Plant Utilities Assignment 2 Kaustubh Sawant - 14CHE1072
Plant Utilities Assignment 2 Kaustubh Sawant - 14CHE1072
Plant Utilities Assignment 2 Kaustubh Sawant - 14CHE1072
Problem
1A
1. 𝑄 = 𝑚𝐶! 𝑑𝑇 = 𝑈𝐴∆𝑇
!!"#$%# !
2. !!"#$%
𝑚𝐶! 𝑑𝑇 = ! 𝑈!"" 2𝜋𝑑!/!"# 𝑇!"#$% − 𝑇!"#$ 𝑑𝐿
,
!!!"" !!!!/!"# !
3. On
integration
-‐
𝑇!"#$%# = 𝑇!"#$ + (𝑇!"#$% − 𝑇!"#$ )×exp ( !!!
)
Here
Effective
heat
transfer
coefficient
can
be
calculated
using
individual
coefficient
–
! ! !! !" !! !! !! !" !! !!
4.
!!""
= ! !! + !!!"!#
+ !!!"#$
(There
is
no
insulation)
! !
Inside
heat
transfer
coefficient
is
found
out
using
Dittus
and
Boelter
equation,
as
flow
is
turbulent.
5. 𝑁𝑢 = 0.023𝑅𝑒 !.! 𝑃𝑟 !.!!
!"# ! !
6. 𝑅𝑒 = !
,
𝑃𝑟 = !!
Substituting
all
the
values
we
get
the
result
as
• T
=
54.60C,
for
L
=
50m
• T
=
54.20C,
for
L
=
100m
• Assumptions:
z
=
5m;
Ksoil
=
1.5
W/mK;
Schedule
40
pipe
with
ID
=
40.894mm
and
thickness
=3.683mm
Problem
2A
Here we need to add U due to insulation, therefore equation (4) changes to
!!"# !" !! !!
!!"# !" !! !!"# !" !! !!!"#
! !!"# !!"# !" !! !! !!!"!#
7. =!! + + +
!!"" ! ! !!!"!# !!!"#$%&'!(" !!!"#$
We see that we cannot solve explicitly for insulation thickness. Therefore we used goal seek
method on Excel to get the value for outlet temperature equal to 54.50C.
Answer – 3.2 mm
Reference: https://www.cheresources.com/invision/blog/4/entry-493-heat-transfer-in-buried-liquid-
pipelines/
7. Steam Cost (Rs/kg) = (Total Fuel*Fuel Cost + Total Air*Air Cost)/(Total Stem)
8. We can back calculate fuel cost if we have steam cost.
Assumptions:
• Density of coal, furnace oil and wood is 833,990,750 kg/m3 respectively.
• Cost of Air = 0.35 Rs/kg; Consider only fuel & air cost in steam cost.
Solution:
Value
Coal
Furnace
oil
Wood
Unit
GCV
16119.7
44309.2
10928.5
(kJ/kg)
2A
NCV
15366.5
42060.7
9132.6
(kJ/kg)
2B
Theoretical
Air
5.316
13.757
3.671
(kg/kg
of
fuel)
2C
Energy
Density
1.342
4.386
0.820
(kJ/m3)
*
10^7
2D
Volume
9.676
3.341
18.476
(m3/day)
Total
Fuel
8060.15
3308.22
13857.242
(kg/day)
Actual
Air
6.380
15.133
4.479
(kg/kg
of
fuel)
Fuel
Cost
51425.65
50064.48
62060.73
(Rs/day)
Air
cost
96907.45
(Rs/day)
2F
Total
Cost
14999.15
111509.59
18101.05
(Rs/day)
Steam
Cost
2.323
(Rs/kg)
Fuel
Cost
to
match
FO
11.974
29.293
6.741
(Rs/kg)
2.Furnace Oil (FO): It has high sulfur content. It has a pour point of 27oC, therefore
transportation is difficult. Storage is relatively difficult and small discharge will cause
explosion. Storage tank leaks are common problem.
3.Wood: As it has low energy density, transportation cost will be higher. It has the lowest
efficiency; therefore carbon monoxide and particulate formation will be highest.