In this summary of the course Transfer Processes (FPE-31306), which is given at Wageningen University, all lectures and all chapters of the reader are worked out in detail. In addition, findings of the assignments made during the course are included in the summary. In short: this summary contains a...
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Transfer Processes (FPE31306)
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This summary contains everything you need: the theory in the reader, the extra explanations of lectures and the knowledge/tricks that have been incorporated into the assignments. Helps me enormously in studying! With this you can really understand the profession. Incl. pictures where necessary. Little layout in doc so nice to print and mark.
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Hugo Cloudt Transfer Processes (FPE-31306)
Summary lectures, reader, and exercises Transfer Processes
(FPE-31306)
Lecture 1 – Introduction & Equilibrium thermodynamics for transfer processes
(Chapter 1 & 2)
Transfer process: a process that involves transfer of heat and/or material.
Transfer: the transport of a component (material) or heat from one phase to another phase. ->
possible types of transfer:
1. Mass transfer: the transport of a component (material) from one phase to another phase.
2. Heat transfer: the transport of heat from one phase to another phase.
Mass transfer occurs when there is a chemical potential (μ) difference, when there is a difference
between the chemical potential of component i in phase A (𝜇𝑖𝐴 ) and the chemical potential of
component i in phase B (𝜇𝑖𝐵 ):
> NO chemical potential difference: 𝜇𝑖𝐴 = 𝜇𝑖𝐵 , (thermodynamic) equilibrium -> NO mass transfer (the
amount of component i that moves from phase A to phase B is exactly the same as the amount of
component i that moves from phase B to phase A, so there is no net transport of component i from
phase A to phase B or vice versa).
> Chemical potential difference: 𝜇𝑖𝐴 ≠ 𝜇𝑖𝐵 , NO (thermodynamic) equilibrium -> mass transfer (the
amount of component i that moves from phase A to phase B is NOT exactly the same as the amount
of component i that moves from phase B to phase A, so there is net transport of component i from
phase A to phase B or vice versa).
The problems addressed during this course are usually complex, hence for solving these problems a
systematic approach is required. The systematic approach for solving the complex problems
addressed during this course exists out of the following steps:
1. Define the question(s) as compact as possible.
2. Make a large schematic drawing -> include:
- All information you have, all known variables (by denoting it with symbols at the correct positions in
the drawing).
- All unknown variables (e.g. by denoting these with symbols with a different colour at the correct
positions in the drawing).
- The system boundaries
3. Devise a solution strategy.
4. Carry out the solution strategy.
5. Check your answer, in particular:
- If the units of the found value are correct.
- If the found value is reasonable.
6. Explicitly formulate an answer (in words!) that answers the complete question(s).
7. Re-evaluate the used solution strategy.
- Was it successful?
- In what types of problems can you use it again?
Process: a system of unit operations.
Unit operation: a step in a process (sometimes one piece of equipment, sometimes multiple pieces of
equipment) that performs one specific transformation. -> 2 possible types of unit operations:
1. Separations: unit operations in which components are separated from each other.
2. Conversions: unit operations in which components are converted into different components.
,Hugo Cloudt Transfer Processes (FPE-31306)
Processes consist out of 3 parts:
1. Upstream processing (USP): all processing that happens before components enter the reactor in
which the conversion takes place, during which the components are prepared for conversion in the
reactor.
2. Conversion
3. Downstream processing (DSP): all processing that happens after components leave the reactor in
which the conversion takes place, during which components are separated from each other (e.g.
products separated from a fermentation broth).
Vapour: a gas that consists largely of components that can readily be condensed. -> a gas is called a
vapour when it consists largely of components that can readily be condensed, otherwise a gas is
simply called a gas.
E.g.:
Gaseous water = vapour (water vapour)
Gaseous nitrogen = gas (nitrogen gas)
Thus, a vapour is always a gas, but a gas not always a vapour. Because of this, for vapours the
thermodynamics of gases apply.
Transfer -> occurs when there is a driving force (𝐹𝑖 ) -> a driving force is present when there is a
potential (𝛹 (psi)) field/potential (𝛹) difference: a difference between the potential of one phase
and the potential of another adjacent phase.
- Potential (𝛹) is a relative concept, the magnitude of a potential depends how you choose the
reference point/standard state. Since you can choose a reference point/standard state in any way
you like, you always choose the magnitude of a potential in any way you like and therefore the
magnitude of a potential thus does not matter, only differences between potentials (potential fields)
matter! -> once you choose a certain reference point/standard state when solving a problem you
have to keep using this exact reference point/standard state all the time when solving this problem.
- The potentials of phases determine if transfer occurs:
> Phases with equal potentials (NO potential field) -> (thermodynamic) equilibrium, NO transfer
occurs.
