Nuclear Production of Hydrogen, Fourth Information Exchange ...
Nuclear Production of Hydrogen, Fourth Information Exchange ... Nuclear Production of Hydrogen, Fourth Information Exchange ...
TRANSIENT MODELLING OF S-I CYCLE THERMOCHEMICAL HYDROGEN GENERATION COUPLED TO PEBBLE BED MODULAR REACTOR Figure 3: Simplified HyS cycle schematic thermochemical hydrogen generation plant, some idea of the behaviour of the coupled system is attained. In this paper, a pebble bed modular reactor (PBMR) is considered as the primary heat source for an S-I/HyS thermochemical hydrogen generation plant. This paper describes previously developed models of the S-I/HyS cycle and a PBMR-268. A general coupling methodology via the IHX is developed, and applied to these models. Finally, two nuclear reactor driven transient scenarios are considered. Simplified S-I/HyS cycle model A simplified transient analysis model of the sulphur iodine and Westinghouse hybrid sulphur cycle was presented by Brown, et al. (2009). This model is utilised in this paper via coupling to a PBMR-268 model and a simple point kinetics model. Some of the key tenants of the analysis model are summarised; however interested readers are referred to the original paper for greater detail. The S-I and HyS analysis model is a control-volume model which treats the chemical plant as a closed system. In this paper the chemical kinetics of the S-I cycle are assumed to be elementary. It is trivial to write each of the reaction rate equations from the chemical reactions themselves. Each reaction rate constant is calculated via an Arrhenius expression. In Section 1, the depletion rate of sulphur dioxide is expressed as (Brown, 2009): [ ] d SO2 2 = k1 ⋅ [ I2 ] ⋅ [ H2O] ⋅ [ SO2 ] (1) dt The chemical kinetics for Section 2 is expressed as: [ SO ] d[ SO ] d H2 dt 4 3 [ SO ] = − = k2 ⋅ 3 (2) dt Thermodynamic calculations reveal that there is a significant reverse reaction rate for the decomposition of HI (Brown, 2009). This reverse reaction rate requires an accurate consideration of several coupled reaction rate equations. These expressions are: [ 2 ] 2 = k3 ⋅ [ HI] − k−3 ⋅ [ H2 ] ⋅ [ I2 ] dt [ ] d[ I ] d H d H2 2 = dt dt 1 d[ HI] = −k3 ⋅ 2 dt 2 [ HI] + k ⋅ [ H ] ⋅ [ I ] −3 2 2 (3) 366 NUCLEAR PRODUCTION OF HYDROGEN – © OECD/NEA 2010
TRANSIENT MODELLING OF S-I CYCLE THERMOCHEMICAL HYDROGEN GENERATION COUPLED TO PEBBLE BED MODULAR REACTOR In the HyS cycle, the production rate of hydrogen is directly proportional to the production rate of SO 2 . The basis for this is Farada’s law of electrolysis, which states: NI n H2 ,rxn = n SO2 (4) 2F Readers with a substantial interest in these expressions, and the related literature review are directed to (Brown, 2009). The steady-state concentrations of reactants are shown in Table 1. Table 1: Steady-state reactant concentrations Section 1: Bunsen reaction (liquid phase, 393 K, 7 bar) Components Concentration, mol/m 3 SO 2 315.1 I 2 9 901.5 H 2 O 14 685.0 HI 2 567.8 H 2 SO 4 206.1 Section 2: H 2SO 4 decomposition (gas phase,1 123 K, 709 kPa) Components Concentration, mol/m 3 H 2 SO 4 0.1 H 2 O 34.7 SO 3 11.8 SO 2 19.5 O 2 9.8 Section 3: HI decomposition (gas phase, 773 K, 2.2 MPa) Components Concentration, mol/m 3 H 2 5.2 I 2 51.6 HI 161.1 H 2 O 148.1 Each of the reactions of the S-I cycle proceeds in a chemical reaction chamber. For each reaction chamber a full mass balance can be written. In the simplified model utilised in this paper the chemical plant is treated as a closed system. Each reaction chamber is considered to have constant volume. Thus, in each reaction chamber we can have flow into, flow out, generation and accumulation. Thus the comprehensive molar balance for each species, i, in the