energy balance
TRANSCRIPT
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Paul Ashall, 2008
Module 9001Energy Balance
Paul Ashall, 2008
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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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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
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Energy balance
systemmass in
Hin
mass out
Hout
W
Q
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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 = 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
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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 = 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
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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)
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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)
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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
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
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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 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
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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!
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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 (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
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Heat (enthalpy) of reaction
ΔHoR –ve (exothermic reaction)
ΔHoR +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 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
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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
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Energy balance techniques
Adiabatic temperature: Qp = 0
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Examples
Reactor Crystalliser Drier Distillation
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References
The Properties of Gases and Liquids, R. Reid
Elementary Principles of Chemical Processes, R.M.Felder and R.W.Rousseau