> Phases with different potentials (potential field) -> NO (thermodynamic) equilibrium, transfer
occurs until (thermodynamic) equilibrium is established again. -> transfer occurs from a high
potential to a low potential, until both potentials have become equal and (thermodynamic)
equilibrium is thus established again. -> the larger the difference between the potentials, the faster
the transfer and the more complete the transfer.
- Possible types of potential fields, the resulting transfer, and the use of these potential fields and
their resulting transfer:
Potential field Results in Used in
Chemical Mass transfer Almost all processes
Heat Heat transfer Almost all processes
Gravity Settling of particles or droplets Settlers
(= example of mass transfer)
Centrifugal (exactly analogous Removal of particles or Centrifuges, cyclones
to gravity, only stronger) droplets (= example of mass
transfer)
Pressure Flow through a pipe (= All pipes and vessels
example of mass transfer)
,Hugo Cloudt Transfer Processes (FPE-31306)
Electric Electric current = flow of Electrodialysis, electrolysis
electrons (= example of mass
transfer)
Governing potential for many (thermodynamic) equilibria used in the process industry = chemical
potential (𝜇): the potential of a phase that is the result of its composition.
- Every component in a phase that is a mixture has its own 𝜇.
- The 𝜇’s of the components in a phase that is a mixture depend on the composition of this mixture.
Chemical potential of component i in a certain phase (𝜇𝑖 ):
𝜇𝑖 = 𝜇𝑖0 (𝑥𝑖 , 𝑝, 𝑇) + 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚
𝜇𝑖0 = 𝜇 of component i in a certain phase at the reference point/standard state. -> function of the
mole fraction of component i (𝑥𝑖 ) (and thus of the composition of the phase in which component i is
present), the pressure (𝑝) and the temperature (𝑇) of the phase in which component i is present. ->
as reference point/standard state usually a pure liquid (𝑥𝑖 = 1) with 𝑝 = 1 𝑏𝑎𝑟 = 105 𝑃𝑎 and 𝑇 =
25 ℃ = 298 𝐾 is chosen.
𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚 -> depends on whether component i is a gas, liquid, or solid:
𝑝 𝑔𝑎𝑠
1) Component i = gas -> 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚 = 𝑅𝑇 ln ( 𝑠𝑖 ) -> 𝜇 of component i when it is a gas (𝜇𝑖 ):
𝑝𝑖
𝑔𝑎𝑠 𝑝
𝜇𝑖 = 𝜇𝑖0 (𝑝𝑖0 , 𝑇) + 𝑅𝑇 ln ( 𝑠𝑖 ) (see page 12 of reader)
𝑝𝑖
𝑅 = gas constant (8.314 J mol-1 K-1)
𝑇 = temperature
𝑝𝑖𝑠 (also sometimes denoted as 𝑝𝑖𝑠𝑎𝑡 ) = saturation pressure/saturated vapour pressure of component
i: the pressure exerted by gaseous pure component i when it is in equilibrium with a liquid of pure
component i (the pressure exerted by a gas with only pure component i that is present above a liquid
with only pure component i). -> can be found by using Antoine’s equation:
𝐵
log(𝑝𝑖𝑠 ) = 𝐴 − (see page 12 of reader)
𝑇+𝐶
𝐴, 𝐵, and 𝐶 = constants that have different values for different compounds, since it are properties of
compounds (see table with values on page 12 of reader).
𝑝𝑖 = partial pressure of component i: the part of the total pressure of a gas mixture containing
component i that is exerted by component i. -> given by:
𝑝𝑖 = 𝑦𝑖 𝑝𝑇 (see page 12 of reader)
𝑦𝑖 = mole fraction of component i in the gas phase.
𝑝𝑇 = total pressure of the gas phase (usually ambient pressure (1 bar = 105 Pa).
𝑝𝑖0 = partial pressure of component i at the reference point/standard state. -> for vapours the
reference point/standard state is usually chosen as such that 𝑝𝑖0 = 𝑝𝑖𝑠 , so the 𝜇 of component i when
𝑣𝑎𝑝𝑜𝑢𝑟
it is a vapour (𝜇𝑖 ) is given by:
𝑣𝑎𝑝𝑜𝑢𝑟 𝑝𝑖
𝜇𝑖 = 𝜇𝑖0 (𝑝𝑖𝑠 , 𝑇) + 𝑅𝑇 ln ( 𝑠 )
𝑝𝑖
𝑝𝑖
Component i = water? -> is also called the relative humidity (𝑅𝐻): the amount of water that is
𝑝𝑖𝑠
present as gas, relative to the amount of water that could be maximally present as gas.
