TBP01x-2.7-bananas2-transcript.pdf

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TBP01x  -­‐  2.7  -­‐  banana  2  
Welcome  to  banana  2,  which  is  that  volumes  are  not  constant,  and  the  banana  is  about  the  
consequences   when   you   neglect   volume   changes.   For   that   I   made   an   example,   which   is  
based   on   batch   experiments,   which   happen   to   be   done   on   lab   scale   and   full   scale.   The  
following   measurements   are   done,   at   different   times,   so   we   have   time   10   hours   and   13  
hours.  And  in  the  lab  scale  we  have  volume  measurements  in  liters,  biomass  concentration  
measurements  in  gram  per  liter,  and  product  concentration  measurements  in  gram  per  liter.  
The   same   of   course   we   have   also   volume   measurements   in   cubic   meter   on   full   scale,  
biomass   concentrations   in   kilograms   per   cubic   meter   on   full   scale,   and   product  
concentrations   in   kilograms   per   cubic   meter.   So   the   following   measurements   were   done:  
1.05  L  and  0.787L,  and  you  see  that  on  lab  scale  we  have  a  sizable  volume  reduction,  which  
might  be  due  to  evaporation  of  water.  Biomass  concentrations  are  5.00  grams  per  liter  and  
9.00   grams   per   liter   three   hours   later.   Product   concentration   is   2.00   grams   per   liter   and  
4.407   grams   per   liter   at   13   hours.   On   the   full   scale   we   have   a   much   bigger   volume   at   10  
hours:  5.00  m3,  and  the  volume  change  is  also  there,  so  at  13  hours  we  have  4.90  m3  .  The  
biomass  and  the  product  concentrations  in  kg/m3  ,  which  is  of  course  the  same  as  grams  per  
liter,   on   lab   and   on   full   scale   are   exactly   the   same   at   10   hours.   But,   at   13   hours,   things   seem  
to   change,   because   we   measure   now   6.88   kg   biomass   per   m3,   and   3.38   kg   product/   m3  
which,  if  you  compare  it  with  the  lab  and  the  full  scale,  students  come  immediately  to  the  
conclusion:   the   organism   on   full   scale   performs   much   less   than   on   lab   scale,   because   the  
biomass   and   product   concentrations   are   much   lower.   And   then   they   come   forward   with  
what   we   call   a   scale   up   effect,   and   make   all   fancy   conclusions,   and   so   is   there   a   scale   up  
effect?   Students   they   say:   yes,   and   I   say:   nonsense,   because   you   followed   the   wrong  
interpretation.  When  you  have  to  compare  the  same  organism  in  two  different  conditions,  
lab  scale  and  full  scale,  the  only  safe  way  to  see  if  there  is  a  difference  in  performance  is  to  
look  at  the  q-­‐values.  In  this  case  we  have  product  and  biomass  measurements,  so  what  we  
should  do  is  µ  and  qp  .  So  what  is  µ  and  qp  ?  We  discussed  this  intensively,  that  µ  and  qp  
come  from  balances,  so  µ  comes  from  the  biomass  balance  which  we  discussed,  and  I  hope  
you   remember   that   we   come   to   the   following   conclusion   the   logarithm   of   the   amount   of  
biomass  at  in  this  case  13  hours,  divided  by  the  amount  of  biomass  at  10  hours,  should  equal  
µ   multiplied   by   the   time   difference,   which   is   3   hours.   Now   the   amount   of   biomass   at   13  
hours  is  easily  calculated  as  the  product  of  biomass  concentration  and  volume,  and  the  same  
for  10  hours.  So  when  you  do  the  calculation  you  will  find  for  the  lab  µ  =  0.1  h-­‐1.  If  you  do  
that  for  the  full  scale  with  the  same  equation,  you  calculate  the  amount  of  biomass  at  13h  
by  the  product  of  concentration  and  volume  and  the  same  for  10h,  then  you  find  at  the  full  
scale   µ   =   0.1   h-­‐1.   Using   a   fundamental   result   of   the   biomass   balance,   which   allows   you   to  
calculate  µ.  qp  ,  we  discussed  that  also  before,  can  be  found  most  conveniently  essentially  
from  the  product  balance  but  it  is  more  convenient  to  have  the  combi-­‐balance  and  I  hope  
you   remember   that   the   combi-­‐balance   tells   you   that   qp   /   µ   equals   the   amount   of   product  
produced,   which   is   basically   Np(13)   minus   Np(10),   divided   by   Nx(13)   minus   Nx(10).   So   the  
only  thing  we  have  to  do  is  now  to  calculate  for  the  lab,  this  ratio  because  this  is  the  gram  
product  in  the  lab,  so  that’s  the  product  concentration  multiplied  by  the  volume  at  13  hours,  
 
minus  the  product  concentration  multiplied  by  the  volume  at  10  hours.  You  fill  it  in.  So  that’s  
the   product,   and   then   we   have   for   the   biomass   9   multiplied   by   the   volume   at   13   hours,  
minus  5  multiplied  by  the  volume  at  10  hours,  so  that  means  that  you  have  then  the  gram  of  
biomass   produced.   If   you   fill   in   all   the   numbers   you   find   that   this   ratio   is   0.75   grams   of  
product   per   gram   of   biomass.   For   the   full   scale   you   find   also,   from   these   data   with   this  
equation,   you   also   find   0.75   gram   product   per   gram   biomass.   And   because   we   know   already  
µ,   this   equation   tells   you   that   qp¬¬   equals   0.75   multiplied   by   µ,   and   it’s   the   same   on   full  
scale   as   on   lab   scale.   So   end   of   story   is:   there   is   no   scale-­‐up   effect,   the   organism   forms  
exactly   the   same   on   lab   scale   and   full   scale,   but   because   volumes   are   changing,  
concentrations  are  changing,  but  still  the  rates  per  organism,  so  the  q-­‐values  qp  and  µ  are  
exactly  the  same.  Thank  you  very  much.  
 

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