Submodels in Settler block

• note: in Matlab, the top layer is denoted by smaller number (top =1 (0) ) and bottom layer is denoted by bigger number (bottom = 10 (9))

Sludge concentration in each layer (i) (Xsc[i])

Above feed layer

• Parameters required in this calculation:

  • h = height of each layer
  • X_t = threshold concentration (g/m^3) = 3000 g/m^3

• Variables required in this calculation

  • v_up = upward velocity
  • v_s = settling velocity
  • Jflow_up[i]= flux due to upward velocity = v_up*(Xsc[i])
  • Jsc[i] = solid flux due to gravity for the sludge layer above the feed layer?
    • if Xsc[i+1] <= X_t, then Jsc[i] = v_s[i]*Xsc[i]
    • if Xsc[i+1] > X_t, then Jsc[i] = min(v_s[i]Xsc[i], v_s[i+1]Xsc[i+1])

• dXsc/dt[i] = ((-Jflow_up[i] + Jflow_up[i+1]) + Jsc[i-1] - Jsc[i])/h

At feed layer

• Parameters required in this calculation:
  • h = height of each layer = 0.4 m
  • A = Area of the settler = 1500 m^2
• Variables required in this calculation:
  • Qf = Q_inflow
  • Xf = TSS_inflow
  • v_up = upward velocity
  • v_dn = downward velocity
  • Jflow_up[i]= flux due to upward velocity = v_up*(Xsc[i])
  • Jflow_dn[i]= flux due to downward velocity = v_dn*(Xsc[i])
  • Js[i] = solid flux due to gravity at feed layer
    • Js[i] = v_s[i]*Xsc[i] at feed layer
• dXsc/dt[i] = ((Qf*Xf)/A + Jsc[i-1] - Jflow_up[i] + Jflow_dn[i]- min(Js[i], Js[i+1])) / h

Below feed layer

• Parameters required in this calculation:
  • h = height of each layer = 0.4 m
  • A = Area of the settler = 1500 m^2
• Variables required in this calculation:
  • Qf = Q_inflow
  • Xf = TSS_inflow
  • v_up = upward velocity
  • v_dn = downward velocity
  • Jflow_up[i]= flux due to upward velocity = v_up*(Xsc[i])
  • Jflow_dn[i]= flux due to downward velocity = v_dn*(Xsc[i])
  • Js[i] = solid flux due to gravity at feed layer
    • Js[i] = v_s[i]*Xsc[i] at feed layer
• dXsc/dt[i] = (Jflow_dn[i-1]-Jflow_dn[i]+min(Js[i],Js[i-1])-min(Js[i],Js[i+1]))/h