distillation process requires a high amount of thermal
energy. Studies carried out by several authors reveal that the distillation process in ethanol
distilleries consumes more than half of the total energy used at the distillery (Pfeffer et al.
2007). It has been estimated that distillation takes up about 7085% of total energy consumed
in ethanol production. Pfeffer et al (2007) estimated that distillation consumes half of the
total production energy 5.6 MJ/Liter out of 11.1 – 12.5 MJ/Liter.
The energy requirements for ethanol production have improved markedly during the past
decade due to a variety of technology and plant design improvements. The energy needed
to produce a liter of ethanol has decreased nearly 50% over the past decade and that trend is
likely to continue as process technology improves ( Braisher et al, 2006).
3. Energy conservation schemes in distillation column
Distillation columns are usually among the major energyconsuming units in the food,
chemical, petrochemical and refining industries. According to Danziger (1979), the most
effective method of economizing energy in a distillation column is energy recovery of which
direct vapour recompression has been regarded as the best solution.
3.1 Heat pumping distillation systems
Basically, the heat pump can be regarded simply as reverse heat engine. The heat pump
requires either work input or external driving thermal energy to remove the heat from a low
temperature source and transform it to a higher level.
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
37
The conventional heat pumps are electrically driven vapour recompression types, which
work on the principle that a liquid boils at a higher temperature if its pressure is increased.
A lowpressure liquid passes into the evaporator, where it takes in heat causing the liquid to
boil at low temperature. The lowpressure vapour is passed to the compressor where it is
compressed by the application of work to a higher pressure. The resulting high pressure
vapour flows to the condenser where it condenses, giving up its latent heat at a high
temperature, before expanding back to a low pressure liquid.
The heat pump cycle may be connected to a distillation column in three ways (Fonyo and
Benko, 1998) . The simplest alteration is to replace steam and cooling water with refrigerant
(closed system). The other two types of heat pump system apply column fluids as
refrigerant . When the distillate is a good refrigerant the vapour recompression can be used.
If the bottom product is a good refrigerant the bottom flashing can be applied.
In this work, the direct vapour recompression system is studied due to its good economic
figures ( Emtir et al, 2003). Also the vapour recompression is the most suitable as the boiling
points of both key components (ethanol and water) are close to each other (Danziger, 1979)
and the appropriate heat transfer medium (ethanol vapour) is available.
3.2 Use of vapour recompression in distillation columns
Vapour recompression system has been extensively studied since 1973, the year of drastic
rise in energy (Null, 1976). The vapour recompression system is accomplished by using
compressor to raise the energy level of vapour that is condensed in reboiler–condenser by
exchange of heat with the bottoms. The condensate distillate is passed into reflux drum
while the bottom product is vaporised into the column.
Vapour recompression consists of taking the overhead vapour of a column, condensing the
vapour to liquid, and using the heat liberated by the condensation to reboil the bottoms liquid
from the same column. The temperature driving force needed to force heat to flow from the
cooler overhead vapours to the hotter bottoms product liquid is set up by either compressing
the overhead vapour so that it condenses at a higher temperature, or lowering the pressure on
the reboiler liquid so it boils at a lower temperature, then compressing the bottoms vapour
back to the column pressure. While conventional column has a separate condenser and
reboiler, each with its own heat transfer fluid such as cooling water and steam, the vapour
recompression column has a combined condenser–reboiler, with external heat transfer fluids.
The advantage of vapour recompression lies in its ability to move large quantities of heat
between the condenser and reboiler of the column with a small work input. This results
from cases where there is only a small difference between the overhead and bottoms
temperature. Also, the temperature, and therefore the pressure, at any point may be set
where desired to achieve maximum separation. This effect is of particular importance where
changing the pressure affects the relative volatility. By operating at more favourable
conditions, the reflux requirement can be reduced and therefore the heat duties. These
advantages can reduce a large amount of energy.
