Project MIA 505
I.
Assumption
We supposed the same values for: temperature, pressure, gas composition, chemical element and the model of cogeneration system than in the book Thermal Design & Optimization (figure 1).
Figure 1 - Base-Case design of the cogeneration system
II.
Initial values
a) Value from the book As defined in the book we have the following initial values. Steps 1 2 3 4 5 6 7 8
Element Air
Combustible Water
Temperature (K)
Pressure (Bar)
298.13 603.74 850.00 1520.00 1006.16 779.78 426.90 298.13
1.013 10.13 9.62 9.142 1.099 1.066 1.013 20
Mass molar M (Kg/Kmol) 28.649
28.254 /
9 10
485 298.15
Methane
20 12
16.043
Tableau 1-Initial values
On the basis of 1 kmol of mixture at step 4, the composition at 25°C, 1atm is :
Fraction of gas for one kmol of air :
λ = = 0.0321
Tableau 2 - enthalpy + entropy initial
h0= - 34117 kJ/kmol s0= 193.17 kJ/kmol
Tableau 3 - Book example Energy va lues
As E=e*m (with m = mass flow (kg/s)) and m is the only variable between our study and the example from the book we can also use the initial mass energy. State 1 2 3
e (kJ/s.Kg) 0 301.70 459.47
4 5 6 7 8 9 10
1091.87 417.384 234.10 29.84 4.4 915.01 51765.60
Tableau 4 - Mass energy
Efficiency: System Compressor (ηcomp) Turbine (ηturb) Heat exchanger (ηhe) Preheater (ηph) Chamber (ηchamb)
Efficiency (%) 92.8 95.2 67.2 84.6 79.9 Tableau 5 - Efficiency
b) Objectif During this study we want : Electricity production : 1000 kW =
Wturbie
Heat production : 1800 kW
III.
Energy determination
a) Mass flow of air and gas We are looking for the mass flow of air (m comb kg/s) and the mass flow of gas (m gas kg/s). We can also define the mass flow of the combustion as m comb=mcair+ mgas We will first try to get m comb :
0 = Wηturbie comp ℎ ℎ 1λ ℎ ℎ ∗ W turbie = 1λ ℎ ℎ ℎ ℎ
With
ℎ = 4713.3 ℎ = 9304.5
= ℎℎ ℎℎ ℎ = ℎ −
As the air composition is fixed, ideal-gas mixture principles allow the isentropic compression to be
described as
O2
We use the table C1 to calculate the follows values :
And we finally get : T2s = 563K h2s = 3293.5 kJ/kmol h2 = 4596.9 kJ/kmol Solving the expression for the turbine isentropic efficiency :
As before with
= 0
= ℎℎ ℎℎ ℎ = ℎ ∗ ℎ ℎ
we obtain :
T2s = 920K h5s = -11792.6 kJ/kmol h5 = -8839 kJ/kmol
We replace the values in this equation
= +−∗ +−
and we get
mair= 3.04 kg/s
=
mfuel=0.054 kg/s mair=3.04kg/s mfuel=0.054 kg/s mcomb= 3.098 kg/s
b) Mass flow for water We want E9=1800 kW and we have e9=915.01 kW/kg
= = 1.97 /
c) Energy destruction analysis i. Initial analysis
To be able to calculate the energy destruction of each component we need to determine the entropies s5, s6 and s7. I also calculated h 5, h6 and h7 by the same occasion. We use the equations follow :
ℎ = 10 ∗ + ∗10− ∗ 2 ∗ 10− ∗ ∗ 10− ∗ − 3 ∗ 10− ∗ = + ∗ln ∗10− ∗ 2 ∗10− ∗ − 2 ∗ 10− ∗
We obtain the following values : Value (kJ/kmol) h5k h6k h7k si5k si6k si7k
N2
O2
CO2
H2O(g)
H2O(l)
22150 14820 3790 229.19 220.94 202.17
81528 60656 28743.1 243.78 235.15 215.87
-255890 -291070 -344568 271.54 258.00 228.48
-145720 -170530 -208140 234.02 223.62 200.96
-175230 -211710 -258670 182.45 151.88 97.17
Tableau 6 - Entropy and isotropy of each element
We evaluate the contribution of k element with xk the molar fraction of the gas k :
, = ln We obtain :
Value (kJ/kmol) s5k s6k s7k
N2
O2
CO2
H2O(g)
H2O(l)
230.35 222.36 204.01
259.07 250.70 231.84
299.09 285.805 256.71
261.57 251.43 229.65
182.45 151.88 97.17
Tableau 7 - Isotropy of gas
And Sxtotal = 0.7507 * sxN2 + 01372 * s xO2 + 0.0314 * s xCO2 + 0.0297 * sxH2O(g) + 0.0510 * sxH2O(l)
S5total = 234.93 kJ/kmol.k S6total = 225.43 kJ/kmol.k S7total = 204.80 kJ/kmol.k ii. Energy destruction
Energy destruction is given by : E d=m*T0*(Δs) Compressor:
Rair = 0.287 and C pair = 1
= ∗ ∗ ∗ ln () ∗ ln ()
EDcomp = 41.0 kW
Airpreheater:
With
= ∗ = ∗ ∗ ln ∗ ln ∗ = 1.04 / =
= 1.08 kW/k
And
Turbine:
= ∗ = 25
Heatexchanger: Cpwater (l) = 4,185 kJ/kg/K
= 11.92 kW
With
= ∗ = ∗ ∗ ln = 4.01 / ∗ = 1.93 / =
And
= 619.06 kW
Combustionchamber:
∗ ∗ ∗
EDcombchamb = E3 + E10 – E4 =
d) Reheat Reheat is defined by :
= 964.82 kW
= ∗ℎ = ∗ ℎ ℎ = 124 = ∗ ℎ ℎ = 323.86
i. Compressor
ii. Turbine
e) Energy With table 4 we can easily find the new values of energy :
State
E x (kW)
1
0
2
918
3
1399
4
3383
5
1293
6
725
7
92
8
9
9
1812
10
2795
Tableau 8 – Energy
I.
