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

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The domino effect — i.e., the occurrence of a cascading chain of events when the fire, explosion, missile projection, etc., generated by an accident in one process unit causes secondary accidents in other units — is a likely scenario in many major industrial plants and has the potential for catastrophic consequences [Refs. 1, 2]. However, while in the literature there is plenty of information about accidents in single process units, the chain-of-accidents phenomenon has received much less attention. Although sophisticated models have been developed to assess the interactions among specific process units in case of accidents, few approaches have attempted to model the overall domino scenario in industrial plants¹. Nevertheless, the cited models are mainly suited for a detailed risk assessment of chains of accidents. In fact, they are quite sophisticated and require a great deal of input data and effort to carry out the analysis. However, a unified framework for preliminary risk assessment of domino effects is still missing.

In a previous paper [Ref. 3], a simplified quantitative method for domino-effect risk assessment was proposed. The method is suitable for a preliminary investigation aimed at assessing whether a domino accident scenario is likely to occur in an industrial plant, in order to determine the necessity of a more in-depth analysis. The model also enables us to quickly identify the most critical units, acting as a potential source or a target of a chain of accidents, so that proper mitigation measures can be identified early. While the method is by no means intended as a substitute for a more detailed quantitative risk assessment, it may help plant managers to carry out a rapid screening of domino-effect hazards. This paper presents an improved model, which is the outcome of an ongoing research effort. In fact, the original manual procedure has been revised and extended to include a more comprehensive set of primary accidents (vapor cloud explosion and boiling liquid expanding vapor explosion were added), improved and more detailed effects computation, and the introduction of revised rating indices and a ranking scale. This paper details all major modifications to the earlier model, and also describes a software tool implementing the proposed risk analysis procedure.

Assessing the Probability of Domino Effect Occurrence

A domino effect occurs when a "primary" accident propagates to other process units, producing "secondary" accidents (Figure 1). The likelihood of a chain of accidental events to be triggered is therefore a function of the probability P_ij that a target unit j has of being involved by the physical effects of an accident occurring in a source unit i (Figure 2). This sustains damage, resulting in a hazardous release of material and energy.

Let us consider a generic process unit i, and a set A of possible accidental events, including explosion, fragment projection, pool fire, jet fire, vapor cloud explosion and boiling liquid expanding vapor explosion which, in the following, will be denoted by subscripts EX, FP, PF, JF, VCE and BLEVE, respectively.

The overall probability P_ij of an interaction between unit i and j triggering a secondary event in unit j, provided that the initiating accident in unit i has occurred, may be expressed as:

Click to enlarge equations

(1)

and can be computed after determining, for each accident scenario, the damage area and the actual probability P_ij,A of damage to the target unit according to the specific initiating event A.

In the following, the criteria adopted for computing the damage radius extension and the value of P_ij,A will be given separately for the various initiating events considered.

Figure 1 — Scheme of a Domino Effect Chain of Accidents.

Figure 2 — Interaction Probability.

Probability of domino effect triggered by overpressure:
a) Determination of damage area radius
In the case of an explosion, either from condensed phase material or a vapor cloud at the unit location, the well-known TNT-equivalent method [Refs. 10-12] is adopted. This is used to compute the radius r_A at which the conservative threshold limit value of peak overpressure p° = 7 kPa suggested by Gledhill and Lines [Ref. 13] is obtained, which determines the boundary of the area where a major damage occurs,

(2)

where W_TNT is the TNT mass equivalent to the amount W_C of actual exploding substance,

(3)

is the equivalency factor (ranging from 0.03 to 0.1, according to the geometry of the explosion scenario), while H_C and H_TNT are the heat values of the exploding substance and TNT, respectively (H_TNT = 4643 kJ/kg). z_A is the scaled distance obtained from Equation 4 [Ref. 11] by setting the specified overpressure threshold and assuming z_A = z_eff. In Equation 4, P_At is the atmospheric pressure (Pa).

(4)

b) Determination of damage probability P_{ij, EXP}
The actual peak overpressure experienced by unit j, located at distance D_eff < r_A from unit i, is obtained by entering Equation 4 with the scaled distance z_eff = D_eff/W_TNT^1/3.

The probability P_{ij, EXP} of actual damage to unit j is then computed adopting a probit model. In this work, reference is made to the probability plots obtained from experimental data by Cozzani and Salzano [Ref. 14, 15], with reference to atmospheric vessels, pressurized vessels, elongated vessels or small equipment as follows:

Atmospheric vessels Y = –18.96 + 2.44 ln (p°)

(5)

Pressurized vessels Y = –42.44 + 4.33 ln (p°)

(6)

Elongated equipment Y = –28.07 + 3.16 ln (p°)

(7)

Small equipment Y = –17.79 + 2.18 ln (p°)

(8)

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