Page 1
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Kinetic Analysis of Sensor-Gas-Calorimeters
as Linear Passive Systems
JUERGEN U. KELLER, WOLFGANG ZIMMERMANN
Inst. Fluid- and Thermodynamics, University of Siegen, D-57068 Siegen, Germany
e-mail: [email protected]
1. Sensor-Gas-Calorimeters (SGC)
2. Calibration experiments
3. Thermodynamics of heat transfer processes
4. Theory of Linear Passive Systems (LPS)
5. Simple models and their inversion
6. Conclusions
Page 2
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Schematic diagram of a
Sensor Gas Calorimeter (SGC)
Schematic Diagram SGC
Air Thermostat
Page 3
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
DifferenzdruckmesserGasversorgung Vakuum
Sorptiv
Gas
Dampf
Druckgas-
sensor p(T)
Vorrats-
behälter
Thermostat
Isolierung
Sorbens
Druckgas-
sensor p(T)
Adsorptions-
raum
Heizung (Q)
VST
QST
QAT0
mS
Q
Sensorgas-
versorgung
Sensor-Gas-
Adsorptionskalorimeter
(SGAK) © IFT 2003
f a
A STH H Q Q
Page 4
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Non-Isothermal Gas Adsorption Processes
1st Law:
2nd Law:
Process Equations
ff
uf f f
1 1 1 1J h J dt 0
T T T T T T
Literature: J.U. Keller, Ber. Bunsenges. Phys. Chem. 91 (1987), p. 528.
f ff
p f
T p 1 1m A c ln Rln h
T p T T
sa a
a
s f
u
s
U U U J
m J
h
m
J
sa f a
q f
1 1U h h m A
T T
Page 5
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Pressure Swing Adsorption Process (Water Vapor / Aerosorb LR4)
Isothermal Process Non-Isothermal Process
Page 6
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Schematic diagram of a sensor gas
calorimeter (SGC)
Sensor gas calorimeter (SGC) for
simultaneous measurements of
adsorption isotherms and enthalpies.
© IFT, University of Siegen, 2003.
Air Thermostat
Page 7
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Calibration experiments in the SGC 0.5J to 5J
Sensor gas N2 (1.6bar), T=298K, =10s
Ohm’s heat release (red lines) Pressure signal (blue lines)
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700 800
Time [s]
Dif
fere
nce
P
ress
ure
[P
a]
0
50
100
150
200
250
300
350
400
450
500
Ele
ctri
cal P
ow
er
[m
W]
Calibration SGC
Page 8
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
0
20
40
60
80
100
120
0 200 400 600 800
Timescale for Difference Pressure Axis [s]
Diffe
rence
Pre
ssure
p(t
) [
Pa]
0
50
100
150
200
250
300
350
400
450
500
0 20 40 60 80 100
Timescale for Electrical Power Axis [s]
Ele
ctr
ical P
ow
er
[m
W]
Difference Pressure
Electrical Power
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6
Ohm's Heat Q [J]
Reduce
d P
eakare
a A
* [k
Pa s
]
2
0 525 6 211
0 9993
kPasA A* . kPas . Q
J
R .
Correlation
Peak Area (A / Pas)
Qhm’s heat (Q / J)
Calibration experiments of the SGC.
Ohm’s heat : Q= (0.5, 1.0 ... 5.0)J
Sensor gas: N2, p*=0.15MPa, T*=298K
Page 9
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Differential and integral heat of adsorption for activated
carbon AC BAX 1500 / n-butane (C4H10) at 298K.
