Energy Balance
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Transcript of Energy Balance
Paul Ashall, 2008
Module 9001Energy Balance
Paul Ashall, 2008
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
Paul Ashall, 2008
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
Paul Ashall, 2008
Energy balance
systemmass in
Hin
mass out
Hout
W
Q
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
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Steady state/non-steady state
Non steady state - accumulation/depletion of energy in system
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
Paul Ashall, 2008
Enthalpy balance
p.e., k.e., W terms = 0 Q = H2 – H1 or Q = ΔH
, 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
Paul Ashall, 2008
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
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 stateQ = Hout – HinQ = [295 x 2793.4] – [(120 x 125.7) + (175 x 272)] Q = + 7.67 x 105 kJ/min
Paul Ashall, 2008
Steam tables
Enthalpy values (H kJ/kg) at various P, T
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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)
Paul Ashall, 2008
Mechanical energy balance
Consider mechanical energy terms only Application to flow of liquidsΔP + Δ v2 + g Δh +F = Wρ 2where W is work done on system by a pump
and F is frictional energy loss in system (J/kg)ΔP = P2 – P1; Δ v2 = v2
2 –v12; Δh = h2 –h1
Bernoulli equation (F=0, W=0)
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.
Paul Ashall, 2008
continued
ΔP/ρ + Δv2/2 + gΔh +F = W
ΔP = P2 – P1 (Pa)Δv2 = v2
2 – v12
Δh = 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
Paul Ashall, 2008
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)
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 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
Paul Ashall, 2008
continued
e.g. Cp = a + bT + cT2 + dT3
,where a, b, c, d are coefficients
ΔH = integralCpdT between limits T2, T1
ΔH = [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!
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 10-2T + 0.572 x 10-5T2 – 2.87 x 10-9 T3, where T is in deg cent)
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, 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’
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.]
Paul Ashall, 2008
Energy balances on systems involving chemical reaction
Standard heat of formation (ΔHof) – 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)
ΔHofA, ΔHo
fB, ΔHofC, ΔHo
fD (heats of formation)
ΔHoR = c ΔHo
fC + d ΔHofD - a ΔHo
fA - bΔHofB
Paul Ashall, 2008
Heat (enthalpy) of reaction
ΔHoR –ve (exothermic reaction)
ΔHoR +ve (endothermic reaction)
Paul Ashall, 2008
Enthalpy balance equation - reactor
Qp = Hproducts – Hreactants + Qr
Qp – heat transferred to or from process
Qr – reaction heat (ζ ΔHoR), where ζ is
extent of reaction and is equal to [moles component,i, out – moles component i, in]/ νi
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systemQr
HreactantsHproducts
Qp
+ve
-veNote: enthalpy values must be calculated with reference to a temperature of 25 deg cent
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
Paul Ashall, 2008
Energy balance techniques
Adiabatic temperature: Qp = 0
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Examples
Reactor Crystalliser Drier Distillation
Paul Ashall, 2008
References
The Properties of Gases and Liquids, R. Reid
Elementary Principles of Chemical Processes, R.M.Felder and R.W.Rousseau