Preamble
Same value than the book for :
: 500 000 $
Component Date project start Reference date for money Life Rate of gas cost increasing Cost gas Life tax purpose Removing Capacity factor Labour rate Number hour working Number of labour Inflation rate Rate increasing r Construction LHV Cost for research …
Value 1994 Mid-year 20 years 6%/year 3$/GJ 15 years Salvage value 100% 28$/h 2080h/labour 30 6% 5% 2 years from 01/1996 50.01 MJ/kg 0
Tableau 9 - Initial values
We also consider that it is a new construction and not an extension.
The project conditions for operate are : 11 months 6 days / week 16 hours/day The tax apply is :
Figure 2- Tax
II.
Analyse a) Initial costs
We will first calculate the cost of each component of our thermal system. To calculate those cost we used values calculates in thermal part. Compressor:
= ∗ ∗ ()∗ln() = 177746$ Combustionchamber:
= ∗ ∗1∗− = 11322$ Turbine:
Airpreheater:
)∗1∗− = ∗ ∗l n ( = 233696$ = ∗ ℎ ∗ℎ ,∗ . = 121635$
Heatrecovery:
. . = ∗ , , ∗ ∗ = 72339$
= 617.10
$
As FCI = 4.80 * PEC And TCI = 6.32 * PEC
FCI = 2960 ∗10$ TCI = 3898∗10$ Onsite cost
$ Purchased equipment cost *Air compressor
177 746
*Air preheater
11 322
*Combustion chamber *Gas turbine
233 696 121 635
*Heat recovery steam generator
72 339
PEC
616 738
*Purchased equipment installation
203 524
*Piping
215 858
*Instrumentation and controls
74 009
*Electrical equipment and materials
80 176
Total onsite costs
1 190 304
Offsite costs *Land
500 000
*Civil, structural + Architectural work
129 515
*Services facilities
215 858
Total offsite costs
845 373
Total direct costs (DC)
2 035 678
Indirect costs *Engineering and supervision *Construction cost and contractor's profit Sum
162 854 305 352 2 503 883
*Contigency Total indirect costs
375 583 843 788
Fixed capital investment (FCI)
2 879 466
Tableau 10 - Initial cost
Number of hours were the system is working : Hours/years = 11 (month)*4 (weeks/month)*6(days/week)*16(hours/day)=4224hours/years We calculate now the annual cost of fuel FC : FC = 0.003 ($/MJ) *LHV * m gas * working-hours * 3600s/h FC=123196 $/year 1994
As FCn=FC*(1+gas inflate)n with n = number of year and that the plan will only work in 1998 : FC = 155532 $ /year 1998
We will now calculate the start-up cost (SUC) as we are building a totally new plant. Startup cost is the sum of : one month of fixed O&M costs, one month of variable operating costs calculated at full load, one week of full-load fuel, and (d) 2% of the plant facilities investment.
We first determine the PFI = FCI-Land = 2 879 466 - 500 000 = 2 379 466 $ in 1994
0. 3 5∗10 155 ∗10 3 . 8 ∗10 = 12 12 12 0.02∗2379466 = 406339$ in 1994
SUC = 470389$ in 1997
As the central is not working one day by week and 1 month by year, we will calculate the working capital (WC) engendered by no fuel consuming or labour plus a contingency of 25% of the total of the above items. The non-running period can be approximate on one year as 2 months and a half. First, we calculate labour cost : LabourC = 30*28*2080 =1747000$ year in 1994
155∗10 1747 ∗10 = 12 ∗2.5 ℎ 12 ∗2.5 ℎ∗10.25 = 495000 $ 1994 = 573000 $ 1997 We now calculate the AFUPC which is the system-financing fractions given by :
AFUDC=0.15 * FCI AFUDC= 431920$ in 1994 AFUDC=500001$ in 1997 Concerning the PFI (plant facilities investment of 2 379 466 $ in 1994), 40% of this amount must be escalated at an annual rate of 5% to the middle of 1996 and the other 60 % be escalated to the middle of 1997.
b) Cost construction
$ in 1997 Cost of land
538000
Escalated PFI
2754529,33
Start-up costs
470389
Working capital Costs of research …
573000 0
Grants in aid of construction
0
Total net outlay
4335918
Tableau 11- cost construction
Total capital investment = 4335918+500001 = 4835918 $ in 1997 I considered than the Total depreciable capital investment ≈ Total net outlay
As tax investment equal to 0 total capital net investment is the same than total capital investment.
c) Calculation of revenue requirements We first calculate the tax per year : Years of commercial operation
Calendar year
MACRS
Annual tax $
End year tax book value $
0
1997
0
0
4835919
1
1998
5
241796
4594123
2
1999
9,5
459412
4134711
3
2000
8,55
413471
3721240
4
2001
7,7
372366
3348874
5
2002
6,93
335129
3013745
6
2003
6,23
301278
2712467
7
2004
5,9
285319
2427148
8
2005
5,9
285319
2141829
9
2006
5,91
285803
1856026
10
2007
5,9
285319
1570707
11
2008
5,91
285803
1284904
12
2009
5,9
285319
999585
13 14
2010 2011
5,91 5,9
285803 285319
713782 428462
15
2012
5,91
285803
142660
16
2013
2,95
142660
0
100
4835919
Total
Tableau 12 – tax
