BALANCE MASICO UNILLANOS-2 ENERGY AND MASS BALANCE IN CHEMICAL PROCESSSES

ENERGY AND MASS BALANCE IN CHEMICAL PROCESSSES

1. Paul Ashall, 2008
Module 9001
Energy Balance
Paul Ashall, 2008

2. Paul Ashall, 2008
Concerned with energy changes and
energy flow in a chemical process.
Conservation of energy – first law of
thermodynamics i.e. accumulation of
energy in a system = energy input –
energy output

3. Paul Ashall, 2008
Forms of energy
Potential energy (mgh)
Kinetic energy (1/2 mv
2
)
Thermal energy – heat (Q) supplied to or removed
from a process
Work energy – e.g. work done by a pump (W) to
transport fluids
Internal energy (U) of molecules
m – mass (kg)
g – gravitational constant, 9.81 ms
-2
v – velocity, ms
-1

4. Paul Ashall, 2008
Energy balance
system
mass in
Hin
mass out
Hout
W
Q

5. Paul Ashall, 2008
IUPAC convention
- heat transferred to a system is +ve and
heat transferred from a system is –ve
- work done on a system is+ve and work
done by a system is -ve

6. Paul Ashall, 2008
Steady state/non-steady state
Non steady state -
accumulation/depletion of energy in
system

7. Paul Ashall, 2008
Uses
Heat required for a process
Rate of heat removal from a process
Heat transfer/design of heat exchangers
Process design to determine energy requirements of a
process
Pump power requirements (mechanical energy balance)
Pattern of energy usage in operation
Process control
Process design & development
etc

8. Paul Ashall, 2008
Enthalpy balance
p.e., k.e., W terms = 0
Q = H
2 – H
1 or Q = ΔH
, where H
2 is the total enthalpy of output
streams and H
1is the total enthalpy of
input streams, Q is the difference in
total enthalpy i.e. the enthalpy (heat)
transferred to or from the system

9. Paul Ashall, 2008
continued
Q –ve (H1>H2), heat removed from
system
Q +ve (H2>H1), heat supplied to
system.

10. Paul Ashall, 2008
Example – steam boiler
Two input streams: stream 1- 120 kg/min.
water, 30 deg cent., H = 125.7 kJ/kg;
stream 2 – 175 kg/min, 65 deg cent, H=
272 kJ/kg
One output stream: 295 kg/min. saturated
steam(17 atm., 204 deg cent.), H =
2793.4 kJ/kg

11. Paul Ashall, 2008
continued
Ignore k.e. and p.e. terms relative to enthalpy
changes for processes involving phase
changes, chemical reactions, large
temperature changes etc
Q = ΔH (enthalpy balance)
Basis for calculation 1 min.
Steady state
Q = Hout – Hin
Q = [295 x 2793.4] – [(120 x 125.7) + (175 x 272)]
Q = + 7.67 x 10
5
kJ/min

12. Paul Ashall, 2008
Steam tables
Enthalpy values (H kJ/kg) at various P,
T

13. Paul Ashall, 2008
Enthalpy changes
Change of T at constant P
Change of P at constant T
Change of phase
Solution
Mixing
Chemical reaction
crystallisation

14. Paul Ashall, 2008
Latent heats (phase changes)
Vapourisation (L to V)
Melting (S to L)
Sublimation (S to V)

15. Paul Ashall, 2008
Mechanical energy balance
Consider mechanical energy terms only
Application to flow of liquids
ΔP + Δ v
2
+

g Δh +F = W
ρ 2
where W is work done on system by a pump
and F is frictional energy loss in system (J/kg)
ΔP = P
2 – P
1; Δ v
2
= v
2
2
–v
1
2
; Δh = h
2 –h
1
Bernoulli equation (F=0, W=0)

16. Paul Ashall, 2008
Example - Bernoulli eqtn.
Water flows between two points 1,2. The
volumetric flow rate is 20 litres/min.
Point 2 is 50 m higher than point 1. The
pipe internal diameters are 0.5 cm at
point 1 and 1 cm at point 2. The
pressure at point 2 is 1 atm..
Calculate the pressure at point 2.

