Chapter 8 EnergyBalance, Weight Control & Eating Disorders Lecture_1 (2 Files Merged)
Module 9001 Energy Balance -...
Transcript of Module 9001 Energy Balance -...
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
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Forms of energy
� Potential energy (mgh) � Kinetic energy (1/2 mv2)
� 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
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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
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Steady state/non-steady state
� Non steady state -
accumulation/depletion of energy in
system
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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
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Enthalpy balance
� p.e., k.e., W terms = 0
� Q = H2 – H1 or Q = ∆H
, where H2 is the total enthalpy of output streams and H1is the total enthalpy of input streams, Q is the difference in total enthalpy i.e. the enthalpy (heat) transferred to or from the system
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continued
� Q –ve (H1>H2), heat removed from
system
� Q +ve (H2>H1), heat supplied to
system.
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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
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continued
Ignore k.e. and p.e. terms relative to enthalpy changes for processes involving phase changes, chemical reactions, large temperature changes etc
Q = ∆H (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 105 kJ/min
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Enthalpy changes
� Change of T at constant P
� Change of P at constant T
� Change of phase
� Solution
� Mixing
� Chemical reaction
� crystallisation
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Latent heats (phase changes)
� Vapourisation (L to V)
� Melting (S to L)
� Sublimation (S to V)
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Mechanical energy balance
� Consider mechanical energy terms only
� Application to flow of liquids
∆P + ∆ v2 + g ∆h +F = W
ρ 2
where W is work done on system by a pump and F is frictional energy loss in system (J/kg)
∆P = P2 – P1; ∆ v2 = v22 –v1
2; ∆h = h2 –h1
� Bernoulli equation (F=0, W=0)
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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.
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continued
∆P/ρ + ∆v2/2 + g∆h +F = W
∆P = P2 – P1 (Pa)
∆v2 = v22 – v1
2
∆h = h2 - h1 (m)
F= frictional energy loss (mechanical energy loss to system) (J/kg)
W = work done on system by pump (J/kg)
ρ = 1000 kg/m3
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continued
Volumetric flow is 20/(1000.60) m3/s
= 0.000333 m3/s
v1 = 0.000333/(π(0.0025)2) = 16.97 m/s
v2 = 0.000333/ (π(0.005)2) = 4.24 m/s
(101325 - P1)/1000 + [(4.24)2 – (16.97)2]/2 + 9.81.50 = 0
P1 = 456825 Pa (4.6 bar)
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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 ∆H = integral Cp(T)dT between limits T2 and T1
� Use of mean heat capacities/specific heats over a temperature range
� Use of simple empirical equations to describe the variation of Cp with T
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continued
e.g. Cp = a + bT + cT2 + dT3
,where a, b, c, d are coefficients
∆H = integralCpdT between limits T2, T1
∆H = [aT + bT2 + cT3 + dT4]
2 3 4
Calculate values for T = T2, T1 and subtract
Note: T may be in deg cent or K - check units for Cp!
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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 10-2T + 0.572 x 10-5T2 –
2.87 x 10-9 T3, where T is in deg cent)
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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, 4th 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, 3rd edition, ch. 8, pp321-324
� ‘PhysProps’
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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.]
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Energy balances on systems
involving chemical reaction
� Standard heat of formation (∆Hof) – 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, νi)
∆HofA, ∆Ho
fB, ∆HofC, ∆Ho
fD (heats of formation)
∆HoR = c ∆Ho
fC + d ∆HofD - a ∆Ho
fA - b∆HofB
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Heat (enthalpy) of reaction
� ∆HoR –ve (exothermic reaction)
� ∆HoR +ve (endothermic reaction)
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Enthalpy balance equation -
reactor
Qp = Hproducts – Hreactants + Qr
Qp – heat transferred to or from process
Qr – reaction heat (ζ ∆HoR), where ζ is
extent of reaction and is equal to [moles
component,i, out – moles component i,
in]/ νi
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system Qr
Hreactants Hproducts
Qp
+ve
-ve Note: enthalpy values must be calculated with reference to a
temperature of 25 deg cent
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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