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: keller@ift.maschinenbau.uni-siegen.de

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

University of SiegenInstitute of Fluid- & Thermodynamics

Jürgen U. KELLER, Wolfgang ZIMMERMANN

Schematic diagram of a

Sensor Gas Calorimeter (SGC)

Schematic Diagram SGC

Air Thermostat

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

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

University of SiegenInstitute of Fluid- & Thermodynamics

Jürgen U. KELLER, Wolfgang ZIMMERMANN

Pressure Swing Adsorption Process (Water Vapor / Aerosorb LR4)

Isothermal Process Non-Isothermal Process

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

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

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

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

]

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

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

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)

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 : ,

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))

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

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.

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.

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)