2. In-containment fission product release model

Figure 1 shows the process of release of FPs from fuel to cladding, cladding to coolant and then to the containment. In this work, a 1000-MW pressurized water reactor (PWR) has been considered with the design specification as shown in Table 1. The PWR system along with the containment system is shown in Figure 2. We have developed a real-time kinetic model to simulate the FP behavior inside the containment. The analytical model is a set of coupled ordinary differential equations (ODEs). The FP activity inside the reactor containment building and on the surfaces and walls of the containment is governed by the following sets of ODEs [8, 32, 33].

$$\frac{dm\_{v,i}(t)}{dt} = -\lambda\_i m\_{v,i}(t) - \mu\_{t,i} \frac{\mathcal{S}}{V} m\_{v,i}(t) - a \frac{F}{V} m\_{v,i}(t) - R\_{vv,i} \frac{\eta\_{vv}}{V} m\_{v,i}(t) - \frac{L\_r}{V} m\_{v,i}(t) + r\_i \frac{\mathcal{S}}{V} m\_{s,i}(t) + P\_i(t) \tag{1}$$

where

condition of such an uncontrolled break is the guillotine type of break. In such type of accident, the envelope of primary systems is breached [1]. If such an accident is not controlled by safety systems, then such accidents may transform into the severe accident.

In severe accidents, FP is released during the progression of accidents [2]. Owing to the strong influence of thermal hydraulics on FP release and transportation, FP release and transport mechanism is very complicated and complex. The FP behavior inside the containment is the fundamental of the source term. The source term results are the outputs of level 2 PSA [3], which are necessary for radiological assessments and consequences. The dominant FPs that constitute in hazardous effects can be categorized as noble gasses (Xe, Kr), volatile (I, Cs, Te), semi-volatile (Ru, Ag, Ba, Sr., Tc, Rh) and nonvolatile (Nb, Zr, Y, Pd, La, Mo, Tc, Nd, Ce) ([4, 5]). The aerosols are 129Te, 127Te, 105Rh, 103Ru, 105Ru, 137Cs, 138Cs, 89Sr, 90Sr and 140Ba. These isotopes release in the particulate form, and going through agglomeration and nucleation process, they form aerosols [6]. However, iodine may transform into volatile species and possess a complex chemistry [7]. The common organic form of iodine is available in chemical forms as CH3I, CsI and HI [8]. The behavior of FP is highly influenced by the in-containment atmosphere, heat loads, containment pressure and steam generation rate. The containment is installed with the spray system and cooling fans to prevent the early over-pressurization due to the heat load. The containment spray system is significant in enhancing the early depletion of radionuclides during early in-vessel release phase from the containment atmosphere. The spray system is automatically activated, as

The FP release from a nuclear power plant (NPP) is known as a key factor affecting both the design of safety equipment and safety evaluation, including safety and risk assessment [10]. Experimental research on FP release behavior was conducted by many investigators [11–13]. Many experiments had played a significant role in understanding the behavior of aerosols, FPs, iodine chemistry, and transportation under accident situations [13–17]. The Phébus-FP project [18] was the most impressive program initiated to study the behavior of FP. The main objectives of this project were (1) to minimize the uncertainty in source term evaluation, (2) to study the FPs, structural and control rod material release transportation and deposition from the degraded core through coolant, and (3) and behavior of FP inside the containment building [19, 20]. Meanwhile, several analytical and computational codes were developed. ASTEC is one of the most popular codes used to study the behavior of FPs in severe accident conditions [21]. MELCOR along with MACCS can be used to assess FP release and assessment of radiological consequence [22]. MAAP is the most popular tool to calculate severe accident source term, and its quick calculation is its prime character. Therefore, MAAP code

Moreover, the numerical simulation of FP activity has been carried out by several researchers. [24] have developed an analytical model FIPRAP "FP Release Analysis Program" for the numerical simulation of FPs released from the fuel. The FIPRAP code can estimate the volatile FPs released from the nuclear fuel under changing irradiation conditions with the incorporation of all physical phenomena and fulfill the requirements of fuel designing, performance, degradation and source term estimation codes. Lewis et al. [25] have presented a review of FPs release modeling in support of fuel failure monitoring analysis for the characterization and allocation of defected fuel. A generalized model for FP transport in the fuel-to-sheath gap was

an emergency designed device to prevent containment integrity [9].

is widely used in the nuclear industry [23].

44 Numerical Simulations in Engineering and Science

$$a = \begin{cases} H\eta\_i & \text{Iodium} \\ \frac{3hEa}{2d} & \text{other FPs} \end{cases} \tag{2}$$

$$\frac{dm\_s(t)}{dt} = \nu\_l m\_v(t) - r m\_s(t) \tag{3}$$

where i indicates the isotope, whereas V and S indicate the volumetric and surface activities of i th isotope. The puff release of FP is mv (t) = fx � ff � fp � fc � Ac/V g.m�<sup>3</sup> . The values of various parameters used in these simulations are listed in Table 2.

