Process Intensification & Hybrid Processes – Ex. 08 CHE.822UF Process Intensification and Hybrid Processes WS 2021/22 Ex. 08: Membrane processes 1 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3: Gas permeation βͺ Many of the coolants currently in commercial use have a high Global Warming Potential (GWP). Alternatives with low GWP, such as R-1234yf, are often more expensive and are therefore mainly used as 1:1 mixture with the commercial R-134a. To recycle the R-1234yf from the mixture, gas permeation is used, which takes advantage of the different permeation of the gases for purification. a) Calculate the max. feed flow rate to achieve a purity of 0.9 with a single membrane unit. b) For a process with two units, determine which of the following four arrangements has the highest recovery, if the membrane area of a unit is half of the area of point a). 2 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3: Process information βͺ Feed stream: π₯πΉ = 0.5 ππΉ = 6 πππ πΉ,αΆ π₯πΉ π ,αΆ π₯π βͺ Permeate stream: ππ = 1 πππ βͺ Product stream: π,αΆ π₯π π₯ππππ = 0.9 βͺ Membrane: π΄ = 3000 π² πππ π«π 1234π¦π = 0.07 πππ β π2 β β πππ π«π 134π = 0.28 πππ β π2 β β 3 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3: Assumptions βͺ The difference in partial pressure can be described by mean logarithmic difference βππ,ππ + βππ,ππ’π‘ πΰ΄₯π = 2 βͺ The permeability is independent of the system pressure π«π ≠ π«π (π) βͺ Pressure loss in system is neglected βππππ π = 0 4 TU Graz I Institute of Chemical Engineering and Environmental Technology πΉ,αΆ π₯πΉ π ,αΆ π₯π π,αΆ π₯π Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3: Necessary equations βͺ Total balance 0 = πΉαΆ − παΆ − π αΆ βͺ Recovery παΆ ππππ ∗ π₯ππππ π= πΉαΆ ∗ π₯πΉ βͺ Component balance αΆ πΉ − π π₯ αΆ π − ππ₯ αΆ π 0 = πΉπ₯ βͺ Flowrate through membrane παΆ = ΰ· π½παΆ ∗ π΄ βͺ Flux through membrane π½παΆ = π«π ∗ βππ 5 βͺ Partial pressure (Dalton) ππ = π ∗ π₯π TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Calculation procedure Find the max. allowed feed stream βͺ Establish transport through membrane βͺ Calculate permeate concentration and flow βͺ Establish balances βͺ Calculate max. molar flow of feed 6 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area Establish transport through membrane π½παΆ = π«π ∗ βππ πΉ,αΆ π₯πΉ π ,αΆ π₯π βͺ Difference in partial pressure is linear βππ,ππ + βππ,ππ’π‘ πΰ΄₯π = 2 ππ,πΉ + ππ,π πΰ΄₯π = − ππ,π 2 π,αΆ π₯π βͺ Partial pressure according to Dalton ππ = π₯π ∗ π 7 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area Establish transport through membrane π½παΆ = π«π ∗ βππ πΉ,αΆ π₯πΉ π ,αΆ π₯π βͺ Difference in partial pressure is linear βππ,ππ + βππ,ππ’π‘ πΰ΄₯π = 2 ππ,πΉ + ππ,π πΰ΄₯π = − ππ,π 2 βͺ Partial pressure according to Dalton ππ = π₯π ∗ π 8 TU Graz I Institute of Chemical Engineering and Environmental Technology π,αΆ π₯π Transport through membrane π₯ + π₯π αΆπ½1 = π«1 ∗ (ππΉ ∗ πΉ − ππ ∗ π₯π ) 2 1 − π₯πΉ + 1 − π₯π αΆπ½2 = π«2 ∗ (ππΉ ∗ − ππ ∗ (1 − π₯π )) 2 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area βͺ Calculate permeate concentration and