𝑝𝑖
𝑅𝐻 = 𝑠
𝑝𝑖
2) Component i = liquid -> 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚 = 𝑅𝑇 ln(𝑎𝑖 ) -> 𝜇 of component i when it is a liquid
𝑙𝑖𝑞𝑢𝑖𝑑
(𝜇𝑖 ):
, Hugo Cloudt Transfer Processes (FPE-31306)
𝑙𝑖𝑞𝑢𝑖𝑑
𝜇𝑖 = 𝜇𝑖0 (𝑝𝑖0 , 𝑇) + 𝑣𝑖 (𝑝 − 𝑝𝑖𝑠 ) + 𝑅𝑇 ln(𝑎𝑖 )
Usually, the reference point/standard state is chosen as such that 𝑝𝑖0 = 𝑝𝑖𝑠 , because then the same
reference point/standard state is chosen as for a vapour and that makes it possible to compare the 𝜇
𝑙𝑖𝑞𝑢𝑖𝑑
of component i when it is a liquid with the 𝜇 of component i when it is a vapour. Therefore, 𝜇𝑖 is
usually given by:
𝑙𝑖𝑞𝑢𝑖𝑑
𝜇𝑖 = 𝜇𝑖0 (𝑝𝑖𝑠 , 𝑇) + 𝑣𝑖 (𝑝 − 𝑝𝑖𝑠 ) + 𝑅𝑇 ln(𝑎𝑖 ) (see page 13 of reader)
𝑣𝑖 = molar volume of component i (m3/moli).
𝑣𝑖 (𝑝 − 𝑝𝑖𝑠 ) = term that corrects the equation as such that it takes into account the actual pressure
(𝑝) instead of the pressure 𝑝𝑖𝑠 that was chosen to be the pressure of the reference point/standard
state. -> in some cases this term is important (e.g. in membrane processes like reverse osmosis),
however in most applications this term is negligibly small compared to the term 𝑅𝑇 ln(𝑎𝑖 ) and
therefore this 𝑣𝑖 (𝑝 − 𝑝𝑖𝑠 ) term is often neglected. Hence, in most applications the following equation
𝑙𝑖𝑞𝑢𝑖𝑑
for 𝜇𝑖 is used:
𝑙𝑖𝑞𝑢𝑖𝑑
𝜇𝑖 = 𝜇𝑖0 (𝑝𝑖𝑠 , 𝑇) + 𝑅𝑇 ln(𝑎𝑖 )
𝑎𝑖 = activity of component i. -> given by:
𝑎𝑖 = 𝛾𝑖 𝑥𝑖 (see page 13 of reader)
𝑥𝑖 = mole fraction of component i in the liquid phase.
𝛾𝑖 = activity coefficient of component i.
> Is a function of the concentration of component i.
> Can be calculated by using semi-empirical models (e.g. Margules, Van Laar, Wilson, NRTL (see page
15 of reader)).
> Approach a certain constant value in a specific situation and can for this situation thus be estimated
to have this certain constant value and can thus be normalised to this certain constant value. ->
situation in which this normalisation of activity coefficients can be performed = situation in which
there is a mixture of 2 components (component 1 & component 2) and in which 𝑥1 approaches 1
(𝑥1 → 1) and 𝑥2 approaches 0 (𝑥2 → 0), or vice versa. -> how this normalisation of activity
coefficients is then performed depends on whether it is done based on Raoult’s law or based on
Henry’s law:
a. Normalisation of activity coefficients based on Raoult’s law (the reference point/standard state is
chosen at pure component 2):
𝑥1 → 1? -> 𝛾1 → 1
𝑥2 → 0? -> 𝛾2 → 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 (can be much higher than 1)
b. Normalisation of activity coefficients based on Henry’s law (the reference point/standard state is
chosen at an ideal dilute solution of component 2 (solute) in component 1 (solvent)):
𝑥1 → 1? -> 𝛾1 → 1
𝑥2 → 0? -> 𝛾2 → 1
The 𝛾 based on Raoult’s law (𝛾) is related to the 𝛾 based on Henry’s law (𝛾 𝐻 ).
E.g. relation between the 𝛾 of component 2 based on Raoult’s law (𝛾2 ) and the 𝛾 of component 2
based on Henry’s law (𝛾2𝐻 ):
𝛾2 𝐻2,1
= 𝑝𝑢𝑟𝑒 (see page 14 of reader)
𝛾2𝐻 𝑎2
𝐻2,1 = Henry coefficient
𝑝𝑢𝑟𝑒
𝑎2 = activity of pure component 2
3) Component i = solid (e.g. the case in a crystallisation) -> 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑒𝑟𝑚 = 𝑅𝑇 ln(𝑎𝑖𝑠 ) -> 𝜇 of
component i when it is a solid (𝜇𝑖𝑠𝑜𝑙𝑖𝑑 ):
𝜇𝑖𝑠𝑜𝑙𝑖𝑑 = 𝜇𝑖0 (𝑝𝑖0 , 𝑇) + 𝑅𝑇 ln(𝑎𝑖𝑠 )
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