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

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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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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