flow π₯πΉ + π₯π π½1αΆ = π«1 ∗ (ππΉ ∗ − ππ ∗ π₯π ) 2 1 − π₯πΉ + 1 − π₯π αΆπ½2 = π«2 ∗ (ππΉ ∗ − ππ ∗ (1 − π₯π )) 2 βͺ Adding both fluxes π½ αΆ = π½1αΆ + π½2αΆ 9 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area βͺ Calculate permeate concentration and flow π₯πΉ + π₯π π½1αΆ = π«1 ∗ (ππΉ ∗ − ππ ∗ π₯π ) 2 1 − π₯πΉ + 1 − π₯π αΆπ½2 = π«2 ∗ (ππΉ ∗ − ππ ∗ (1 − π₯π )) 2 βͺ Adding both fluxes π½ αΆ = π½1αΆ + π½2αΆ π½ αΆ = ππΉ ∗ π«1 ∗ 10 π₯πΉ + π₯π π₯πΉ + π₯π + π«2 1 − 2 2 TU Graz I Institute of Chemical Engineering and Environmental Technology − π«2 ∗ ππ − π«1 − π«2 ∗ ππ ∗ π₯π Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area βͺ Calculate permeate concentration and flow π₯πΉ + π₯π π½1αΆ = π«1 ∗ (ππΉ ∗ − ππ ∗ π₯π ) 2 1 − π₯πΉ + 1 − π₯π αΆπ½2 = π«2 ∗ (ππΉ ∗ − ππ ∗ (1 − π₯π )) 2 βͺ Adding both fluxes π½ αΆ = π½1αΆ + π½2αΆ π΅ = 0.000518 π½ αΆ = π΅ + π ∗ π₯π π = 0.00021 βͺ Introducing it into one of the flux equations π₯πΉ + π₯π 2 π΅ ∗ π₯π + π ∗ π₯π = π«1 ∗ ππΉ ∗ − π«1 ∗ ππ ∗ π₯π 2 11 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area βͺ Introducing it into one of the flux equations π₯πΉ + π₯π 2 π΅ ∗ π₯π + π ∗ π₯π = π«1 ∗ ππΉ ∗ − π«1 ∗ ππ ∗ π₯π 2 12 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 a) Necessary membrane area π₯π = 0.475 βͺ Calculate the permeate flow π½1αΆ π΄ π₯πΉ + π₯π αΆ π=π΄∗ = ∗ π«1 ∗ (ππΉ ∗ − ππ ∗ π₯π ) ππππ αΆ π = 1.65 π₯π π₯π 2 β Establish the balance 0 = πΉαΆ − παΆ − π αΆ αΆ πΉ − π π₯ αΆ π − ππ₯ αΆ π 0 = πΉπ₯ βͺ Rearrange the balances παΆ ∗ (π₯π − π₯π ) πΉαΆ = Purity 0.9 π₯πΉ −π₯π ππππ πΉαΆ = 1.75 β 13 TU Graz I Institute of Chemical Engineering and Environmental Technology Yield 0.103 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas Parallel Serial Permeate βͺ Membrane: π΄ = 1500 π² Serial Retentate 14 TU Graz I Institute of Chemical Engineering and Environmental Technology Recycle Permeate Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Calculation procedure Determine the recovery βͺ Establish balances βͺ Establish transport through membrane βͺ Calculate streams βͺ Determine recovery 15 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: parallel 16 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: parallel βͺ Establish blalances 0 = πΉαΆ − παΆ − π αΆ αΆ πΉ − π π₯ αΆ π − ππ₯ αΆ π 0 = πΉπ₯ βͺ Establish transport through membrane 17 παΆ = π΄ π₯π παΆ = π΄ 1−π₯π ∗ π«1 ∗ ππΉ ∗ π₯πΉ +π₯π 2 …(1) …(2) − ππ ∗ π₯π …(3) π₯πΉ +π₯π ) 2 …(4) ∗ π«2 ∗ ππΉ ∗ (1 − TU Graz I Institute of Chemical Engineering and Environmental Technology − ππ ∗ 1 − π₯π 4 unknowns 4 equations Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: parallel βͺ Same process as with point a) βͺ Rearrange and insert the equations 18 Purity 0.982 Yield 0.050 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: parallel βͺ Same process as with point a) (1) into (2) αΆ πΉ − ππ₯ αΆ π πΉπ₯ π₯π = πΉαΆ − παΆ βͺ Eleminating παΆ in equation (3)&(4) 19 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: serial permeate p=3 bar 20 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: serial permeate βͺ Same process with all shemas Purity Yield 21 