A summary of the course Separation Process Design, given in the second year of the bachelor Biotechnology. This summary includes all content needed for the exam.
Sedimentation is a phase separation: suspended objects separate from the
surrounding liquid by the action of a force field (F G = mp*g). A particular case
of sedimentation is centrifugation.
The calculation of the settling velocity can be done using a force balance.
Hereby, we assume that the velocity of the particle is constant. The
important forces are the ones from gravity, buoyancy (the force of
gravity acting on the fluid displaced by an immersed particle) and the
friction -> 0 = FG + FBUOY + FFRIC. In the formulas on the right, the η is used
to describe the viscosity (stickiness) of the fluid. Substitution of the
formulas and rearrangement of the force
balance gives a formula for the velocity of a single
particle in an infinite bath of stagnant fluid.
Sometimes, there are many particles close to each
other. Richardson and Zaki found that moving
particles started to interact and added a term to the formula of velocity: the
formula has to be multiplied with (1-εs)n. n ranges between 4 and 5 here, with
an average of 4.65.
For a given height, the settling time is given by: t = H/vꙭ. The loss of suspended
cells by sedimentation can also be calculated: (v ꙭ*t)/H.
Industrial sedimentation tanks and centrifuges are mainly continuous with
respect to the liquid input and output. Solid particles can either be continuously or periodically
discharged as a slurry. In the stream, there are two phases, the solids and the liquids. A drawing can
be made just like the ones showed on the left of the page. The mass
balances are shown on the right. The efficiency of separation (Y s and Yl)
can also be calculated. For a complete separation, ε s = 0 and Ys = 1.
A sedimentation tank can be
designed. The horizontal velocity vx is
determined by φin/WH and the vertical
velocity vy by -vꙭ.
The settling time of each particle needed to reach the horizontal position: t =
LWH/ φin. The largest settling time is: t = H/ vꙭ.
Using the formulas described above, a new equation for the efficiency can be determined: Ys = (Atank*
vꙭ)/ φin.
CENTRIFUGATION
The most used centrifuges for industrial applications are:
Tubular: solids accumulate on the wall of the bowl until the bowl is almost full.
Disk: high throughput, with both continuous or intermittent solids discharge (for cells)
Decanter: particles that sediment rapidly
, Centritech: special used for harvesting animal cells, which has a low rotation speed
The centrifuge performance is related to the
geometry and the centrifugal acceleration. This
last is determined by the gravity (see image on
the left). F is the rotation frequency. The sigma
factor is often calculated for a centrifuge, which is
determined as the area (Σ = φin/vꙭ). The sigma
factor differs per type of centrifuge. A list of equations of the sigma factor is on the right. These
formulas are provided at the exam.
The efficiency of solid separation will be: Yp = (Σ*vꙭ)/φin < 1.
The main cost of a sedimentation tank is the investment, the main costs of a
centrifuge are the energy costs. Centrifuges take a lot of electrical power input to
accelerate the suspension and a lot of cooling is needed. The power and cooling
requirements can be calculated with an energy balance. The maximum speed is equal to the kinetic
energy (Ek). The total power consumption rate and the required cooling rate (P) can then be
calculated. With the sigma theory, it can be verified that P ∝ f4.
The main cost of a sedimentation tank can be calculated as followed: C investment = Cm2*Atanka. The a here
is between 0.5 and 0.6. The main cost of a centrifuge is the energy consumption.
FILTRATION
Filtration can be classified into three ways:
1. Particle filtration versus molecule filtration (different sizes of pores). Molecule filters are
always membranes.
2. Batch-wise versus continuous (rotating drum filter) filtration
3. Dead-end filtration (much dryer particle stream) versus cross-flow filtration
Batch: assume that the filter retains all particles (ε p = 0), the
particle fractions in inlet and cake (ε in and εr) don’t change in
time and the density of the fluid and of the particles are
constant.
The mass balances (on the left) can be solved by the echelon
method to find the values of Vr and Vp. The superficial velocity
can be calculated, which is the average velocity over the whole filter,
defined as: uin = φin/A.
The driving force for fluid permeation is
usually a pressure difference that is conferred to the fluid by a pump.
On the cake and the membrane, friction forces occur defined by
Darcy’s law. With this, a force balance can be made (see image on
the right).
In the beginning of a dead-end filtration process, only the filter itself
gives a significant pressure drop, so ζ cLc is equal to 0 here. In the filters, two situations can occur:
1. Constant pressure (Δppump), here φp is calculated over time
2. Constant flow rate (φp), here Δppump is calculated over time.
In some cases, not only the inlet flow contains V in, but also the
outlet. This gives new mass balances, as shown on the left. The
bottom term can be substituted into the force balance.
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