Paul Ashall, 2008 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

Paul Ashall, 2008 Forms of energy Potential energy (mgh) Kinetic energy (1/2 mv 2 ) 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 system mass 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

Paul Ashall, 2008 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 = H 2 – H 1 or Q = ΔH, where H 2 is the total enthalpy of output streams and H 1 is 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.

Paul Ashall, 2008 Example – steam boiler Two input streams: stream kg/min. water, 30 deg cent., H = 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 = 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 state Q = Hout – Hin Q = [295 x ] – [(120 x 125.7) + (175 x 272)] Q = x 10 5 kJ/min

Paul Ashall, 2008 Steam tables Enthalpy values (H kJ/kg) at various P, T

Paul Ashall, 2008 Enthalpy changes Change of T at constant P Change of P at constant T Change of phase Solution Mixing Chemical reaction crystallisation

Paul Ashall, 2008 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 liquids ΔP + Δ v 2 + g Δh +F = W ρ 2 where W is work done on system by a pump and F is frictional energy loss in system (J/kg) ΔP = P 2 – P 1 ; Δ v 2 = v 2 2 –v 1 2 ; Δh = h 2 –h 1 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 + Δv 2 /2 + gΔh +F = W ΔP = P 2 – P 1 (Pa) Δv 2 = v 2 2 – v 1 2 Δh = h 2 - h 1 (m) F= frictional energy loss (mechanical energy loss to system) (J/kg) W = work done on system by pump (J/kg) ρ = 1000 kg/m 3

Paul Ashall, 2008 continued Volumetric flow is 20/( ) m 3 /s = m 3 /s v 1 = /( π(0.0025) 2 ) = m/s v 2 = / ( π(0.005) 2 ) = 4.24 m/s ( P 1 )/ [(4.24) 2 – (16.97) 2 ]/ = 0 P 1 = 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 T 2 and T 1 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 + cT 2 + dT 3,where a, b, c, d are coefficients ΔH = integralCpdT between limits T 2, T 1 ΔH = [aT + bT 2 + cT 3 + dT 4 ] Calculate values for T = T 2, T 1 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 = x T x T 2 – 2.87 x T 3, 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, 4 th 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, 3 rd edition, ch. 8, pp ‘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 (ΔH o f ) – 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, ν i ) ΔH o fA, ΔH o fB, ΔH o fC, ΔH o fD (heats of formation) ΔH o R = c ΔH o fC + d ΔH o fD - a ΔH o fA - bΔH o fB

Paul Ashall, 2008 Heat (enthalpy) of reaction ΔH o R –ve (exothermic reaction) ΔH o R +ve (endothermic reaction)

Paul Ashall, 2008 Enthalpy balance equation - reactor Qp = H products – H reactants + Qr Qp – heat transferred to or from process Qr – reaction heat (ζ ΔH o R ), where ζ is extent of reaction and is equal to [moles component,i, out – moles component i, in]/ ν i

Paul Ashall, 2008 system Qr H reactants H products Qp +ve -ve Note: 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

Paul Ashall, 2008 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