A study on the use of fireproof protection in offshore topside steel structures subject to localised fires

Abstract

Localised fires are an important accidental scenario for the offshore industry due to the extent of their potential damage. Its consequences may be localised damage, weakening of structural elements, blast when a storage tank reaches its critical temperature, or the structure's progressive collapse. The correct sizing of the fire protection (passive and/or active) system allows reducing or delaying the potential structure's damage. This article evaluates the use of the LF-ESF methodology at the design stage to estimate the efficiency of the passive fire protection layer (PFP) in upper offshore structures exposed to localised fires. Fire conditions are assumed to result from a typical process involving the combustion of hydrocarbons. Three fire scenarios are evaluated using the LF-ESF model proposed by the authors and based on updates of simple methodologies widely used in the literature. In order to verify its accuracy, its results are compared with a model developed in a CFD-based package for a fire scenario. Thermo-mechanical analysis is performed employing a finite element model that considers the temperature-dependent physical and geometric non-linearities. The estimated thermal load is entered into the thermo-mechanical model in combination with the pre-existing operational loads to evaluate the structure's behaviour. Despite the slight overestimation of the thermal field from the LF-ESF model, compared to the CFD-FEM methodology, the results obtained allow the selection of the PFP without being too conservative and at low computational cost.

Annex I: LF-ESF model

The model is limited to cases where the height of the flame (${H}_{fl(t)}$ [m]) estimated according to the Heskestad model [28]) is less than the height of the compartment ${H}_{c}$ (${H}_{ {\text{fl}} }<{H}_{\rm{c}}$).

$${H}_{ {\text{fl}} (t)}=-1.02D+0.235{\left({ {\text{HRR}}}_{(t)}\right)}^{2/5}$$

(A.1)

1.1 Convective heat flux

According to Heskestad & Hamada—H&H [28] the plume centerline temperature ${\Delta \theta }_{o}$ [^oC] is calculated according to Eq. (A.2) [28, 30, 38].

$${\Delta \theta }_{\rm{o}(t)}=0.25{\left[1000\left(1-{\chi }_{\rm{r}}\right){ {\text{HRR}}}_{(\rm{t})}\right]}^{2/3}{\left(z-{z}_{\rm{o}}\right)}^{-5/3}$$

(A.2)

where ${\Delta \theta }_{\rm{o}}$ is at most 900 °C [30], ${\chi }_{\rm{r}}$ is the radiative fraction of the ${\text{HRR}}$ (taken as 0.2 in [30]), $z$ [m] is the height of the selected point, ${z}_{\rm{o}}$ [m] is the height of the virtual source calculated from Eq. (A.3) [32]:

$${z}_{\rm{o}(t)}=-1.02D+0.083{\left({ {\text{HRR}}}_{(t)}\right)}^{2/5}$$

(A.3)

LF-ESF model proposes a modification of the H&H [28] gas temperature distribution as shown in Eq. (A.4).

$${\stackrel{-}{\theta }}_{(\omega ,t)}=\frac{\Delta {\theta }_{(\stackrel{-}{r},{\stackrel{-}{H}}_{ {\text{fl}} },t)}}{\Delta {\theta }_{o(t)}}={{\stackrel{-}{H}}_{ {\text{fl}} }}^{a}\left(0.3785-0.02\stackrel{-}{r}\,\right)+0.57.\rm{exp}\left[1.30{{\stackrel{-}{H}}_{ {\text{fl}} }}^{b}\left(1-\stackrel{-}{r}\right)\right]$$

(A4)

where $r$[m] is the radial distance to flame axis, $\stackrel{-}{r}$[-] is the normalized distance to the flame axis ($\stackrel{-}{r}=r/(D/2))$, ${\stackrel{-}{H}}_{ {\text{fl}} }\,[-]$ is the normalized height (${\stackrel{-}{H}}_{ {\text{fl}} }=z/{H}_{ {\text{fl}} }$), $z$[m] is the height where the temperature is evaluated and a, b are coefficient that are equal to − 1 y 1, respectively when ${\stackrel{-}{H}}_{ {\text{fl}} }\ge 1$ and 0 otherwise.