0 1 2 3 4 5 6
0
10
20
30
40
50
60
70
80
90
100
Heat of Condensation for n-butane (20,95 kJ/mol)
Mesured differential heat of adsorption
Differenciated from integral heat of adsorption
Dif
fere
nti
al
hea
t o
f ad
sorp
tio
n [
kJ
/mo
le]
n-butane ads. [mmole/g]
0
50
100
150
200
250
300
350
400
Measurend integral heat of adsorption
Interpolated integral heat of adsorption
In
teg
ral
hea
t o
f ad
sorp
tio
n [
J/g
]
Page 10
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Calibration Experiment in SGC: Periodic Electric Power /
Ohm’s Heat and Resulting Pressure Difference
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000
Time [s]
Ele
ctr
ic P
ow
er
[mW
]
3680
3700
3720
3740
3760
3780
3800
3820
3840
Pre
ssu
re G
au
ge S
ign
al
Page 11
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Calibration Experiment in SGC: Step Funktion Electric Power
Supply / Ohmian Heat and Resulting Pressure Difference
0
20
40
60
80
100
120
0 500 1000 1500 2000 2500 3000
Time [s]
Ele
ctr
ica
l P
ow
er
[mW
]
3000
3200
3400
3600
3800
4000
4200
4400
4600
4800
Pre
ss
ure
Ga
ug
e S
ign
al
Electrical Power [mW]
Pressure Gauge Signal
Page 12
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Heat Transfer in the Sensor Gas Calorimeter
1st Law CEOS Heat Transfer
Sorbens / Sorbate
Sorptive Gas
Sensor Gas
Heat supply :
s s s sU P J C T s s f
sfJ L (T T )
f s f fU J J C T
*U J J CT * *
sgbJ L (T T )
f a a
e eP U I h h m
f
fsgJ L (T T)
p(t)-p*
p*
Sorptiv Gas (f)
Sensor Gas (sg) p(t) T(t)
T*
U
pf(t)
Tf(t)
J
J*
Ts
s
Js
f
Adsorbens (s)
Page 13
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Determination of Heat Supply (P) from Sensor Gas Temperature (T)
1st Approximation:
2nd Approximation:
Experiment:
s f *
sf *
sgb
T T T T
P(t) C T L (T T )
s f *
sf sgsgb sf sg
ssg ssg
*
sgb
T T T T
LC CP(t) T 1 C C T
L L
L (T T )
sf sg
ssg sgb 1 2T(t), C , C ,L ,L : ,
Page 14
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
3rd Approximation:
Experiment:
s f *T T T T
s f sg f s sg s f sgsgb fsg
sf fsg sf fsg fsg sf fsg
sgb sgb sgbs f sg
fsg fs fsg
*
sgb
L LC C C C C C C C CP(t) T 1 1 T
L L L L L L L
L L LC 1 C 1 C T
L L L
L (T T )
s f sg
sf fsg sgb 1 2 3T(t), C , C , C ,L ,L ,L : , ,
Determination of Heat Supply (P(t)) from Sensor Gas Temperature (T(t))
Page 15
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Transfer Functions SGC:
(rad/s)
10-4 10-3 10-2 10-1
Am
plitu
de
(U
nit
s/W
)
101
102
103
104
105
N2, 1,6 bar; (
1=355s/
2=35s)
He, 1,6 bar; (1=151s/
2=19s)
N2, 1 bar; (
1=363s/
2=26s)
N2,1,6bar ( 1=95s/ 2=42s) *)
*) Instrument modified
2 2 2 2
1 21 1
KAR
Bode Diagram of SGC (T*=25°C)
Amplitude Ratiomax min emax eminAR p p P P
Page 16
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
0
50
100
150
200
250
0 100 200 300 400 500 600 700 800
Time [s]
Pre
ssu
re D
iffe
ren
ce (
pS
G-p
*)
[Pa
]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Pressure Difference
Temperature Difference
Tem
per
atu
re D
iffe
ren
ce (
TS
G-T
*)
[K]
Adsorption of n-butane on AC BAX 1500 at 25°C.
Sensor gas temperature (SGT) and pressure (SGP), pSG(0)=1.6bar, N2.
Page 17
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Time [s]
0 200 400 600 800
Rel
ati
ve
Ch
an
ge
of
SG
-Tem
per
atu
re (
TS
G-T
*)
[K]
0,0
0,1
0,2
0,3
0,4
0,5
Der
iva
tiv
es
-0,06
-0,04
-0,02
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
SG temperature
first derivative
second derivative
Adsorption of n-butane on AC BAX 1500 at 25°C.
Sensor gas temperature (SGT), pSG=1.6bar, N2.
Page 18
University of SiegenInstitute of Fluid- & Thermodynamics
Jürgen U. KELLER, Wolfgang ZIMMERMANN
Conclusions (SGC – LPS)
1. Non-isothermal gas adsorption process experiments:
(p(t) – p*) → (T(t) – T*) →
2. Calibration experiments Ohm’s resistors:
2nd order model (Bode diagram, 10-2 s-1 < 1, 2 <10-1 s-1)
3. Resonance frequencies ( 1, 2) depend on
- sorbent (type, ms)
- sorptive gas (type, T, p)
- sensor gas (type, T, p)
4. Mixture gas adsorption processes:
Modifications of SGC needed.
f a aP(t)= h h m (t)