17. Paul Ashall, 2008
continued
ΔP/ρ + Δv
2
/2 + gΔh +F = W
ΔP = P
2
– P
1
(Pa)
Δv
2
= v
2
2
– v
1
2
Δh = h
2 - h
1 (m)
F= frictional energy loss (mechanical energy
loss to system) (J/kg)
W = work done on system by pump (J/kg)
ρ = 1000 kg/m
3

18. Paul Ashall, 2008
continued
Volumetric flow is 20/(1000.60) m
3
/s
= 0.000333 m
3
/s
v
1 = 0.000333/(π(0.0025)
2
) = 16.97 m/s
v
2 = 0.000333/ (π(0.005)
2
) = 4.24 m/s
(101325 - P
1
)/1000 + [(4.24)
2
– (16.97)
2
]/2 + 9.81.50 = 0
P
1
= 456825 Pa (4.6 bar)

19. Paul Ashall, 2008
Sensible heat/enthalpy
calculations
‘Sensible’ heat – heat/enthalpy that must be transferred
to raise or lower the temperature of a substance or
mixture of substances.
Heat capacities/specific heats (solids, liquids,
gases,vapours)
Heat capacity/specific heat at constant P, Cp(T) = dH/dT
or ΔH = integral Cp(T)dT between limits T
2 and T
1
Use of mean heat capacities/specific heats over a
temperature range
Use of simple empirical equations to describe the
variation of Cp with T

20. Paul Ashall, 2008
continued
e.g. Cp = a + bT + cT
2
+ dT
3
,where a, b, c, d are coefficients
ΔH = integralCpdT between limits T
2
, T
1
ΔH = [aT + bT
2
+ cT
3
+ dT
4
]
2 3 4
Calculate values for T = T
2, T
1 and subtract
Note: T may be in deg cent or K - check units for Cp!

21. Paul Ashall, 2008
Example
Calculate the enthalpy required to heat a
stream of nitrogen gas flowing at 100
mole/min., through a gas heater from 20
to 100 deg. cent.
(use mean Cp value 29.1J mol
-1
K
-1
or Cp
= 29 + 0.22 x 10
-2
T + 0.572 x 10
-5
T
2
–
2.87 x 10
-9
T
3
, where T is in deg cent)

22. Paul Ashall, 2008
Heat capacity/specific heat data
Felder & Rousseau pp372/373 and Table B10
Perry’s Chemical Engineers Handbook
The properties of gases and liquids, R. Reid et al, 4
th

edition, McGraw Hill, 1987
Estimating thermochemical properties of liquids part
7- heat capacity, P. Gold & G.Ogle, Chem. Eng.,
1969, p130
Coulson & Richardson Chem. Eng., Vol. 6, 3
rd
edition,
ch. 8, pp321-324
‘PhysProps’

23. Paul Ashall, 2008
Example – change of phase
A feed stream to a distillation unit contains an equimolar
mixture of benzene and toluene at 10 deg cent.The
vapour stream from the top of the column contains
68.4 mol % benzene at 50 deg cent. and the liquid
stream from the bottom of the column contains 40
mol% benzene at 50 deg cent.
[Need Cp (benzene, liquid), Cp (toluene, liquid), Cp
(benzene, vapour), Cp (toluene, vapour), latent heat
of vapourisation benzene, latent heat of vapourisation
toluene.]

24. Paul Ashall, 2008
Energy balances on systems
involving chemical reaction
Standard heat of formation (ΔH
o
f
) – heat of
reaction when product is formed from its
elements in their standard states at 298 K, 1
atm. (kJ/mol)
aA + bB cC + dD
-a-b+c+d (stoichiometric coefficients, ν
i)
ΔH
o
fA
, ΔH
o
fB
, ΔH
o
fC
, ΔH
o
fD
(heats of formation)
ΔH
o
R= c ΔH
o
fC + d ΔH
o
fD - a ΔH
o
fA - bΔH
o
fB

25. Paul Ashall, 2008
Heat (enthalpy) of reaction
ΔH
o
R –ve (exothermic reaction)
ΔH
o
R +ve (endothermic reaction)

26. Paul Ashall, 2008
Enthalpy balance equation -
reactor
Qp = H
products – H
reactants + Qr
Qp – heat transferred to or from process
Qr – reaction heat (ζ ΔH
o
R), where ζ is
extent of reaction and is equal to [moles
component,i, out – moles component i,
in]/ ν
i

27. Paul Ashall, 2008
system
Qr
H
reactants
H
products
Qp
+ve
-ve
Note: enthalpy values must be calculated with reference to a
temperature of 25 deg cent

28. Paul Ashall, 2008
Energy balance techniques
Complete mass balance/molar balance
Calculate all enthalpy changes between
process conditions and standard/reference
conditions for all components at start (input)
and finish (output).
Consider any additional enthalpy changes
Solve enthalpy balance equation

29. Paul Ashall, 2008
Energy balance techniques
Adiabatic temperature: Qp = 0

30. Paul Ashall, 2008
Examples
Reactor
Crystalliser
Drier
Distillation

31. Paul Ashall, 2008
References
The Properties of Gases and Liquids, R.
Reid
Elementary Principles of Chemical
Processes, R.M.Felder and
R.W.Rousseau