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(Mass) Balance

<question type="BALANCE">

  <text>
    Please setup a product balance over a typical cultivation with non-growth-associated production in a batch reactor.
    Select all relevant entries, so ignore entries that are zero.
  </text>

  <hint mintries="1">Draw a picture of a batch reactor.</hint>

  <hint mintries="2">You only need one term for accumulation, none for transfer and one for reaction</hint>

  <hint mintries="4">The answer for reaction is q<sub>p</sub> • M<sub>x</sub>.</hint>

  <acc>

    <option correct="0">

      <choice>d(M<sub>s</sub>)/dt</choice>

      <feedback>The d(M<sub>s</sub>)/dt term isn't appropiate for the product balance.</feedback>

    </option>

    <option correct="0">

      <choice>d(M<sub>x</sub>)/dt</choice>

      <feedback>While there is biomass in this reactor, you where asked to set up a product balance, not a biomass balance.</feedback>

    </option>

    <option correct="1">

      <choice>d(M<sub>p</sub>)/dt</choice>

    </option>
    <correct>Your accumulation section is correct.</correct>

  </acc>

  <flow>

    <option correct="0">

      <choice>C<sub>p,in</sub></choice>

      <feedback>C<sub>p,in</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>-C<sub>p,in</sub></choice>

      <feedback>-C<sub>p,in</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>C<sub>p,out</sub></choice>

      <feedback>C<sub>p,out</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>-C<sub>p,out</sub></choice>

      <feedback>-C<sub>p,out</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>V • C<sub>p,in</sub></choice>

      <feedback>V • C<sub>p,in</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>- V • C<sub>p,in</sub></choice>

      <feedback>- V • C<sub>p,in</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>V • C<sub>p,out</sub></choice>

      <feedback>V • C<sub>p,out</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>- V • C<sub>p,out</sub></choice>

      <feedback>- V • C<sub>p,out</sub> does not have the correct units for a biomass balance (kg/s)</feedback>

    </option>

    <option correct="0">

      <choice>Φ<sub>v</sub> • C<sub>p,in</sub></choice>

      <feedback>There is no biomass in the ingoing stream!</feedback>

    </option>

    <option correct="0">

      <choice>- Φ<sub>v</sub> • C<sub>p,in</sub></choice>

      <feedback>Incoming biomass is not a negative transfer, it is positive!</feedback>

    </option>

    <option correct="0">

      <choice>Φ<sub>v</sub> • C<sub>p,out</sub></choice>

      <feedback>Outgoing biomass is not a positive transfer, it is negative!</feedback>

    </option>

    <option correct="0">

      <choice>- Φ<sub>v</sub> • C<sub>p,out</sub></choice>

    </option>

    <option correct="0">

      <choice>Φ<sub>v</sub> • V • C<sub>p,in</sub></choice>

      <feedback>There is no biomass in the ingoing stream!</feedback>

    </option>

    <option correct="0">

      <choice>- Φ<sub>v</sub> • V • C<sub>p,in</sub></choice>

      <feedback>Incoming biomass is not a negative transfer, it is positive!</feedback>

    </option>

    <option correct="0">

      <choice>Φ<sub>v</sub> • V • C<sub>p,out</sub></choice>

      <feedback>Outgoing biomass is not a positive transfer, it is negative!</feedback>

    </option>

    <option correct="0">

      <choice>- Φ<sub>v</sub> • V • C<sub>p,out</sub></choice>

    </option>

     <correct>Your transfer section is correct.</correct>

  </flow>

  <prod>

    <option correct="0">

      <choice>Y<sub>px</sub> • M<sub>x</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>Y<sub>px</sub> • M<sub>x</sub> • μ</choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>Y<sub>px</sub> • C<sub>x</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>Y<sub>px</sub> • C<sub>x</sub> • μ</choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>M<sub>x</sub> / Y<sub>px</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>M<sub>x</sub> • μ / Y<sub>px</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>C<sub>x</sub> / Y<sub>px</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>C<sub>x</sub> • μ / Y<sub>px</sub></choice>

      <feedback></feedback>

    </option>


    <option correct="1">

      <choice>q<sub>p</sub> • M<sub>x</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>q<sub>p</sub> / M<sub>x</sub></choice>

      <feedback></feedback>

    </option>

    <option correct="0">

      <choice>M<sub>x</sub> / q<sub>p</sub></choice>

      <feedback></feedback>

    </option>



     <correct>Your reaction section is OK</correct>

  </prod>

  <correct>Very good! The product balance over a typical cultivation with non-growth-associated production in a batch reactor is:
    d(M<sub>p</sub>)/dt = q<sub>p</sub> • M<sub>x</sub>.<br/>
    q<sub>p</sub> can have all sorts of relations and is different for every product.
  </correct>

</question>