tube curve tracer

Transcription

tube curve tracer

Praktikum Polymer Science/Polymerisationstechnik
Versuch „Residence Time Distribution“
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Polymerization Technology – Laboratory Course
Residence Time Distribution of Chemical Reactors
If molecules or elements of a fluid are taking different routes through the volume of a continuous
operated reactor, they will spend different times within such a reactor. The distribution of these
holding times is called the residence time distribution (RTD) of the fluid.
The RTD can affect the performance of a reactor and may also have a strong input on the
selectivity of a chemical reaction. In case of polymerization reactions the RTD can have an effect
on the molecular weight distribution of the polymer formed. This will be mainly the case when the
mean life time of the active species of the polymerization reaction is in the same order of
magnitude like the mean residence time of the reactor. In this case polymers with a narrow
molecular weight distribution can only be formed in a reactor with narrow RTD. The RTD in case
of polymerization reactions can also play a major role if the reaction mixture is a segregated
system. Segregation in the reaction mixture can easily occur if the reaction mixture is of high
viscosity or heterogeneous nature with elements which act as individual micro reactors without
exchange of mass. The RTD of a polymerization reactor is therefore an important parameter
which may affect the performance of the reactor but also the properties of the polymer formed.
1. Experimental methods for determination of RTD
Most important for determination of the RTD of a reactor is the application of a suitable tracer. A
suitable tracer should be easy to detect and the total amount of injected tracer should be
detectable at the exit of reactor.
The most important methods for the determination of the RTD are the so called pulse and step
experiments. They are easy to perform and interpret.
The pulse experiments
In this case a certain amount of a tracer is added pulse wise to the fluid entering the reactor and
the concentration-time relation of the tracer at the exit of reactor is recorded. This is shown
schematically in Fig. 1. From the balance of material for the reactor the mean time of the
concentration-time distribution can be found.
∞
Mean time (holding time):
t=
∫tCdt
0
∞
∫Cdt
=
∑ t i C i ∆t i
i
∑ C i ∆t i
[s]
i
0
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Residence Time Distribution (SS 2007)
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introduced amount
of tracer, M [kg]
Tracer
concentration
[kg/m3]
∞
Area =
∫Cdt
=
∑
C i ∆ti
i
0
time [s ]
Tracer pulse input
Flow rate, v [m3/s]
Reactor
V [m3]
Tracer pulse output
Fig. 1: Tracer concentration-time correlation of a pulse experiment
To find the RTD which is also called the exit age distribution E concentration-time distribution
has to be normalized in such a way that the area under the distribution curve is unity. For doing
this the concentraion readings have to be divided by the area under the concentration curve. This
is shown in Fig. 2. The relationship between C and E curves only hold s exactly for reactors with
so called closed boundary conditions. This means that the fluid only enters and only leaves the
reactor one time. No dispersion of tracer at the boundaries of reactor should happen. Very often it
is convenient to use a dimensionless Eθ curve for reasons of comparison of reactors. In this case
time is measured in terms of mean residence time θ = t / t . Then Eθ = t ⋅E .
v
M
[1/s]
E =C
C
[kg/m3]
Area = M/v
time [s]
Area = 1
time [s]
Fig. 2: Transforming the experimental concentration curve into the exit age curve
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The step experiment
In this case the tracer is not introduced pulse wise into the fluid entering the reactor but is
introduced in a continuous way by injecting a constant side stream of tracer to the fluid entering
the reactor and measuring the outlet tracer concentration C versus time as shown in Fig. 3. The
mean residence time is given by following equation:
Cmax
t=
∫tdC
0
Cmax
∫dC
=
1
Cmax
C max
0
∫tdC
0
Fig. 3: Tracer concentration-time correlation of a step experiment
The dimensionless form of the concentration curve is called F curve or transition function. Here
the tracer concentration is rising from zero to unity with time (see Fig. 4).
Fig. 4: Transforming the experimental tracer concentration curve into the F curve (transition
function)
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2. RTD of plug flow and mixed flow reactors
Fig. 5 is showing the residence time distribution of a plug flow tubular reactor, a single well mixed
stirred tank reactor and of a cascade of N equal size well mixed stirred tank reactors which are
connected to each other in series. The most narrow distribution is shown by the plug flow tubular
reactor and the cascade of stirred tank reactors with an infinite number of vessels. The broadest
RTD results in case of a single stirred tank reactor. The RTD of equal sized stirred tank reactors
with mixed flow is given by the following equations:
N− 1
1 t 
E=  
t t 
−
NN
e
(N − 1)!
Nt
t
with t = N ⋅t i (N = number of reactors).
F = 1− e
−
Nt
t
N− 1
 Nt 1  Nt 2
1
 Nt  
+
1 +
  + ... +
  
