**6.3. Assumptions**

138 Nuclear Power – Practical Aspects

The following application is a case study that represents the evaluation of the probability of occurrence of an external explosion pressure wave that takes place near a plant. The probability of occurrence is assessed on the condition that an accident with combustible gas

The application is not restricted to a special field of industry; plants of process industry might be in the focus as well as nuclear power plants. The application is depicted in Figure 5. It consists of plant-1 (in the focus of this study), plant-2 (gasholder e.g.), street 1 and 2 (frequented by tank-lorries that carry explosive liquids) and a river (frequented by gas-tanker that carry explosive liquids). The river is subdivided into 6 subsections; each subsection is characterised by an individual length, width and gas-tanker accident

**Figure 5.** Case study: plant-1, plant-2, river, road and hazardous scenario (gas-tanker accident)

development of explosive gas mixture (gas-tanker accident e.g. - Figure 5).

All relevant application parameters of Figure 5 are given in Table 2.

**Description Parameters** length of street 1: lS1 4,800m length of street 2: lS2 800m width w 1,860m plant 1 area: 10,000m2

radius rP 150m

**Table 2.** Relevant application parameters

plant 2 area: 13,000m2

An accident (plant-2, street 1, street 2 or river) at the coordinate (xi, yi) may cause the

Depending on the wind direction φi the cloud of gas mixture can drift to the plant. An ignition of the gas mixture close to plant-1 (within the radius rP) is in the focus of this study.

**6.2. Application** 

already occurred.

frequency.

The case study depends on the following assumptions:

**Figure 6.** Empirical accident river-section frequencies

	- plant-2: Fixed accident-coordinate (x, y) on condition that the accident already occurred.

Probabilistic Assessment of Nuclear Power Plant Protection Against External Explosions 141

**Description Distribution**

river: accident river-section empirical

wind direction φ empirical

wind speed vW empirical

**Table 3.** Parameters and distribution models

**Figure 8.** Empirical wind-speed frequencies

**6.4. Case study 1 – gas holder accident** 

time τ to ignition Exp(λ): Exp(0.01 s-1)

development of explosive

gas mixture

plant-2: accident (x, y)-coordinate fixed coordinate

street 1: accident (x, y)-coordinate U(a, b) depending on length of 4,800m and

street 2: accident (x, y)-coordinate U(a, b) depending on length of 800m and

river: accident (x, y)-coordinate U(a, b) depending on river-section area

The first case study (Figure 9) deals with a gas holder accident at plant-2. The accident at the plant-2 coordinate (x, y) may cause the development of explosive gas mixture. Depending on the wind direction φi the cloud of gas mixture can drift to the plant. An ignition of the gas mixture close to plant-1 (within the radius rP) is in the focus of this study. It is assumed that the accident coordinate (x, y) is fixed. The minimal distance dP2 from plant-2 to plant-1 is approx. 570m. Further relevant application parameters of Figure 9 are given in Table 2 and Table 3.

width of 10m

width of 10m

fixed probability: 0.3


The parameters and distribution models are given in Figures 6 to 8 and Table 3.

**Figure 7.** Empirical wind-direction frequencies


Accident-coordinate:

occurred.

occurred.

curves than in straight river-sections.

 Empirical-distributed wind direction. Empirical-distributed wind speed.

**Figure 7.** Empirical wind-direction frequencies

plant-2: Fixed accident-coordinate (x, y) on condition that the accident already

 street 1 and 2: Uniformly-distributed accident-coordinate (xi, yi) depending on the length lS1 and lS2 of the streets on condition that the accident already

 river: Uniformly-distributed accident-coordinate (xi, yi) depending on the subsection of the river on condition that the accident occurred in the river-section i. It is assumed, that the accident frequency is higher in sections with confluences or

The development of explosive gas mixture occurs with fixed probability wG.

An explosion within the radius rP around the plant is in the focus of this study.

The parameters and distribution models are given in Figures 6 to 8 and Table 3.

Exponentially-distributed ignition probability depending on the time.

**Figure 8.** Empirical wind-speed frequencies

#### **6.4. Case study 1 – gas holder accident**

The first case study (Figure 9) deals with a gas holder accident at plant-2. The accident at the plant-2 coordinate (x, y) may cause the development of explosive gas mixture. Depending on the wind direction φi the cloud of gas mixture can drift to the plant. An ignition of the gas mixture close to plant-1 (within the radius rP) is in the focus of this study. It is assumed that the accident coordinate (x, y) is fixed. The minimal distance dP2 from plant-2 to plant-1 is approx. 570m. Further relevant application parameters of Figure 9 are given in Table 2 and Table 3.

