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TRANSIENT MODELLING OF S-I CYCLE THERMOCHEMICAL HYDROGEN GENERATION COUPLED TO PEBBLE BED MODULAR REACTOR
The extent of reaction in each reaction chamber is calculated via the above kinetics expressions.
These expressions are dependent on the concentrations of the reactant and the temperature of the
reaction chamber, via the Arrhenius expressions. This is expressed generally as:
( , )
X = X T
(9)
R C i
Ideal gas law is assumed as the equation of state in the S-I/HyS cycle model. Comparison between
ideal gas law and the Peng Robinson equation of state yielded a relative error of only 0.18% (Brown,
2009). Thus, the assumption of ideal gas law in the model of the S-I/HyS cycle is justified.
PV = M RT
(10)
R
R
The heat transfer through the intermediate heat exchanger is the crux of the coupled system. The
heat transfer through the intermediate heat exchanger is given via the following simple expression:
HX
He
R
( h − h )
Q = U ⋅ A ⋅ ΔT
= m
(11)
He,in
He,out
PBMR-268 model
The PBMR-268 is a pebble bed type high temperature gas-cooled reactor with a design power of
268 MWth. The PBMR-268 is helium-cooled and graphite-moderated, with a dynamic inner reflector
composed of graphite balls. This reactor design has many important characteristics, namely passive
safety. Additionally, the high coolant temperature makes it ideal for thermochemical hydrogen
generation. A thermal model of a PBMR-268 was developed utilising the thermal-hydraulics code
THERMIX-DIREKT. THERMIX-DIREKT solves the 2-D mass, energy and momentum balance equations
for the Ergun’s resistance model for pebble bed reactors.
A PBMR is a thermal reactor, thus delayed neutrons are the important factor in reactor response.
A thermal reactor has a time constant of about 55 seconds. In the chemical plant, Section 2 and
Section 3 have different response times. Section 2 has a response time on the order of 20 seconds,
whereas Section 3 has a response time on the order of 500 seconds. The limiting reaction rate in the
chemical plant is that of Section 3. Since the chemical plant is composed of cyclic processes, we know
that the slowest reaction rate will occur in Section 3, the HI decomposition section. The response rate
of Section 3 provides at least a first-order approximation of the overall plant response.
The PBMR-268 model is derived from the PBMR-268 design. Numerous assumptions were made
regarding the geometry of the PBMR-268 design in the benchmark specification. Some of the most
important geometric simplifications are (Seker, 2005):
• core is assumed to be 2-D (r,z);
• flattening of the pebble bed’s upper surface;
• flow channels within the reactor are parallel;
• removal of the bottom cone;
• removal of the de-fuel channel.
The intra-pebble coolant flow is simplified such that the flow occurs at equal speed in parallel
channels (Seker, 2005). The side reflector control rods are modelled as concentrations of boron in a
concentric cylinder (Seker, 2005).
A scaling analysis of the hydrogen generation by the thermochemical plant was performed. For a
steady-state power of 268 MWth in the heat exchanger, the simplified model hydrogen production
rate was scaled to 142.3 mol/s. In a transient scenario, this steady-state production rate will change.
The nuclear reactor kinetics was modelled using simple point kinetics. The point kinetics model
utilised in the calculation was developed as an analogue to the point kinetics module of the RELAP5
code. The number of delayed neutron groups considered was six. A Doppler feedback coefficient of
-0.0095 was used. Xenon feedback was also modelled, although due to the time scales considered in
this document the xenon feedback is not relevant and has almost no impact on the results.
368 NUCLEAR PRODUCTION OF HYDROGEN – © OECD/NEA 2010