4. Ethanolwater vapour recompression distillation column
Figure 1 shows a schematic illustration of the distillation column with direct vapour
recompression heat pump. An ethanolwater solution in a feed storage tank (FST) at
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Distillation – Advances from Modeling to Applications
38
Fig. 1. Schematic Diagram of Column with Direct Vapour Recompression Heat Pump
ambient conditions, is preheated with bottom product and condensate in heat exchangers,
preheaters PH1 and PH2, and fed to the column. An auxiliary reboiler (AR) is used to start
the unit. This reboiler supplies the auxiliary heat duty, which is the heat of vaporization
because the main reboiler can work only if there is some compressed vapour already
available. The overhead vapours from the top are compressed in the compressor (CP) up to
the necessary pressure in such a way that its condensing temperature is greater than the
boiling temperature of the column bottom product. The vapour is then condensed by
exchanging heat within the tubes of the reboilercondenser (RC). In a condenser, the inlet
temperature is equal to the outlet temperature. Ethanol vapour will only lose its latent heat
of condensation. At the same time, the cold fluid (ethanolwater mixture) in the reboiler will
absorb this latent heat and its temperature will increase to boil up the mixture to
temperature TCEV. The liberated latent heat of condensation provides the boilup rate to the
column while the excess heat extracted from the condensate is exchanged with the feed in
preheater PH2. The condensate, which is cooled in the cooler (CL) up to its bubble point at
the column operating pressure, expands through the throttling valve (TV) at the same
pressure and reaches the flash tank (FT). After expansion, the output phases are a vapour
phase in equilibrium with a liquid phase. One part of the product in the liquid phase is
removed as distillate and stored in the tank (DST), while the remainder is recycled into the
column as reflux L1. The excess of vapour is recycled to the compressor.
4.1 Methodology
Like this work, nearly all publications in this field are based on modelling and simulation
(Brousse et al., 1985; Ferre et al., 1985; Collura and Luyben, 1988; Muhrer et al, 1990; Oliveira
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
39
et al. 2001). The mathematical modeling of the distillation system is derived by applying
energy, composition and overall material balances together with vapourliquid equilibrium
under some assumptions (see Muhrer et al, 1990 and Enweremadu, 2007). These and other
assumptions are aimed at simplifying the otherwise cumbersome heatand masstransfer,
and the fluid flow equations Mori et al (2002).
4.2 Calculation of the distillation column
In this system, there is a direct coupling between the distillation column and the rest of the
system, as the heat pump working fluid is the column’s own fluid which, is a binary mixture
of ethanol and water at composition XD. Therefore, the set of equations are not solved
separately as in distillation column assisted by an external heat pump.
The detailed calculation of the overall material and component material balance such as the
bottom flow rate, B and distillate flow rate, D; reflux ratio, Rr; the molar vapour flow rate
which leaves the column top and feeds the condenser, V1; feed vapour flow rate, VF; feed
vapour fraction, q; vapour molar flow rate remaining at the bottom of the column, L2 are
given (see Enweremadu, 2007).
The overall (global) energy balance equation applied to a control volume comprising the
distillation column and the feed preheaters provides the total energy demand in the reboiler:
Qreb = DhD + BhB + L1hLV, e + Qlosses – FhF – Q1 – Q2 (1)
where Qreb is the total heat load added to the reboiler, Qlosses represents the heat losses in the
column, which are to be determined; Q1 and Q2 are the heat loads of the preheaters; hLV,e is
latent heat of vaporisation downstream of throttling valve; hD, is the enthalpy of the
distillate; hB is the enthalpy of the bottom product; hF, is the enthalpy of the feed. The details
of the mass balance variables are determined in Enweremadu (2007).