Parameters Value Coolant outlet temperature (k) 592.98 Control rods 1104

Figure 2. A schematic diagram of a typical PWR system with the containment spray system.

Containment free volume V (m3

Containment free surface S (m<sup>2</sup>

Leakage rate Lr (m3

Recirculation rate Rres (m3

Mixing rate wx (s<sup>1</sup>

Spray flow rate F (m<sup>3</sup>

Parameters Symbol Value

Core damage fraction fc (%) 35% Fuel release fraction ff (%) 9.0 <sup>10</sup><sup>1</sup> Water release fraction fp (%) 3.00 <sup>10</sup><sup>1</sup>

Recirculation filtration efficiency ηres (%) 10–90% Exhaust filter efficiency ηex (%) 90–98 Fraction of immediately released radioisotopes fx (%) 2.0 <sup>10</sup><sup>1</sup>

) 57,600

) ~34,374

/s) 14.15

/s) 1–5

) 0.1–1.0

/s) 0.1–1.0

–1.0 <sup>10</sup><sup>2</sup>

Table 1. Design parameters of typical 1000 MW reactor [34, 35].

Control rod material Ag (80%)-In (15%)-Cd (5%)

Numerical Simulation of Fission Product Behavior Inside the Reactor Containment Building Using MATLAB

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47

Figure 1. The calculation process of the FP behavior inside the reactor building.


Numerical Simulation of Fission Product Behavior Inside the Reactor Containment Building Using MATLAB http://dx.doi.org/10.5772/intechopen.70706 47


Table 1. Design parameters of typical 1000 MW reactor [34, 35].

Accumulation of nuclide in reactor core for one complete fuel

Release of nuclides from damaged fuel to cladding

Leakage from Rector Vessel to coolant

Removal of iodine in coolant by absorption

natural process and spray

Leakage from to containment vessel to the environment

) 66.6

) 3.81

Particulate Elemental

Reduction by natural process and

Organic Iodine

Figure 1. The calculation process of the FP behavior inside the reactor building.

Reduction is Reduction by

Parameters Value Reactor PWR Fuel type UO2 Average fuel enrichment wt% 2.4% Specific power (MWth/kg U) 33.3

System pressure (MPa) 15.166 System pressure (MPa) 14.96 Coolant flow (kg/s) 17387.7 Core height (m) 12.41 Core active region (m) 3.65

Fuel assemblies 177 Control rod assemblies 69 Cladding material Zircaloy Fuel rod outer diameter (cm) 1.092 Rod pitch (cm) 1.443 Fuel assembly matrix 15 15 Coolant inlet temperature (k) 564.81

Other particle nuclides

Removal by natural decay a

Noble gasses reduction by absorption and deposition and

46 Numerical Simulations in Engineering and Science

spray is ignored

Power density (MWth/m<sup>3</sup>

Core diameter (m<sup>2</sup>

Figure 2. A schematic diagram of a typical PWR system with the containment spray system.



Table 2. Important parameters used for simulation [36].

### 2.1. Kinetic source of fission product

The last term in Eq. (1) is the source of FP from the reactor pressure vessel. The kinetic source is modeled as [37].

$$P(t) = \left(1 - f\_x\right) \mathbf{A}\_{\varsigma} f\_{\not\slash} f\_{\not\ll} \frac{\mathbf{K}}{V} e^{(-w\_{\overline{x}}t)} \tag{4}$$

$$K = \frac{w\_{\text{x}} \times (w\_{\text{x}}/T)}{w\_{\text{x}} - w\_{\text{x}}/T} \tag{5}$$

DL <sup>¼</sup> <sup>7</sup>:<sup>4</sup> � <sup>10</sup>�<sup>8</sup> � � � ffiffiffiffiffiffiffiffiffiffiffiffi

The values of these parameters in Eqs. (9)–(12) are listed in Table 3.

Parameters Symbols Values

Reynolds number Re 1.29 Schmitt number Sc 1.742 Molar weights of solvent Ml (g/mole) 18.01528 Temperature T (K) 80 + 273.15

Viscosity μl (centipoise) 0.35

Table 3. Numerical data for spray removal term ([36, 38]).

Step 2 Fission product coolant inventory

Step 4: Amount of Fission in available to release from Containment

Figure 3. Flow chart of incontinent FP source term estimation.

ssion pr

Step 3: Amount of Fission product release with coolant

Molecular volume of I2 υ (cm<sup>3</sup>

Spray flow rate F (m<sup>3</sup>

3. Deterministic computational methodology

Step 1. Fission Product Core inventory Determination of failed fuel fraction and

Degree of solvent x 2.6 for H2O

μl

Partition coefficient H 200 (for pH 5.0), 5000 (for pH 9.5) and 10,000 (Na2S2O3)

/g) 71.5

/sec) 0.35

Several steps are involved in the simulation of FP behavior inside the reactor building starting from the generation of FP in fuel along with the fuel burn-up. Leakage of FP into the coolant and then from the coolant to containment along with the leakage of coolant. The computational steps are listed in Figure 3. A two-stage methodology has