1.2 Radiant heat flux

LF-ESF model proposes the use of a flame with an ellipsoidal form to improve the representation of the radiant flux, as described in the Eq. (A.5):

$$\frac{{x}^{2}}{{\left(D/2\right)}^{2}}+\frac{{y}^{2}}{{\left(D/2\right)}^{2}}+\frac{{x}^{2}}{{H}_{ {\text{fl}} }^{2}}=1$$

(A.5)

The thermal radiant intensity to an element outside the flame envelope is given by the Eq. (A.6):

$${\dot{q}}_{re}^{\prime\prime}={{F}_{ij}\tau E}_{\rm{a}\rm{v}}$$

(A.6)

where ${F}_{ij}$[-] is the geometric view factor, $\tau$ [-] is the atmospheric transmissivity [39] and ${E}_{\rm{a}\rm{v}}$[kW/m²] is the flame average emissive power.

This methodology describes the atmospheric transmissibility according to Casal [39] as a function of the distance $d$ [m] between the flame and target as shown in Eq. (A.7) [40]:

$$\tau =\left\{\begin{array}{cc}0.976{d}^{-0.06}& ,\,d<5.0\,\rm{m}\\ 1.029{d}^{-0.09}& ,\,d\ge 5.0\,\rm{m}\end{array}\right.$$

(A.7)

The MSFM [41] considers the flame average emissive power ${E}_{\rm{a}\rm{v}}$[kW/m²] (140 kW/m² for hydrocarbon fires [1]) as a correlation between flame emissive power (${E}_{ {\text{fl}} }={E}_{\rm{b}}{\varepsilon }_{ {\text{fl}} }$ [kW/m²]) and thermal radiation emitted by smoke ${E}_{\rm{s}\rm{o}\rm{o}\rm{t}}$ [kW/m²] (20 kW/m² [1, 42]), as shown in Eq. (A.8):

$${E}_{\rm{a}\rm{v}}={\chi }_{\rm{l}\rm{u}\rm{m}}{E}_{\rm{b}}{\varepsilon }_{ {\text{fl}} }+\left(1-{\chi }_{\rm{l}\rm{u}\rm{m}}\right){E}_{\rm{s}\rm{o}\rm{o}\rm{t}}$$

(A.8)

where ${\chi }_{\rm{l}\rm{u}\rm{m}}$ [−] is the percentage of visible flame (0.80 and 0.20 for gasoline and ethanol, respectively [42]), ${\varepsilon }_{ {\text{fl}} }\,[-]$ is the flame emissivity (taken as 1 for simplicity), ${E}_{\rm{b}}$[kW/m²] is the black body emissive power calculated following the Eq. (A.8.a):

$${E}_{\rm{b}} = \sigma \left[{{\theta }_{ {\text{fl}} }}^{4}-{{\theta }_{\infty }}^{4}\right]$$

(A.8a)

where ${\theta }_{ {\text{fl}} }$ [K] is the flame's radiation temperature and ${\theta }_{\infty }$ [K] is the environmental temperature (assumed to be constant and equal to 293 K).

From Eq. (A.6) and Eq. (A.8) the equivalent flame temperature (${\theta }_{ {\text{fl}} ,\rm{e}\rm{q}}$ [K]), assumed uniform, can be calculated as:

$${\theta }_{ {\text{fl}} ,\rm{e}\rm{q}}=\sqrt[4]{{\left({\varepsilon }_{ {\text{fl}} }\sigma {{\theta }_{\infty }}^{4}+{E}_{\rm{a}\rm{v}}\tau \right)/\varepsilon }_{ {\text{fl}} }\sigma }$$

(A.9)