The first step in the design of a distillation column is the determination of the number of
theoretical plates required for the given separation. The theoretical trays are numbered from
the top down, and subscripts generally indicate the tray from which a stream originates
with n and m standing for rectifying and stripping sections respectively. The design
procedure for a tray distillation column consists of determining the liquid and vapour
composition or fraction from top to bottom, along the column. In calculating the
composition profile of the column two equations relating liquid mole fraction to
temperature and vapour mole fraction to the liquid fraction are used. The compositions at
the top (XD) and bottom (XB) of the column are previously preestablished data. In this work,
the minimum number of theoretical stages (Nmin) is calculated using Fenske’s equation:
min
1
log.
1
log
D
X
B
D
B
X
X
X
N
(2)
where α is the relative volatility in the column. The actual number of plates is given by:
min
T
N
N
(3)
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Distillation – Advances from Modeling to Applications
40
where
T
is the tray efficiency.
4.2.1 Heat losses from distillation column
The heat loss from the distillation column is the main factor that affects heat added and
removed at the reboiler and condenser respectively. Most distillation columns operate above
ambient temperature, and heat losses along the column are inevitable since insulating
materials have a finite thermal conductivity. Heat loss along the distillation column increase
condensation and reduces evaporation. Thus, the amount of vapour diminishes in the
upward part of the column, where the flow of liquid is also less than at the bottom.
To prevent loss of heat, the distillation column should be well insulated. Insulation of
columns using vapour recompression varies with the situation. Where the column is hot and
extra reboiler duty is used, the column should be insulated (Sloley, 2001). The imperfect
insulation of the column causes some heat output.
In determining the heat loss from the distillation column, it is assumed that the temperature
is uniform in the space between two plates. The heat transfer between the column wall and
the surrounding is then determined from the wellknown relationship for overall heat
transfer coefficient:
Losses
o
PP
QU AT
(4)
where Up, the overall heat transfer coefficient is given by Gani, Ruiz and Cameron (1986), as
1
,,,,,,
p
poiomins
Uf h h K A A At
(5)
where the temperature difference,
p
T
, is given as
pamb
p
TTT
ho, the heat transfer coefficient between the surroundings and the column external surface,
is given as
ho = f(Nu, Kins, do, tins) (6)
hi is the heat transfer coefficient inside the column; Kp is the thermal conductivity of the tray
material; Ao is the external area of heat exchange; Ai is the internal area of heat exchange;
Am is the logarithmic mean area; tins is the thickness of insulation.
The heat output is calculated with the general expression for convection around cylindrical
objects.
K
ln/
A
ln/
11
wall
o
r
wall
i
inswall
o
amb
P
loss
wallwall
iioo
insm
TT
Q
rrr
h Ah A
KA
(7)
The column inner surface heat transfer resistance is neglected as the heat transfer coefficient
for condensing vapor is large and therefore will have little effect on the overall heat transfer.
Based on the assumptions in Enweremadu (2007), the heat transfer due to free convection
between the surroundings and the external column wall and due to conduction through the
insulation materials is predicted.
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
41
Also, from geometry of the insulated cylinder (Fig.2), the external diameter of insulation is
given as
dins = do + 2tins (8)
Details of how the logarithmic mean diameter of the insulating layer (dins,m), external area of
heat exchange (Ao) and the logarithmic mean area (Am) can be found in Enweremadu (2007).
From dimensional analysis,
2
ins
o
o ins
K
d
Nu
t
h
(9)
where, tins is the thickness of insulation; Kins – thermal conductivity of the insulation
materials; Nu – Nusselt number; do – external diameter of column; Tamb – temperature of the
surrounding; Tp – plate temperature.
Fig. 2. Hypotethical Section of the Distillation Column with Insulation
For vertical cylinders, the commonly used correlations for free convection are adapted from
Rajput (2002) as:
For laminar flow,
1/4
Nu0.59 Gr.Pr
for (104<Gr.Pr<109) (10)
For turbulent flow,
1/3
0.10 Gr.Pr
Nu
for (109<Gr.Pr<1012) (11)
where Gr is the Grashof number and Pr is Prandtl.
