1. Introduction

The nuclear reactor systems are sufficiently complex that there could be the possibility of an accident followed by the release of fission product (FPs). Such a release could require multiple failures of safety systems and barriers. In the case of a break in the hot/cold leg in a pressurized water reactor (PWR), coolant and energies are first released from the reactor coolant system to the containment through the break. The FP also released along with the coolant. This type of accident usually occurs in the high-pressure cold leg. The worst

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

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.

given by [26]. Koo et al. [27] have proposed a model describing pallet oxidation and bubble formation at grain boundaries, their interlinkages, and release into exposed surfaces. Avanov [28] described a good model for the description release of FPs from the porous ceramic fuel, its leakage from cladding and mixing with the primary coolant. Tucker and white [29] have proposed an analytical model for the estimation of FPs from ceramic UO2 fuel. In this model, the PF leakage probabilities from the fuel interior through grain are figured out. These probabilities strongly depend on the interconnectivity of pores in the ceramic fuel. Awan et al. [30] have also carried out the numerical simulation of FP activity in the reactor primary coolant. The proposed developed model is hybrid and analyzes the static and dynamic FP activity in

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

The goal of this chapter is to carry out the numerical simulation of FP behavior inside the reactor containment building under LOCA using MATLAB. The calculation process of iodine and other FPs is shown in Figure 1. A semi-kinetic model has been developed and implemented in MATLAB to carry out the sensitivity analysis of FPs during postulated LOCA for typical 1000 MW PWR. The kinetic model is presented in section II, which contains the deterministic as well as the kinetic approach. The deterministic computational methodology and computational steps flow chart are described in Section III. Next, the flow chart of model and implementation of model in MATLAB are described in Section IV. The examples and outcomes of the simulation

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].

8 < :

<sup>V</sup> mv,iðÞ� <sup>t</sup> Rres,i

3hEa

Hη<sup>i</sup> Iodine

where i indicates the isotope, whereas V and S indicate the volumetric and surface activities of

<sup>2</sup><sup>d</sup> other FPs

ηrc <sup>V</sup> mv,iðÞ� <sup>t</sup> Lr

dt <sup>¼</sup> <sup>υ</sup>tmvð Þ� <sup>t</sup> rmsð Þ<sup>t</sup> (3)

<sup>V</sup> mv,ið Þþ <sup>t</sup> ri

S

http://dx.doi.org/10.5772/intechopen.70706

45

<sup>V</sup> ms,ið Þþ <sup>t</sup> Pið Þ<sup>t</sup> (1)

. The values of various

(2)

results are presented in Section V. Finally, Section VI is the conclusion.

2. In-containment fission product release model

S

<sup>V</sup> mv,ið Þ� <sup>t</sup> <sup>α</sup> <sup>F</sup>

α ¼

dmsð Þt

th isotope. The puff release of FP is mv (t) = fx � ff � fp � fc � Ac/V g.m�<sup>3</sup>

parameters used in these simulations are listed in Table 2.

the primary coolant of the reactor [31].

dmv,ið Þt

where

i

dt ¼ �λimv,ið Þ� <sup>t</sup> ut,i

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

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 is widely used in the nuclear industry [23].

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 given by [26]. Koo et al. [27] have proposed a model describing pallet oxidation and bubble formation at grain boundaries, their interlinkages, and release into exposed surfaces. Avanov [28] described a good model for the description release of FPs from the porous ceramic fuel, its leakage from cladding and mixing with the primary coolant. Tucker and white [29] have proposed an analytical model for the estimation of FPs from ceramic UO2 fuel. In this model, the PF leakage probabilities from the fuel interior through grain are figured out. These probabilities strongly depend on the interconnectivity of pores in the ceramic fuel. Awan et al. [30] have also carried out the numerical simulation of FP activity in the reactor primary coolant. The proposed developed model is hybrid and analyzes the static and dynamic FP activity in the primary coolant of the reactor [31].

The goal of this chapter is to carry out the numerical simulation of FP behavior inside the reactor containment building under LOCA using MATLAB. The calculation process of iodine and other FPs is shown in Figure 1. A semi-kinetic model has been developed and implemented in MATLAB to carry out the sensitivity analysis of FPs during postulated LOCA for typical 1000 MW PWR. The kinetic model is presented in section II, which contains the deterministic as well as the kinetic approach. The deterministic computational methodology and computational steps flow chart are described in Section III. Next, the flow chart of model and implementation of model in MATLAB are described in Section IV. The examples and outcomes of the simulation results are presented in Section V. Finally, Section VI is the conclusion.
