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Energy Balance (1).ppt

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Energy Balance (1).ppt

  1. 1. Paul Ashall, 2008 Module 9001 Energy Balance Paul Ashall, 2008
  2. 2. 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
  3. 3. 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
  4. 4. Paul Ashall, 2008 Energy balance system mass in Hin mass out Hout W Q
  5. 5. 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
  6. 6. Paul Ashall, 2008 Steady state/non-steady state  Non steady state - accumulation/depletion of energy in system
  7. 7. 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
  8. 8. 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
  9. 9. Paul Ashall, 2008 continued  Q –ve (H1>H2), heat removed from system  Q +ve (H2>H1), heat supplied to system.
  10. 10. Paul Ashall, 2008 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
  11. 11. 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 2793.4] – [(120 x 125.7) + (175 x 272)] Q = + 7.67 x 105 kJ/min
  12. 12. Paul Ashall, 2008 Steam tables  Enthalpy values (H kJ/kg) at various P, T
  13. 13. 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
  14. 14. Paul Ashall, 2008 Latent heats (phase changes)  Vapourisation (L to V)  Melting (S to L)  Sublimation (S to V)
  15. 15. Paul Ashall, 2008 Mechanical energy balance  Consider mechanical energy terms only  Application to flow of liquids ΔP + Δ v2 + 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 = P2 – P1; Δ v2 = v2 2 –v1 2; Δh = h2 –h1  Bernoulli equation (F=0, W=0)
  16. 16. 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.
  17. 17. Paul Ashall, 2008 continued ΔP/ρ + Δv2/2 + gΔh +F = W ΔP = P2 – P1 (Pa) Δv2 = v2 2 – v1 2 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
  18. 18. 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)
  19. 19. 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
  20. 20. 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!
  21. 21. 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)
  22. 22. 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’
  23. 23. 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.]
  24. 24. Paul Ashall, 2008 Energy balances on systems involving chemical reaction  Standard heat of formation (ΔHo 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, νi) ΔHo fA, ΔHo fB, ΔHo fC, ΔHo fD (heats of formation) ΔHo R = c ΔHo fC + d ΔHo fD - a ΔHo fA - bΔHo fB
  25. 25. Paul Ashall, 2008 Heat (enthalpy) of reaction  ΔHo R –ve (exothermic reaction)  ΔHo R +ve (endothermic reaction)
  26. 26. Paul Ashall, 2008 Enthalpy balance equation - reactor Qp = Hproducts – Hreactants + Qr Qp – heat transferred to or from process Qr – reaction heat (ζ ΔHo R), where ζ is extent of reaction and is equal to [moles component,i, out – moles component i, in]/ νi
  27. 27. Paul Ashall, 2008 system Qr Hreactants Hproducts Qp +ve -ve Note: enthalpy values must be calculated with reference to a temperature of 25 deg cent
  28. 28. 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
  29. 29. Paul Ashall, 2008 Energy balance techniques  Adiabatic temperature: Qp = 0
  30. 30. Paul Ashall, 2008 Examples  Reactor  Crystalliser  Drier  Distillation
  31. 31. Paul Ashall, 2008 References  The Properties of Gases and Liquids, R. Reid  Elementary Principles of Chemical Processes, R.M.Felder and R.W.Rousseau

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