Based on the assumptions of neglecting hi, Ai and the effect of thermal resistance, equation
(5) reduces to:
ri
row
rins
hot
fluid
Cold fluid
(air)
QLo
ho
Ti
Tins
To
Tsurf
Kins
Kwal
Tp
hi
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Distillation – Advances from Modeling to Applications
42
UP = f(ho, Kp, Ao, Am, tins) (12)
while equation (7) is given as
K
()
ln/
A
1
inswall
o
p amb
r
s
losses
Q
pmoo
T
r
T P N
h A
(13)
where
K
1
ln
1
wall
o
P
ins
r
pmoo
U
r
Ah A
The heat loss from the column trays is given by
2
loss from trays
Q
,.
( )2
ln
1
.
2
()
2
ln 1
ambs
P
o
ins
r
s ins
ins
o
d
ins
pins m
d
s
o ins
TT P N
r
P t
K
d
Nu
t
KP
t
(14)
The total heat loss from the column is expressed as
loss from trays
loss
QQ Heat loss from the two cylinder heads
(15)
Based on the assumptions made, heat loss through the cylinder heads is given by
2
o
pamb
loss at cylinder heads
Q
ins
t
K
p
2(T  T ) r
1
o h
(16)
Therefore,
,.
( )2
ln
1
2.
2
()
2
ln 1
ambS
P
loss
o
ins
r
s ins
ins
o
d
ins
ins m
d
Ps
o ins
TT P N
Q
r
P t
K
d
Nu
t
KP
t
2
o
P amb
ins
t
K
p
2(T  T)
1
h
o
r
(17)
4.3 Calculation of heat pump and compressor parameters
The heat pump is thermodynamically linked to the column through the heat load from the
pump to the column QHPC and from the column to the pump QCHP, and reboiler–condenser
temperature. These parameters provide the basis for the heat pump calculation.
The calculation of the heat pump parameters begins with the estimation of the working fluid
condensation temperature obtained from the reboiler temperature and temperature drop
across the heat exchangers.
TCHP = TCEV + ∆TCHP (18)
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
43
where TCEV is the column vapourization (reboiler) temperature and ΔTCHP, a preestablished
mean temperature difference across the heat exchangers (temperature drop in reboiler
condenser). Next is the estimation of the relevant thermodynamic properties of the working
fluid. These are obtained from thermodynamic correlations.
The thermodynamic properties are determined as functions of temperature. The
relationships used for calculating the working fluid density, viscosity, thermal
conductivity and heat capacity for input at various locations are presented in
Enweremadu (2007). The condensation pressure, PCHP is expressed as a function of
condensation temperature as
PCHP = f(TCHP) (19)
while the condensation pressure is determined from ideal gas equation.
The latent heat of condensation from column to heat pump is numerically exactly equal to
the latent heat of vaporisation, but has the opposite sign: latent heat of vaporisation is
always positive (heat is absorbed by the substance), whereas latent heat of condensation is
always negative (heat is released by the substance). Latent heat of condensation is expressed
as a function of condensation temperature and is determined from the relationship
(Ackland, 1990):
CHP
T
CHP
C
C
LV,CHP
h
bp
C
vap
T
AB 1
T
1T
H
T
1T
(20)
where
temperature; A and B are constants.
vap
H
is the heat of vapourisation at the boiling point of ethanol; TC is the critical
The vapour specific volume at location “a” (entrance to the compressor) is expressed as a
function of column condensation temperature, TCC and pressure at the top of the column,
PTOP:
cc
P
T Rx
a
TOP
v
(21)
Since compression is polytropic, at location “b” (compressor discharge), the vapour specific
volume is determined by:
b
1
n
v
TOP
a
CHP
P
PP
v
(22)
where n is the polytropic index and ΔP is the pressure increase across the compressor.
