Paul Ashall, 2008

Module 9001

Energy 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

system

mass 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 = ∆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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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 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

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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