Patent ID: 11873541
Assignee: JIANGXI UNIVERSITY OF SCIENCE AND TECHNOLOGY
Field: Materials, metallurgy (Chemistry)
Classification: CPC C  G  Y | IPC C  G

Claim 5:
6. The method for determining the source sink term in the ionic type rare earth ore leaching process according to claim 1, wherein the method of building the source sink term model is that the rare earth leaching of the ionic type rare earth ore sample comprises three processes:
(1) ammonium ions reach the surfaces of rare earth ore sample particles through a diffusion layer,
(2) the ammonium ions and the rare earth ions adsorbed on the surfaces of the rare earth ore sample particles undergo ion exchange reaction, and
(3) the desorbed rare earth ions get into an external solution through the diffusion layer;
the process that the ammonium ions and the rare earth ions pass through the diffusion layer is described by the Fick law, and the ammonium ions and the rare earth ions pass through the diffusion layer may be respectively calculated through a relational expression (2) and a relational expression (3):
the relational expression (2) and the relational expression (3) are, -
          
            
              dN
              RE
            
            dt
          
        
        =
        
          
            1
            3
          
          ⁢
          
            m
            s
          
          ⁢
          
            
              
                C
                lq
                
                  NH
                  4
                
              
              -
              
                C
                in
                
                  NH
                  4
                
              
            
            
              
                α
                
                  NH
                  4
                
              
              ⁢
              
                M
                
                  NH
                  4
                
              
            
          
        
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          
            -
            
              
                dN
                RE
              
              dt
            
          
          =
          
            
              m
              s
            
            ⁢
            
              
                
                  C
                  in
                  RE
                
                -
                
                  C
                  lq
                  RE
                
              
              
                
                  α
                  RE
                
                ⁢
                
                  M
                  RE
                
              
            
          
        
        ;
      
    
    
      
        (
        3
        )
      
    
  

wherein in the relational expression (2) and the relational expression (3), NRE is the number of moles of the rare earth ions adsorbed on the surfaces of rare earth ore particles; t is time; d is a derivative symbol; ms is the mass of the rare earth ore sample; ClqNH4 and ClqRE are the concentrations of the ammonium ions and the rare earth ions in the external solution, respectively; CinNH4 and CinRE are the concentrations of the liquid phase ammonium ions and the liquid phase rare earth ions near the surfaces of the rare earth ore sample particles, respectively; αNH4 and αRE are parameters related to diffusion coefficients of the ammonium ions and the rare earth ions in the diffusion layer, respectively; MNH4 and MRE are the molar masses of the ammonium ions and the rare earth ions, respectively;
the ion exchange reaction between the ammonium ions and the rare earth ions adsorbed on the surfaces of the rare earth ore sample particles is described by a relational expression (4);
the relational expression (2), the relational expression (3) and the relational expressions (5) to (7) are substituted into the relational expression (4) to obtain a relational expression (8):, K
          =
          
            
              
                
                  (
                  
                    
                      
                        
                          M
                          RE
                        
                        
                          3
                          ⁢
                          
                            M
                            
                              NH
                              4
                            
                          
                        
                      
                      ⁢
                      
                        C
                        
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                        
                          NH
                          4
                        
                      
                    
                    -
                    
                      
                        
                          V
                          L
                        
                        
                          m
                          s
                        
                      
                      ⁢
                      
                        C
                        
                          lq
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                        RE
                      
                    
                    +
                    
                      
                        
                          V
                          L
                        
                        
                          m
                          s
                        
                      
                      ⁢
                      
                        C
                        lq
                        RE
                      
                    
                  
                  )
                
                3
              
              ⁢
              
                (
                
                  
                    C
                    lq
                    RE
                  
                  -
                  
                    
                      α
                      RE
                    
                    ⁢
                    
                      
                        dC
                        s
                        RE
                      
                      dt
                    
                  
                
                )
              
            
            
              
                
                  
                    
                      
                        (
                        
                          
                            
                              
                                M
                                RE
                              
                              
                                3
                                ⁢
                                
                                  M
                                  
                                    NH
                                    4
                                  
                                
                              
                            
                            ⁢
                            
                              C
                              
                                lq
                                ⁢
                                
                                  
                                
                                ⁢
                                0
                              
                              
                                NH
                                4
                              
                            
                          
                          +
                          
                            
                          
                          ⁢
                          
                            C
                            
                              lq
                              ⁢
                              
                                
                              
                              ⁢
                              0
                            
                            RE
                          
                          -
                          
                            
                          
                          ⁢
                          
                            C
                            lq
                            RE
                          
                          +
                          
                            
                          
                          ⁢
                          
                            
                              α
                              
                                NH
                                4
                              
                            
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                dC
                                s
                                RE
                              
                              dt
                            
                          
                        
                        )
                      
                      3
                    
                    ⁢
                    
                      
                    
                     
                  
                
              
              
                
                  
                    (
                    
                      
                        C
                        
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                        RE
                      
                      +
                      
                        
                      
                      ⁢
                      
                        
                          
                            V
                            L
                          
                          
                            m
                            s
                          
                        
                        ⁢
                        
                          C
                          
                            lq
                            ⁢
                            
                              
                            
                            ⁢
                            0
                          
                          RE
                        
                      
                      -
                      
                        
                          
                            V
                            L
                          
                          
                            m
                            s
                          
                        
                        ⁢
                        
                          C
                          lq
                          RE
                        
                      
                    
                    )
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        8
        )
      
    
  

in the relational expression (8), K is the ion exchange selection coefficient; MNH4 and MRE are the molar masses of the ammonium ions and the rare earth ions, respectively; Cs0NH4 and Cs0RE are the concentrations of the ammonium ions and the rare earth ions which are adsorbed on the surfaces of the rare earth ore particles before the ore leaching, respectively; Clq0NH4 and Clq0RE are the concentrations of the ammonium ions and the rare earth ions in the external solution before the ore leaching, respectively; ClqRE is the concentration of the rare earth ions in the external solution; CsRE is the concentration of the rare earth ions adsorbed on the surfaces of the rare earth ore sample particles; αNH4 and αRE are parameters related to diffusion coefficients of the ammonium ions and the rare earth ions in the diffusion layer, respectively; t is the time; d is the derivative symbol; ms is the mass of the rare earth ore sample; VL is the volume of the external solution;
in the relational expression (8), dCsRE/dt is the rate of change over time of the concentration of the rare earth ions adsorbed on the surfaces of the rare earth ore particles, namely the source sink term of the leaching process; dCsRE/dt is taken as a basic unknown, and the relational expression (8) is a one-unknown cubic equation, and the relational expression (8) is solved by the Cardano's formula to obtain the source sink term of the ionic type rare earth ore leaching process; a result is expressed by a relational expression (9); and parameters in the relational expression (9) can be determined by a relational expression (10) to a relational expression (15).