Chemical Engineering December 2013 - 58

Table 1.
CapaCiTy ConsTrainTs
for The power GeneraTor
mG
mG
mG
mG
mG
mG
HML
HML
HM
HM
ML
ML
P
≤ mG
≥ mG
≤ mG
≥ mG
≤ mG
≥ mG
≥
HMLmax
HMLmin
HMmax
HMmin
MLmax
MLmin
Pbasecase
These constraints must be satisfied
for the steam-turbo generator's material
balance
turbines from the cost of HP or MP
steam (estimated based on the cost
of production). This method reflects
the true value of steam at any level,
and should be used to evaluate the
true benefits of energy conservation
projects [10]. Using this approach,
for sites installed with cogeneration
plants, LP steam cost can
be negative.
Optimization objective
The base-case steam network for
this optimization model is shown
in Figure 8. It involves a total of 93
steam-turbine drivers: 35 HP to LP,
15 HP to MP, 3 HP to vacuum (condensing-type),
40 MP to LP steam
turbine drivers and one steamturbo
generator. Out of these, 65
are switchable and 28 are nonswitchable
steam-turbine drivers.
Steam generation and consumption
amounts for the network are shown
in Figure 8 [12]. The following assumptions
were made in obtaining
the optimum solution for the base
case:
* Negligible pressure and temperature
drops in the steam headers
* HP steam pressure of 43 bars and
HP steam temperature of 3,600ºC
for the steam-turbine drivers
and 3,800ºC for the steam-turbo
generator
* MP steam pressure of 11.5 bars
* LP steam pressure of 4.5 bars
* Total HP, MP and LP steam generation
and consumption from
process units are constant
* All the steam generated at MP
and LP steam levels by the process
units are at saturated conditions,
corresponding to the header
pressure
* The total boiler feed-water flowrate
requirement for the base case
and optimized case is assumed to
be 102% of the total steam generation,
accounting for overall
blowdown
Process
334
129.55
HP-MP
114.2
HP-LP
129.55
47.9
47.9
110
Process
10
MP-LP
114.2
87
Process
Loss
110
50
Loss
LP condensate header
DM water header
Total power generation: 34,554 kW
Figure 9. This diagram shows the optimized solution for the base-case network.
Some of the steam flows (shown in m.t./h) between turbines were altered, and the
resulting total power generation increased
HP BFW
231
Fluegas
Parameter
Process
334
Steam turbo generator (HP-MP-LP) extraction flow, m.t./h 49.69
Process
135.1
99
62.57
10
30
83.8
Steam turbo generator (HP-MP-LP) exhaust flow, m.t./h
Loss
HP-MP
HP-LP
Power from turbo generator, kW
32.93
129.55
Total power generation, kW
MP-LP
32.93
110
135.1
87
Total annual savings (compared to base case), $
(Note that total savings were calculated by assuming a
power cost of $0.15/kWh and 8,760 annual operating
hours)
Process
114.34
1313
* Steam flowrates through the steamturbine
drivers are considered constant
Process
Process
Loss
The
ultimate objective of this MILP
optimization exercise is to maximize
the total power generation from the
base-case steam network. Here, power
consists of the total shaft power from
the steam turbine drivers and the
electrical power from the steam-turbo
generator. Equation (13) defines this
objective function.
p
110
Total power generation: 32,589 kW
P ∑ SRHL Yi
=
i=1
r
k=1
+∑ SRHC
HM
+−
HML
G
()+−
=
nm Wn mW
1


mk
HC
k


s
l
+∑ SRML Yl
ML


ML
l


INT
HM
ML
G


mi
HL
i


q
j=1
HL +∑ SRj
ml


mj
HM
HM Yj


ML
()
(13)
ML
INT
In Equation (13), note that there
HML, mG
HM and mG
are only three continuous variables
(mG
ML), but the
number of binary variables is 65, one
58 ChemiCal engineering www.Che.Com DeCember 2013
HM
50
Loss
LP condensate header
DM water header
Loss
WCS
104
for each switchable turbine in the
base-case scenario. These binary variables
are defined as:
* Yi
* Yj
WCR
214
99
11
Condensate
drum
* Yl
HL for i = 1,...,p
HM for j = 1,...,q
ML for l = 1,...,s
203
255
The binary variable, Y, is used for
selecting the operating mode of a
steam turbine. If its value is zero,
the steam turbine is considered to
be in stopped condition. If its value
is one, the steam turbine is considered
to be in operation [12]. Additionally,
many constraints must be
considered when evaluating Equation
(13), including the steam material
balances for the HP, MP and LP
headers, given in Equations (14), (15)
and (16), respectively.
p
HL
blrHPG
+ ++ HM
G
H
MLM
mm
HPCld
i
== =
i 11 0
j
k
q
j
r
mm mm m
m
+= ++ HC
HM
∑∑ ∑
k
Deaerator
HP BFW
613
75
Process
Process
27.9
HP-COND
Process
HP-MP-LP34.11
49.69
Process
6,435 33
Table 2. key parameTers for opTimizaTion
Boilers
16.51
Base
case
206
Fuel and air
Steam turbo generator (HP-MP-LP) inlet flow, m.t./h
129.55
83.8
Optimized
case
104.66
64.66
39.99
8,375
34.11
1.1
HP steam
HP-MP-LDV
0.0
32,589 34,554
MP-LP-LDV
0.0
Vent
MP steam
2,581,883
0.0 0.0
Vent
LP steam
45.84
104
203
255
Process
114.34
13
99
HP-COND
HP BFW
231
16.51
Boilers
206
62.57
Process
Fuel and air
30
Process
Loss
64.66
75
Process
Loss
WCS
WCR
214
99
11
Condensate
drum
Process
MP-LP-LDV
27.9 40
1.1
Deaerator
HP BFW
613
104.66
HP-MP-LP
Process
33
HP steam
HP-MP-LDV
0.0
0.0
Vent
MP steam
0.0 0.0
Vent
LP steam
46.01
Fluegas
(14)
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Chemical Engineering December 2013

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