TU Graz I Institute of Chemical Engineering and Environmental Technology 0.634 0.891 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: serial retentate 22 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: serial retentate 23 Purity 0.760 Yield 0.491 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: recycle permeate p=3 bar 24 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas βͺ Four different shemas: recycle permeate βͺ Solved in an iterative way Purity Yield 25 TU Graz I Institute of Chemical Engineering and Environmental Technology 0.637 0.8837 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-3 b) Comparing process shemas Parallel Serial Permeate Purity Yield 0.982 Purity 0.050 Yield Serial Retentate 26 0.634 0.891 Recycle Permeate Purity 0.76 Purity Yield 0.491 Yield TU Graz I Institute of Chemical Engineering and Environmental Technology 0.637 0.8837 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4: Pervaporation βͺ Pervaporation is used to overcome the azeotropic point of ethanol and water and produce pure ethanol. The distillate coming from a rectification column with a mass flow of 30 kmol/h and a purity of 82% is fed into a pervaporation cell. There it will be refined to a purity of 99.9 % ethanol. a) Calculates the stream of pure ethanol gained by the secondary treatment. b) How high is the energy demand of the membrane unit to keep all streams at the same constant temperature? 27 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 Further information Process: βͺ Temperature π = 78 °πΆ βͺ Distillate pressure π = 1.0 πππ βͺ Permeate pressure π = 0.1 πππ Membrane: βͺ Membrane permeability 28 π ,αΆ π₯π π·,αΆ π₯π· π,αΆ π₯π kmol βͺ Ethanol π1 = 0.00003 barΞm2Ξh βͺ Water π2 = 0.0016 barΞm2Ξh kmol cp Δhvap78°C Ethanol 2.65 kj / kgK 851 kj / kg Antoineparameters Water 4.19 kj / kgK 2308 kj / kg (bar, °K, ln) Substance data παΆ TU Graz I Institute of Chemical Engineering and Environmental Technology A B C 12.2917 3803.98 - 41.68 11.6839 3816.44 - 46.13 Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 Assumptions βͺ Raoult's and Dalton's laws may be used for the calculation of partial pressures. ππ = πππ ∗ π₯π ππ = π ∗ π¦π βͺ The difference in partial pressure can be assumed to be linear βππ,ππ + βππ,ππ’π‘ πΰ΄₯π = 2 βͺ The enthalpy of the mixture can be calculated by adding up the pure substance enthalpies. 29 TU Graz I Institute of Chemical Engineering and Environmental Technology παΆ π·,αΆ π₯π· π,αΆ π₯π βπππ₯ = ΰ· π₯π ∗ βπ π Graz, 16.12.2021 π ,αΆ π₯π Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 Necessary equations βͺ Total balance 0 = πΉαΆ − παΆ − π αΆ βͺ Component balance αΆ πΉ − π π₯ αΆ π − ππ₯ αΆ π 0 = πΉπ₯ βͺ Antoine equation πππ = π΅ π΄−πΆ+π π βͺ Energy balance αΆ πΉ − π β αΆ π − πβ αΆ π + παΆ 0 = πΉβ βͺ Flowrate through membrane παΆ = ΰ· π«π ∗ βππ ∗ π΄ 30 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 a) Calculation procedure Stream of pure Ethanol (99.9%) βͺ Establish transport through membrane βͺ Calculate permeate concentration and flow βͺ Establish balances βͺ Calculate the mass flow of