(N − 1 )! ) t  
t
2!  t 


1
plug flow
2
N
mixed flow in series
mixed flow
1
N=1
5
∞
t
t
∞
5
1
t
1
t
t
∞
1
1
5
1
1
θ
Fig. 5: RTD of different ideal reactors: PFTR, HCSTR and Cascade of HCSTRs (from
Levenspiel)
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3. RTD of reactors with non-ideal flow pattern
In reality the flow pattern of reactors deviate from plug or mixed flow patterns. This is especially
the case for polymerization reactors in which a polymer solution or dispersion with high viscosity
is flowing through the volume of reactor causing a non-ideal flow pattern. Non-ideal flow patterns
can result for example if the reactor volume contains so called dead or stagnant regions or if
bypass or recycle flow is present next to the active flow through reactor regions of plug and
mixed flow. If these non-ideal flow patterns are present in a given reactor they can be seen easily
by looking at the corresponding experimental RTD. The following models can be used to describe
the measured RTD of real reactors with deviation from ideal flow:
•
•
•
•
Compartment Model
Dispersion Model
Tanks-In-Series Model
Convection Model (for laminar flow)
In Fig. 6 compartment flow models are given for a tubular and a stirred tank reactor which are
characterized by the presence of dead zones and bypass. The dispersion and tanks-in-series
E
E
t
E
E
t
Fig. 6: Compartment models for tubular and stirred tank reactor with dead
zone and bypass (from Levenspiel)
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model is used in general when small deviations from plug flow are expected. They are one
parameter models. A dispersion number is used in case of the dispersion model whereas the
number of stirred tanks is used in case of the tanks-in-series model. In Fig. 7 the correlation
between dispersion and hydrodynamics of different liquids flowing in pipes are given.
water
Dispersion
number
Reynolds number
Fig. 7: Correlation between dispersion number and Reynolds number of three different
liquids flowing in pipes. Dispersion number: Dax uL , Reynolds number: udρ η ,
Schmidt number: η ρD
The convection model is used if a viscous liquid is pumped through a tubular reactor. In general
the flow is of laminar characteristic with a parabolic velocity profile. Thus the spread in residence
times is caused only by velocity variations. The velocity profile of a laminar flow is shown
together with the corresponding RTD in Fig. 8.
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L
u max = 2u
d
4
Eθ
3
2
1
0
0,5
1
1,5
θ=
t
t
Fig. 8: Parabolic flow velocity profile and residence time distribution of laminar
flow in pipe
4. Experimental
RTD of tubular reactor and continuous stirred tank reactor
4.1 Pulse experiments in tubular reactor
• Put selector valve of laboratory set to tubular reactor position
• Switch on conductimeter. Put selector switch for test data to “Strömungsrohr”.
• Settings of conductimeter:
Temp.: 20°C
Coeff%K-1: 1
• Settings of recorder:
Speed: 200 mm/min
Range: 20 mV
Zero line to 90 % scales on the paper
• 3 measurements at various flow rates:
50 l/h with 1,5 ml KMnO4/KCl solution for marking
(see diagram for flow rates).
Marking solution with 12,5% KCl
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• Before starting each measurement check the flow rate at the rotameter and wait for
constance of the zero line.
• Inject the marking solution quickly and mark the starting point on the recorder paper.
• Measurement is finished at constant conductivity.
4.2
Pulse experiments in stirred tank reactor:
• Close water cock!!!
• Put selector valve to stirred tank reactor position
• Flow rate at the rotameter: 60 l/h
• When the stirring tank is filled with water, switch on the stirrer.
• Stirrer: 50 and 600 RPM
• Reactor volume: 1400 ml
• Settings of recorder:
Speed: 50 mm/min
Range: 20 mV
Zero line to 90 % scales on the paper
• 2 measurements at each stirring rate with and without dead water zone (100ml)
for each experiment use 2,0 ml of the KMnO4/KCl solution for marking.
• Marking solution with 25% KCl
4.3 Step experiments in stirred tank reactor:
• Flow rate at the rotameter: 60 l/h
• Stirrer: 200 RPM
• Reactor volume: 1400 ml
• Settings of recorder: like 2
• 2 measurements with and without dead water zone (100ml pipette)
for each experiment use 25% KCl solution and the flexible-tube pump for marking.
4.4 Report:
• Estimate E and F curves for all pulse and step experiments
• Compare hydrodynamic residence time (VR / V& ) with experimental residence time (mean
time).
• Determine influence of stirrer speed, dead water zone and flow rate on residence time
distribution and discuss extensive all results
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tube curve tracer

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