Fission Product removal with natural

fission product escape rate Determination of escape rate of fission products

Process Fission Product Scrubbing with Spray system

Fission product leakage from fuel

Fission product removal in coolant

ð Þ xMl <sup>p</sup> � <sup>T</sup>

Numerical Simulation of Fission Product Behavior Inside the Reactor Containment Building Using MATLAB

<sup>υ</sup><sup>0</sup>:<sup>6</sup> (12)

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49

The (1�fx) exp.(�wxt) is the airborne FP activity released along with the coolant with mixing rate wx. Where K is the normalization constant and expressed as follows. The overall radioactive mass inventory, including kinetic and static parts, is depicted in Eq. (6).

$$A\_c = f\_x A\_c + \left(1 - f\_x\right) A\_c B \int\_0^T e^{-w\_x t} dt\tag{6}$$

### 2.2. Fission product removal with spray

The removal of iodine and aerosols from the containment with the spray system can be expressed as depicted in Eqs. (7) and (8), where mri and mra are the removal rates of iodine and aerosols, respectively.

$$\frac{dm\_{\rm rL,i}(t)}{dt} = P\_i(t) - \frac{H\eta\_i F}{V} m\_{v,i}(t) \tag{7}$$

$$\frac{d m\_{\rm ra,i}(t)}{dt} = P\_i(t) - \frac{\Im hFEa}{2dV} m\_{v,i}(t) \tag{8}$$

where

$$\eta\_i = \mathbf{1} - e^{-6\left(\mathbf{K}\_{\mathbb{G}} \times t\_d/d \times \left(\mathbf{H} + \mathbb{K}\_{\mathbb{G}}/\mathbf{r}\_{\mathbb{L}}\right)\right)}\tag{9}$$

and

$$K\_{G} = \frac{D\_{L}}{d} \left\{ 2.0 + 0.60 \times \text{Re}^{0.5} \times \text{Sc}^{0.33} \right\} \tag{10}$$

$$K\_L = \frac{2\pi^2 D\_L}{3d} \tag{11}$$

Numerical Simulation of Fission Product Behavior Inside the Reactor Containment Building Using MATLAB http://dx.doi.org/10.5772/intechopen.70706 49

$$D\_L = \frac{\left(7.4 \times 10^{-8}\right) \times \sqrt{\left(\text{xM}\right)} \times T}{\mu\_l v^{0.6}}\tag{12}$$


The values of these parameters in Eqs. (9)–(12) are listed in Table 3.

Table 3. Numerical data for spray removal term ([36, 38]).

2.1. Kinetic source of fission product

48 Numerical Simulations in Engineering and Science

Table 2. Important parameters used for simulation [36].

Resuspension rate s

2.2. Fission product removal with spray

and aerosols, respectively.

where

and

modeled as [37].

The last term in Eq. (1) is the source of FP from the reactor pressure vessel. The kinetic source is

� �Ac<sup>f</sup> <sup>f</sup> <sup>f</sup> <sup>p</sup><sup>f</sup> <sup>c</sup>

<sup>K</sup> <sup>¼</sup> wx � ð Þ wx=<sup>T</sup>

The (1�fx) exp.(�wxt) is the airborne FP activity released along with the coolant with mixing rate wx. Where K is the normalization constant and expressed as follows. The overall radioac-

� �AcB

The removal of iodine and aerosols from the containment with the spray system can be expressed as depicted in Eqs. (7) and (8), where mri and mra are the removal rates of iodine

> Hη<sup>i</sup> F

3hFEa

�<sup>6</sup> KG�td=d� <sup>H</sup>þKG <sup>=</sup>KL � � � �

KL <sup>¼</sup> <sup>2</sup>π<sup>2</sup>DL

K V e

> ð T

0 e �wxt

ð Þ �wxt (4)

dt (6)

<sup>V</sup> mv,ið Þ<sup>t</sup> (7)

<sup>2</sup>dV mv,ið Þ<sup>t</sup> (8)

<sup>3</sup><sup>d</sup> (11)

<sup>d</sup> <sup>2</sup>:<sup>0</sup> <sup>þ</sup> <sup>0</sup>:<sup>60</sup> � Re<sup>0</sup>:<sup>5</sup> � Sc<sup>0</sup>:<sup>33</sup> � � (10)

(9)

wx � wx=<sup>T</sup> (5)

�<sup>1</sup> <sup>≤</sup>2.3 � <sup>10</sup>�<sup>6</sup>

P tðÞ¼ 1 � f <sup>x</sup>

Parameters Symbol Value Droplet size d (micron) 100–1000 Deposition velocity (ud) (m/s) 5.5 � <sup>10</sup>�<sup>4</sup>

tive mass inventory, including kinetic and static parts, is depicted in Eq. (6).

dmrI,ið Þt

dmra,ið Þt

η<sup>i</sup> ¼ 1 � e

KG <sup>¼</sup> DL

dt <sup>¼</sup> Pið Þ� <sup>t</sup>

dt <sup>¼</sup> Pið Þ� <sup>t</sup>

Ac ¼ f <sup>x</sup>Ac þ 1 � f <sup>x</sup>
