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Extraction - Coggle Diagram

- - - - follow the line to extract & raffinate layer
    - - lever-arm rule
      - algebra
    - - Steps to solve problems for countercurrent single-stage extractions
        
        Amounts and compositions for L0 and V2 are usually known
        
        Calculate M, Xam, and Xcm
        
        locate M on the phase diagram
        
        draw a tie-line through point M, which locates the values of L1 and V1
        
        if the amounts of L1 and V1 are required, they can be found using lever-arm rule
    - - L0 + V2 = L1 + V1 = M (based on material balance)
        
        M = total amount of mixture in the extractor at any time
      - L0xA0 + V2yA2 = L1xA1 + V1yA1 = MXam (based on material balance)
      - L0xC0 + V2yC2 = L1xC1 + V1yC1 = MXcm (based on material balance)
  - - - calculate Xam & Xcm
      - draw L0 to Vn+1
      - connect Ln to M to extract layer
      - composition at extract and raffinate layers
    - - Vn+1 = Vn+1min
      - Vn+1
- - - - combining both equations and rearranging gives...
        
        Xcm = L0Xc0 + Vn+1yCn+1/L0+Vn+1 = LnxCn + V1yC1/Ln+V1
      - similarly, a material balance on component A can be performed
        
        Xam = L0xA0+Vn+1yAn+1/L0+Vn+1 = LnxAn+V1yA1/Ln+V1
        
        solving problems
        
        the previous equations can be used to calculate the coordinates of point M which ties together the 2 entering streams L0 and Vn+1 and the 2 exit streams V1 and Ln
        
        usually, flow and composition L0 and Vn+1 and Xan are known
        
        Ln, M, and V1 must lie in a straight line
        
        furthermore, Ln and V1 must lie on the phase envelope