reaction chamber is given as: dyi dX dX MR + yimin + Δν = mi,in + νi (5) dt dt dt The reaction chamber energy balance is written in terms of the total internal energy, U. In each reaction chamber, reactant with a given energy is added, reactant with a given energy leaves, and heat is added via the intermediate heat exchanger. Thus: dU = ( m ,in i,in ) − ( i,out i,out ) i h m h + Q HX dt (6) i i Similarly the energy balance in each reaction chamber is written in terms of the total enthalpy, H: dH dP = ( mi ,inhi,in ) − ( mi,outhi,out ) + Q HX + VR dt (7) dt i i In terms of the average specific heat, this energy balance can be rewritten as: dTR dX dP MR cP = mi,in ( hi,in hi ) hRXN Q HX VR dt − − Δ + + (8) dt dt i NUCLEAR PRODUCTION OF HYDROGEN – © OECD/NEA 2010 367
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TRANSIENT MODELLING OF S-I CYCLE THERMOCHEMICAL HYDROGEN GENERATION COUPLED TO PEBBLE BED MODULAR REACTOR<br />
In the HyS cycle, the production rate <strong>of</strong> hydrogen is directly proportional to the production rate <strong>of</strong><br />
SO 2 . The basis for this is Farada’s law <strong>of</strong> electrolysis, which states:<br />
NI<br />
n H2 ,rxn = n<br />
SO2<br />
(4)<br />
2F<br />
Readers with a substantial interest in these expressions, and the related literature review are<br />
directed to (Brown, 2009). The steady-state concentrations <strong>of</strong> reactants are shown in Table 1.<br />
Table 1: Steady-state reactant concentrations<br />
Section 1: Bunsen reaction (liquid phase, 393 K, 7 bar)<br />
Components Concentration, mol/m 3<br />
SO 2 315.1<br />
I 2 9 901.5<br />
H 2 O 14 685.0<br />
HI 2 567.8<br />
H 2 SO 4 206.1<br />
Section 2: H 2SO 4 decomposition (gas phase,1 123 K, 709 kPa)<br />
Components Concentration, mol/m 3<br />
H 2 SO 4 0.1<br />
H 2 O 34.7<br />
SO 3 11.8<br />
SO 2 19.5<br />
O 2 9.8<br />
Section 3: HI decomposition (gas phase, 773 K, 2.2 MPa)<br />
Components Concentration, mol/m 3<br />
H 2 5.2<br />
I 2 51.6<br />
HI 161.1<br />
H 2 O 148.1<br />
Each <strong>of</strong> the reactions <strong>of</strong> the S-I cycle proceeds in a chemical reaction chamber. For each reaction<br />
chamber a full mass balance can be written. In the simplified model utilised in this paper the chemical<br />
plant is treated as a closed system. Each reaction chamber is considered to have constant volume.<br />
Thus, in each reaction chamber we can have flow into, flow out, generation and accumulation. Thus<br />
the comprehensive molar balance for each species, i, in the reaction chamber is given as:<br />
dyi<br />
dX <br />
dX<br />
MR<br />
+ yimin<br />
+ Δν = mi,in<br />
+ νi<br />
(5)<br />
dt dt <br />
dt<br />
The reaction chamber energy balance is written in terms <strong>of</strong> the total internal energy, U. In each<br />
reaction chamber, reactant with a given energy is added, reactant with a given energy leaves, and<br />
heat is added via the intermediate heat exchanger. Thus:<br />
dU = ( m ,in i,in ) −<br />
( i,out i,out )<br />
i h m h + Q HX<br />
dt<br />
(6)<br />
i<br />
i<br />
Similarly the energy balance in each reaction chamber is written in terms <strong>of</strong> the total enthalpy, H:<br />
dH<br />
dP<br />
= ( mi ,inhi,in<br />
) − ( mi,outhi,out<br />
) + Q HX + VR<br />
dt <br />
(7)<br />
dt<br />
i<br />
i<br />
In terms <strong>of</strong> the average specific heat, this energy balance can be rewritten as:<br />
dTR<br />
dX<br />
dP<br />
MR cP<br />
= mi,in<br />
( hi,in<br />
hi<br />
) hRXN<br />
Q HX VR<br />
dt − − Δ + +<br />
(8)<br />
dt<br />
dt<br />
i<br />
NUCLEAR PRODUCTION OF HYDROGEN – © OECD/NEA 2010 367
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