pure Ethanol 31 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 a) Flowrate pure ethanol Establish transport through membrane ππαΆ = ΰ· π«π ∗ βππ ∗ π΄ παΆ π·,αΆ π₯π· βͺ Introducing the linear difference in partial pressure ππ,πΉ − ππ,π + ππ,π − ππ,π ππαΆ = π«π ∗ ∗π΄ 2 βͺ Introducing Dalton`s and Raoult`s law π,αΆ π₯π πππ ∗ π₯π,πΉ + πππ ∗ π₯π,π − 2 ∗ ππ ∗ π₯π,π ππαΆ = π«π ∗ ∗π΄ 2 32 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 π ,αΆ π₯π Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 a) Flowrate pure ethanol P_1=........ = P/xp 1) P_2=........= P/1-xp 2) Calculate permeate concentration and flow βͺ Dividing the two permeate flows π₯π π«1 ∗ (π1π ∗ π₯πΉ + π1π ∗ π₯π − 2 ∗ π ∗ π₯π ) = 1 − π₯π π«2 ∗ (π2π ∗ (1 − π₯πΉ ) + π2π ∗ (1 − π₯π ) − 2 ∗ π ∗ (1 − π₯π )) Dividing P_1/P_2 = (P/xp)/(P/1-xp) = (1-xp)/(xp) = ...... βͺ Rearranging the Equation π₯π ∗ π«2 ∗ π2π ∗ 1 − π₯πΉ + π2π ∗ 1 − π₯π − 2 ∗ π ∗ 1 − π₯π = 1 − π₯π ∗ π«1 ∗ π1π ∗ π₯πΉ + π1π ∗ π₯π − 2 ∗ π ∗ π₯π 2 ∗ π«2 ∗ π ∗ π₯π2 + π«2 ∗ π2π ∗ 1 − π₯πΉ + π2π ∗ 1 − π₯π − 2 ∗ π ∗ π₯π = 2 ∗ π«1 ∗ π ∗ π₯π2 − π«1 ∗ π1π ∗ π₯πΉ + π1π ∗ π₯π + 2 ∗ π ∗ π₯π ∗ π₯π + π«1 ∗ π1π ∗ π₯πΉ + π1π ∗ π₯π 33 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 a) Flowrate pure ethanol Calculate permeate concentration and flow Quadratic equation π π 2 2 ∗ (π«2 − π«1 ) ∗ π ∗ π₯π + (π«1 ∗ π1 ∗ π₯πΉ + π1 ∗ π₯π + 2 ∗ π + π«2 ∗ π2π ∗ 1 − π₯πΉ + π2π ∗ 1 − π₯π − 2 ∗ π ) ∗ π₯π − π«1 ∗ π1π ∗ π₯πΉ + π1π ∗ π₯π = 0 βͺ Calculate the vapor pressure with Antoine πππ =π π΅ π΄−πΆ+π Ethanol 0.9998 bar Water 0.4369 bar π₯π = 0.679 34 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 a) Flowrate pure ethanol Establish balances βͺ mass balance 0 = πΉαΆ − παΆ − π αΆ βͺ Component balance αΆ πΉ − π π₯ αΆ π − ππ₯ αΆ π 0 = πΉπ₯ πΉαΆ ∗ (π₯πΉ − π₯π ) π αΆ = π₯π − π₯π 35 TU Graz I Institute of Chemical Engineering and Environmental Technology ππππ π αΆ = 13.22 β Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 b) Calculation procedure Calculate energy demand of unit βͺ Establish heat balance βͺ Calculate all enthalpies βͺ Calculate the energy demand 36 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 b) Energy demand heating βͺ Establish heat balance αΆ πΉ − π β αΆ π − πβ αΆ π + παΆ 0 = πΉβ βͺ Determine all the enthalpies βπΉ = ππ,1 ∗ π1 ∗ π₯πΉ + ππ,2 ∗ π2 ∗ 1 − π₯πΉ παΆ π·,αΆ βπ· ∗π π,αΆ βπ βπ = ππ,1 ∗ π1 ∗ π₯π + ππ,2 ∗ π2 ∗ 1 − π₯π ∗π 78°πΆ βπ = π ∗ ππ,1 + Δh78°πΆ ∗ π ∗ π₯ + π ∗ π + Δh 1 π π,2 π£ππ,1 π£ππ,2 ∗ π2 ∗ 1 − π₯π 37 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 π ,αΆ βπ Process Intensification & Hybrid Processes – Ex. 08 Ex. 08-4 b) Energy demand heating hF 8502.66 kj/kmol hR 9504.57 kj/kmol hP 48260.19 kj/kmol βͺ Calculate the energy demand παΆ π·,αΆ βπ· π,αΆ βπ αΆ π + πβ αΆ π − πΉβ αΆ πΉ παΆ = π β παΆ = 188.99 kW 38 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021 π ,αΆ βπ Process Intensification & Hybrid Processes – Ex. 08 CHE.822UF Process Intensification and Hybrid Processes WS 2021/22 Ex. 08: Membrane processes 39 TU Graz I Institute of Chemical Engineering and Environmental Technology Graz, 16.12.2021