The vapour specific enthalpy at “a” is a function of top pressure,PTOP and top temperature,
TTOP.
ha=f(TTOP, PTOP) (23)
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Distillation – Advances from Modeling to Applications
44
The vapour specific enthalpy at “b” may be determined as a function of compressor
discharge temperature Tb and condensation pressure PCHP but in this study, it is determined
by the development of numerical computation with calculations utilizing the Redlich –
Kwong equation of state. The Redlich – Kwong equation of state is given as
12
)
RT
V
a
P
b
T V Vb
(24)
Where
a = 0.42747
52
c
2
c
R T
P
b = 0.08664
c
c
RT
P
and P = pressure (atm); V = molar volume (liters/gmol); T = temperature (K); R = gas
constant (atm. Liter/gmol.K); Pc = critical pressure (atm).
Taking the reference state for the enthalpy of liquid ethanol
o
L
h , temperature, To and the
enthalpy of vaporisation Δ
o
vap
H, then the enthalpy of ethanol vapour as an ideal gas at
temperature T can be calculated from
o
b
o
L
hh
o
T
o
vap
o
p
T
HC dT
(25)
Using the isothermal enthalpy departure and the RedlichKwong equation of state, the
enthalpy of ethanol vapour at T and P can be calculated from
1.5
1.5
bRT
1ln 1
o
T
o
L
o
vap
o
p
b
T
ab
V
hhH C dTRT Z
(26)
where Z is the compressibility factor, Cpo is the molar specific heat capacities of gases at
zero pressure given as a polynomial in temperature.
Equations 24–26 are then solved with POLYMATH(R) Simultaneous Algebraic Equation
Solver (See Enweremadu, 2007).
The vapour specific heat at location “e” is calculated thus (Oliveira et al, 2002):
e,
h
L
L c SC
h CpT
(27)
The specific liquid enthalpies have been assumed to be simple functions of temperature.
The liquid specific enthalpy at location “c” is determined from EZChemDB Thermodynamic
Properties Table for Ethanol (AM Cola LLC, 2005) using the expression
L,c CHP
h f(T)
(28)
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
45
while the liquid specific enthalpy at location e (at the exit of the throttling valve) is
determined from
hL,e=f(TCC) (29)
The temperature at compressor discharge is determined from the knowledge of the
compressor efficiency. The ideal discharge temperature (the temperature that gives an
overall change in entropy equal to zero) is calculated before correcting with the compressor
efficiency.
CHP
TOP
TOP
b TOP
0.263
PP
T1
P
TT
pol
(30)
The dryness fraction after the isenthalpic expansion is given by
,
,
L
LV
ee
e
e
hh
h
(31)
where the molar latent heat of vaporization at location “e” is adapted from Ackland (1990):
,
*111
LV
bp
edd
vapC bpCC
hH T TTTAB T T
(32)
Since this is a throttling process, Td = Te and hd = he
The molar vapour flow rate which is recycled in the flash tank and conveyed to the
compressor is calculated by
1
1
e
R
e
V
V
(33)
Therefore, the molar flow rate across the compressor is expressed as
1R
M
VV
(34)
While the dryness fraction at condenser exit is determined by
,
23
L
LV CHP
h
P CHP
T
d
c
QM
CT
(35)
where Q23 is the distribution of excess heat between the preheater Q2 and the cooler Q3 and
CpL is the molar specific heat of the working fluid in the liquid phase.
The energy balance, applied to the heat pump working fluid, yields the available energy for
exchange at the condenser, as follows:
,
1
v
cdb CHP
T
cLV CHP
hQ M Cp T
(36)
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Distillation – Advances from Modeling to Applications
46
A comparison is made between this energy available at the condenser, Qcd, with the
energy required by the column reboiler, Qreb. This brings about the following heat load
control.
i.
