Steady-State Volume in terms of the Feed Rate

We shall try to express the volume V and the steady-state substrate conversion Xsss = (Csf — Csss)/Csf in terms of the feed rates with the help of equations (4.25) and (4.26) for general and specific data. 

4 Steady-State Volume as a Function of the Feed Rate 

Next we multiply (4.28) by its right-hand side denominator q- Ho-Csss -V)/(KS + Csaa). After multiplying out the resulting expression on the left-hand side we obtain 

Solving (4.29) for V gives us the following function in terms of the input parameter Cxf  

If we consider a conversion (removal of substrate) rate of 99%, then there is 1% of the substrate left at the output, or Csss = 14 g/m3 since the digester receives Csf = 1400 g/m3 of substrate at its input. Notice that the variable in (4.30) is Csss and that all parameters in (4.30) are now specified. 

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