A Software Tool for Domino Effect Risk Assessment in Industrial Plants

by Antonio C. Caputo, Ph.D., L'Aquila, Italy

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Probability of domino effect triggered by jet fire:
a) Determination of damage area radius
In case of jet fire, given the complexity of the phenomenon, an average exposure condition is hypothesized, intermediate between the two limit conditions of a horizontal jet pointed at the target unit and a vertical jet. In both cases, it is assumed that the jet flame is stationary (i.e., burning rate equal to emission rate), with fixed shape and size dictated by a mass flow rate of m' = 30 kg/s.

In the case of a horizontal jet, the damage area radius is assumed to be equal to the flame length which, according to Cook et al. [Ref. 23], is

(18)

In the case of a vertical flame, the same procedure utilized for pool fires is adopted. Setting I_S = 12.5 kW/m² as the threshold value of thermal radiation flow, the resulting damage area radius (m) from Equation 13 is

(19)

With the actual numerical values of the involved parameters, it is always L > r. Therefore, it is conservatively assumed that the radius of the damage area is L.

b) Determination of damage probability P_ij,JF

The damage probability is computed as

(20)

where F_V accounts for the shielding effect of obstacles interposed between source and target unit, and is computed as shown in the case of a pool fire. Also, F_RP and F_RT are computed as in the case of a pool fire.

The damage factor DF is computed in a similar manner as for a pool fire on the basis of the DTR value, but assumes that the actual radiation intensity I is computed as the average of the radiation level, considering horizontal flame impinging on the target (I₁ = 280kW/m² s) and vertical flame (I₂ computed from Equation 13)

I = I1 F0 + I2 (1 - F0)

(21)

where is the orientation factor, being the impingement angle (i.e., the angle of view of the target unit from the source unit), which represents the probability that the jet actually points toward the considered target unit.

To compute DTR, the burning time t_B is the ratio of the overall fuel mass to the emission rate (in this case, assumed to be 30 kg/s).

Probability of domino effect triggered by vapor cloud explosion:
a) Determination of damage area radius
In this case, there is no predefined damage area because the vapor cloud can be transported by wind anywhere over the plant area.

b) Determination of damage probability P_ij,VCE
This probability is computed as

(22)

where P_W is the probability that wind blows from the source unit toward the quadrant where the target unit lies with respect to the source unit. P_W is assumed, based on the prevailing atmospheric conditions of the site. P_I is the cloud ignition probability and depends on the cloud mass M_C. If M_C < 1 t, then PI = 10^–3. If MC > 10 t, then P_I = 10^–1, while in the intermediate cases, P_I = 10^–2. P_K, instead, is the damage probability to the target unit, provided that the vapor cloud actually explodes in the surroundings of the unit (this occurs with probability P_D x P_I). P_K is computed from the previously adopted probit models (Equations 5-8) according to the vessel type, but assuming a mean peak overpressure p⁰_Avg, which is representative of the average value of the overpressure experienced at the target location when the cloud explodes at different possible locations along the path linking the source to the target. The generic distances of the exploding cloud to the target unit is computed as D_i=|D-PL_i|, where D is the source-target distance and PL_i = W T_i is the length of the path traveled by the cloud along the source-target direction before it explodes after the time delay T_i, with W being the average wind speed. For the sake of simplicity, four values of ignition delay times and the corresponding probability values p_Ti were assumed, namely T₁ = 0.5 min, p_T1 = 0.25; T₂ = 2.5 min, p_T2 = 0.35; T₃ = 7.5 min, p_T3 = 0.25; T₄ = 15 min, p_T4 = 0.15. Corresponding to each D_i distance, the scaled cloud-target distance z_eff,i is computed. The peak overpressure at target location p_i⁰ is computed from Equation 4. Then the average peak overpressure is computed as

(23)

where the ½ factor accounts for the fact that the explosion occurs in open air off the ground level, instead of at the ground level.

Probability of domino effect triggered by BLEVE:
a) Determination of damage area radius
The BLEVE phenomenon is considered only for those process units containing a pressurized superheated liquid. Effects of a BLEVE are overpressure, fragment projection and a fireball. Due to the typically short duration of a fireball, it is often assumed that it cannot damage process equipment. Therefore, the fireball effects are neglected here. The damage radius of a BLEVE occurring at unit i is the maximum of the damage radii computed for the fragment projection and explosion effects separately: i.e., R_i,BLEVE = max (R_i,EXP, R_i,FP).

b) Determination of damage probability P_ij,BLEVE
Damage probability of a target unit j from a BLEVE occurring at unit _i is P_ij,BLEVE = min (1, P_ij,EXP + P_ij,FP).

Domino Effect Rating Indices

According to the described model, each process unit may be either an initiator and/or a target of a chain of accidents. A domino effect may occur if an accident in unit i may affect unit j and trigger in this secondary unit a release of materials and energy with a high damage potential in the surrounding environment. Therefore, for each combination of units (i,j), two domino interaction potentials may be assessed as follows: either a Domino Source Potential DSP_i,j when unit i is the source of the primary accident and unit j is the target unit generating the secondary accident, and a Domino Target Potential DTP_j,i when unit j is the target and unit i is the primary accident source. However, according to this definition, DSP_i,j = DTP_j,i, but it should also be noted that in general, P_ij P_ji.

It follows that for each i-th major equipment or process unit that can be an initiator of the domino effect, a Domino Source Index DSI_i = f (DSP_i,j , j) is defined. This expresses the risk that the considered unit can trigger a domino effect in any other j process units located within its damage range. Conversely, for each i-th process unit, there is a defined Domino Target Index, DTI_i = f(DTP_i,j , j). This rates both the probability that the unit i can be involved in an accident initiated by the j-th unit and the amount of damage resulting from the release of materials and energy from the secondary unit. For the entire plant, a Domino Effect Potential (DEP) Index is then defined as a combination of the previous indices, computed for all units in the plant. The higher the DEP index, the higher the risk of a domino scenario occurring, while the single equipment indices DSI_i and DTI_i indicate which process unit is more critical as either a source or a target, in order to properly focus preventive and protective actions.

The Domino Source Potential of unit i with reference to unit j (or Domino Target Potential of unit j with respect to unit i) has been defined as

(24)

where P_ij has been computed as shown before and is the overall probability that unit j may be damaged by unit i, thus generating a secondary accident, S_ij is an effects amplification factor described below, M_j is the damage magnitude coefficient, and C_M,j is an effect mitigation factor.

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