Probabilistic Assessment of Nuclear Power Plant Protection Against External Explosions 143

The methods, number of trials, the simulation time and the results like mean value, variance

The results in Figure 10 reflect the empirical distributed wind-direction, where the cloud of

**method trials time [s] mean variance fom** 

MCS-lee 1E05 6.97 3.25E-03 3.24E-03 4.43E06

biased 1E05 25.99 3.26E-03 5.35E-05 7.19E07

MCS-ffe 1E05 7.47 3.28E-03 4.44E-04 3.01E07

biased 1E05 28.19 3.33E-03 4.49E-05 7.90E07

**Table 4.** Gas holder accident - conditional probability of an explosion event within the plant area with

As the different Monte Carlo methods (Table 4) are compared it can be found out that all solutions fit a mean about approx. 3.3E-03 which verifies the results as well as the adopted different Monte Carlo algorithms. If the variance and the figure of merit are regarded the MCS in combination with the ffe and biasing techniques is the most efficient approach.

The second case study (Figure 11) deals with a tank-lorry accident on street 1 or street 2. It is assumed that the accident coordinate (xi, yi) is uniformly-distributed depending on the length of street 1 and street 2. The minimal distance dS1 from street 1 to plant-1 is approx. 595m and the minimal distance dS2 from street 2 to plant-1 is approx. 605m. Further

relevant application parameters of Figure 11 are given in Table 2 and Table 3.

gas mixture is moved in most cases into the direction north-east and north-west.

and figure of merit (fom) are listed in Table 4.

**6.5. Case study 2 – tank-lorry accident** 

**Figure 11.** Tank-lorry accident on street 1 or street 2

MCS-lee

MCS-ffe

radius rP

**Figure 9.** Gas holder accident at plant-2

### *6.4.1. Analysis*

The MCS depends on a sequence of single events:


## *6.4.2. Results*

Different ranges of conditional explosion-probability PE are depicted in Figure 10. The denotation of the different ranges of the explosion event probability PE, which is normalised on 1m2, is as follows: red area (> 1E-07/m2), orange area (≤ 1E-07/m2), yellow area (≤ 5E-08/m2), green area (≤ 1E-08/m2).

**Figure 10.** Gas holder accident - ranges of conditional explosion event probability PE/1m2

The methods, number of trials, the simulation time and the results like mean value, variance and figure of merit (fom) are listed in Table 4.


The results in Figure 10 reflect the empirical distributed wind-direction, where the cloud of gas mixture is moved in most cases into the direction north-east and north-west.

**Table 4.** Gas holder accident - conditional probability of an explosion event within the plant area with radius rP

As the different Monte Carlo methods (Table 4) are compared it can be found out that all solutions fit a mean about approx. 3.3E-03 which verifies the results as well as the adopted different Monte Carlo algorithms. If the variance and the figure of merit are regarded the MCS in combination with the ffe and biasing techniques is the most efficient approach.

### **6.5. Case study 2 – tank-lorry accident**

142 Nuclear Power – Practical Aspects

**Figure 9.** Gas holder accident at plant-2

Accident (x, y)-coordinate: fixed.

08/m2), green area (≤ 1E-08/m2).

The MCS depends on a sequence of single events:

 Wind-direction φ: empirical-distributed (Figure 7). Wind-speed vW: empirical-distributed (Figure 8). Time τ to ignition: Exp(0.01 s-1)-distributed.

Development of explosive gas mixture: fixed probability (0.3).

Different ranges of conditional explosion-probability PE are depicted in Figure 10. The denotation of the different ranges of the explosion event probability PE, which is normalised on 1m2, is as follows: red area (> 1E-07/m2), orange area (≤ 1E-07/m2), yellow area (≤ 5E-

**Figure 10.** Gas holder accident - ranges of conditional explosion event probability PE/1m2

*6.4.1. Analysis* 

*6.4.2. Results* 

The second case study (Figure 11) deals with a tank-lorry accident on street 1 or street 2. It is assumed that the accident coordinate (xi, yi) is uniformly-distributed depending on the length of street 1 and street 2. The minimal distance dS1 from street 1 to plant-1 is approx. 595m and the minimal distance dS2 from street 2 to plant-1 is approx. 605m. Further relevant application parameters of Figure 11 are given in Table 2 and Table 3.

**Figure 11.** Tank-lorry accident on street 1 or street 2