If the rate of energy available at the heat pump condenser, Qcd, is greater than the rate
of energy required by the reboiler Qreb, then the condenser gives up Qreb to the reboiler
and the remaining energy is conveyed to the preheaters (Q2) and cooler (Q3)
if
cd reb
QQ
then
HPC
reb
QQ
(37)
ii. But if Qcd is smaller than or equal to Qreb, then all energy available is transferred to the
reboiler and the auxiliary reboiler will provide the “extra” Qreb i.e.
if
cdreb
QQ
then
HPC
cd
QQ
(38)
where QHPC is the energy yield by the heat pump to the distillation column. The factor by
which the heat pump contributes to the heat load of the reboiler is given as
HPC
reb
Q
Q
f
(39)
For a distillation column with vapour recompression, driving the compressor uses the most
energy. Thus, the power consumption must be known so as to assess the feasibility of such a
system. For a perfect gas, that is, a gas having a constant specific heat, Cp = Cpo, then the
specific enthalpy rise between the compressor inlet and outlet is
o
p
baba
hhhCTT
(40)
And if the change of state is isentropic,
1
1
1
b
b
a
a
P
P
Ru T
M
hvdp
(41)
In reality, ideal gases do not exist and therefore improvements are made on equation (41).
Therefore, compression is polytropic and the isentropic index γ, is replaced by the
polytropic index, n (see Enweremadu, 2007). The compressor polytropic efficiency
= 0.7  0.8 is used.
pol
Also, because a saturated vapour, especially at higher pressures, shows deviations from the
ideal gas behaviour, the compressibility factor, Z is used. Hence equation (41) becomes
1
1
1
n
n
u
ab
eff
pola
Z R
T
P
P
n
h
nM
(42)
Therefore, the power input for driving the compressor is the energy that increase the
enthalpy of the gas
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Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
47
1
1
1
n
n
b
cpa a
P
pola
P
P
M
n
W
n
(43)
Equation (43) shows that the pressure ratio
b
a
P
P
is crucial to the power requirement. This
ratio or the pressure increase to be provided by the compressor of a column with vapour
recompression is influenced by the following (Meili, 1990; Han et al, 2003):
Pressure drop in vapour ducts (pipes) and over valves and fittings, ∆Pp.
Pressure drop across the column, ∆Pcl.
The difference in boiling points between the top and bottom products, ∆Pb.
Temperature difference in the reboiler, ∆PCHP.
4.3.1 Determination of the pressure increase over the compressor
Pressure drops in the vapour ducts may be caused by frictional loss, ∆Pf; static pressure
difference, due to the density and elevation of the fluid, ∆Ps; and changes in the kinetic
energy, ∆Pk. Since, there are elbows, valves and other fittings along the pipes then the
pressure drop is calculated with resistance coefficients specifically for the elements.
Therefore, the pressure drop along a circular pipe with valves and fittings is given by
PsfK
PPPP
2
1
2
p
P
ul
d
(44)
and u is the fluid velocity; dp is the pipe diameter and ρ is the fluid density; is the Fanning
friction factor which is a function of Reynolds number; lp is the pipe length; is the dynamic
viscosity of the fluid and ξ is the resistance coefficient.
The pressure drop over the entire distillation column, ∆Pcl is caused by losses due to vapour
flowing through the connecting pipes and through pressure drop over the stages in
rectifying and stripping section. This depends mainly on the column internals, number of
stages, gas load and operating conditions. ΔPcl =0, if zero vapour boil up is assumed. But
constant pressure drop is assumed in this work. The pressure drop over a stage consists of
dry and wet pressure drop. The dry pressure is caused by vapour passing through the
perforation of the sieve tray. The aerated liquid (static head) on the tray causes the wet
pressure drop. Constant pressure drop per tray have been estimated from several authors to
be equal to 5.3mmHg per tray (Muhrer, Collura and Luyben 1990). The total column
pressure drop has been found by summing plate pressure drops ΔPcl
0.13332 5.30.707
cl
Px xNN
(45)
The top and bottom products have different compositions and boiling points. For a fixed
bottom temperature of the column, there is a vapour – pressure difference, ∆Pb due to the
difference in boiling points.
