FRAUNHOFER INSTITUTE FOR SOLAR ENERGY SYSTEMS ISE
Using driving temperature difference equivalents to compare heat
and mass transport limitations in sorption modules and adsorption
heat exchangers
U. Wittstadt, E. Laurenz, G.Füldner, A. Velte, L. Schnabel
Fraunhofer Institute for Solar Energy Systems ISE, Heidenhofstrasse 2, 79110 Freiburg, Germany, Phone +49 761/4588-5408, ursula.wittstadt@ise.fraunhofer.de
PROBLEM
EXAMPLE 1: ADSORPTION SAMPLE
 The performance of adsorption modules can be limited by evaporator,
condenser or adsorber.
 Adsorption kinetics of adsorption heat exchangers (AdHX) are influenced by
different transport mechanisms (heat and mass transfer).
 For the development of both sorption modules and heat exchangers it is
important to identify the component or transfer process to be improved first,
i.e. the highest transport resistance.
Small samples, representing cutouts of an adsorber heat exchanger, are
characterized by large pressure jumps in a constant volume set-up, where the
decrease in system pressure can be directly converted into water uptake.
IDEA
 Compare transport
resistances
 In a series connection with
the same energy flow:
1
10
Time / s
Figure 1: Effective driving temperature differences in
adsorption modules and samples (cutout from AdHX)
 Saturation temperature equivalent determined by chamber pressure 𝑝 and
space averaged loading 𝑋� through working pair’s equilibrium properties
𝑇𝑠𝑠𝑠,𝑠𝑠𝑠𝑠 = 𝑇𝑠𝑠𝑠,𝑠𝑠𝑠𝑠 𝑋�, 𝑝
 Loading 𝑋� may be determined by
 weighing (if experiment allows)
𝑉
�
 mass balance in canonical set up: 𝑋 𝑡 = 𝑋0 +
(𝑝0 − 𝑝 𝑡 )
𝑚𝑠 𝑅𝑅
 energy balance in sorption modules:
𝑡
1
𝑑𝑑
̇ 𝑇𝑖𝑖 − 𝑇𝑜𝑜𝑜 − 𝑄̇𝑙𝑙𝑙𝑙 d𝑡
𝑋� 𝑡 = 𝑋0 + �
𝐶𝐴𝐴𝐴𝐴
− 𝐶𝑓𝑓
𝑑𝑑
𝑡0 𝑚𝑎𝑎 Δℎ𝑎𝑎
 Driving temperature difference for heat exchangers (with 𝑇𝑠𝑠𝑠 const. in space)
𝑇𝑜𝑜𝑜 − 𝑇𝑖𝑖
Δ𝑙𝑙 𝑇 =
𝑇𝑜𝑜𝑜 − 𝑇𝑠𝑠𝑠
ln
𝑇𝑖𝑖 − 𝑇𝑠𝑠𝑠
 Driving temperature differences are time dependent and can be reduced to
time averaged values per cycle/step, weighing with 𝑋̇ emphasizes relevant part
𝑡1
1
� Δ𝑇𝑖 𝑡 𝑋̇d𝑡
Δ𝑇�𝑖 =
𝑋1 − 𝑋0 𝑡0
T / °C
Sample
80
70
60
50
40
30
①
1
∆𝑇𝑚𝑚𝑚
② ∆𝑇𝑎𝑎−𝑤𝑤
10
Time / s
Δ𝑇�
T equivalent
10.5
5.6
100
Pressure
80
70
60
50
40
30
80
70
60
50
40
30
LPJ: 1.1  11.5 mbar
Uptake
1
10
Time / s
100
Cold plate
① ∆𝑇𝑚𝑚𝑚
②
1
∆𝑇𝑎𝑎−𝑤𝑤
25
20
15
10
5
0
∆X /wt-% // p /mbar
 Driving forces may be
compared if mapped to
temperature differences
(TD)
80
70
60
50
40
30
Temperature
25
20
15
10
5
0
100
T / °C
T / °C
LPJ: 4.0  22.3 mbar
T / °C
Transport resistance
~
Driving force
∆X /wt-% // p /mbar
Figure 2: Measurement of adsorption kinetics: Surface temperature and pressure in
measuring chamber are evaluated after large pressure jump (LPJ) (opening vale 1)
Δ𝑇�
10
Time / s
5.8
5.2
100
Figure 3: Measurement signals for LPJ (above) and temperature differences (below)
EXAMPLE 2: ADSORPTION MODULE
Sorption modules, i.e. valve-free
combinations of one AdHX with one
evaporator/condenser, are
characterized through periodic
variation of inlet temperatures. Only
the heat exchanger fluids temperatures
and mass flows as well as the vessel
pressure are measured. Losses are
quantified by steady state
measurements.
Figure 4: Set up for sorption modules
Δ𝑇�𝑖
CONCLUSION
 Driving temperature differences and inlet-outlet temperature differences are of
different nature (determined either by transport resistances or by capacity
flow) but contribute both to effective temperature lift of sorption modules
 The proposed method can be used to identify the main transport limitations of
different components within one sorption module as well as one small sample.
 To compare different modules or small samples the method can be extended
to effective transport resistances (in K/W) taking into account the energy flows
Des
Ads
Figure 5: Measured adsorption cycle of a typical sorption module with temperature
difference equivalents, averaged values as bar chart on the right
This work is supported by the German Federal Ministry of Economic Affairs and
Energy (FKZ 03ET1127 B).