b
P
TOPBOTTOM
PP
(46)
Page 14
Distillation – Advances from Modeling to Applications
48
where,
TOP
C
TOP
TOP
TOPTOP

B
A
P
10
T
(47)
BOTTOM
B
BOTTOM
BOTTOM
BOTTOM
T
BOTTOM
C

A
P
10
(48)
The temperature difference in the reboiler condenser is expressed by means of the vapour –
pressure equation as a pressure difference, ∆PCHP. Temperature differences of 8 – 17oC are
quite common for ethanolwater distillation (Gopichand et al, 1988; Canales and Marquez,
1992). Using the Clausius – Clapeyron equation for a two point fit,

e
R.
CHP
CEV
T
CHP
CHP
Hvap
T
P
T
(49)
Therefore the total pressure increase over the compressor becomes
bcl CHPp
P PPPP
(50)
For this distillation system, the compression (pressure) ratio is
CHP
P
TOP
P
b
a
P
P
P
(51)
where PTOP is inlet pressure (vapour pressure at top temperature).
Other compressor parameters are calculated by the following equations:
i.
Compressor power input is determined from equation (43) and (51)
1
1
1
n
n
CHP
P
TOP
P
TOP
P
cpa
pol
M
n
P
W
n
(52)
ii. Compressor heat load rate (energy balance)
pol
cp
cpba
QW
M h
h
(53)
iii. Compressor volumetric efficiency
1
m
11
CHP
P
vv
TOP
P
P
Cr
(54)
where Cv is empirical volumetric coefficient and r is the compressor clearance ratio.
iv. Compressor nominal capacity or compressor displacement rate
c
v
a
M
V
(55)
Page 15
Energy Conservation in EthanolWater
Distillation Column with Vapour Recompression Heat Pump
49
where Vc is compressor displacement volume (m3) and ω is angular velocity (rad s–1).
4.3.2 Determination of the reboilercondenser parameters
The overall heat transfer coefficient between condenser and reboiler is given by
HPC
T
HPC
CHP
Q
UA
(56)
However, a careful analysis reveals that the overall heat transfer coefficient U is an explicit
function of Prandtl, Reynolds and Nusselt numbers, and depends on other properties such
as viscosity and thermal conductivity. The overall heat transfer coefficient referenced to
inner surface is given by
1
U
1
h
1
h
ln(
2
/ )r
( / )
i
r
ioi
o
io wall
rr
r
K
(57)
As thermal resistance of the wall is negligible, (Kwall is large and ln(ro/ri)) ≈ 0, it is then
compared with the inner tube diameter (ri/ro ≈1)
Then
1
U
11
ex ex
io
hh
(58)
0.80.40.14
)
0.023
d
(Re )(Pr )(
ex
ex
m wall
omm
om
K
h
(59)
where μm is the mean bulk fluid viscosity and μw all is the viscosity of the liquid at the wall.
The expression for condensation at low velocities inside tubes is adapted from (Holman,
2005).
0.25
3'
()
0.555
()
llv
ex
CHP
ex
L
fg
i
L i
d
wall
K gh
T
h
T
(60)
where
fg fgp CHP
L
'
wall
hh 0.375C (TT)
where KL is thermal conductivity of the liquid, diex is the inside diameter of the reboiler
condenser tubes and μL is the density of the condensate (liquid).
Therefore, the overall heat transfer coefficient may be determined from
0.80.14
3'
0.4
111
(
d
)
0.023
d
0.555
()
HPC
LLvL
T
fg
mm pmwall
ex
L CHP
mmm
ex
o
iwall
o
ex
UA
K gh
Kud
C
K
T
(61)
Assuming adiabatic expansion at the throttling valve, then
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