Optimal Safe Layout of Fuel Storage Tanks Exposed to Pool Fire: One Dimensional Deterministic Modelling Approach

Abstract

Fire hazard is one of the main risks associated to fuel storage tanks in petroleum and in the petrochemical industries. Such a hazard includes pool fires in the storage tanks or in the bunds, fire propagation from the source tank to target tanks both in absence and in presence of wind, and also the cascading/domino effect due to confined and unconfined vapour cloud explosion and or BLEVE associated with the source tank. In the present work, a radiation shield of flowing water has been introduced at a distance from the source fuel storage tank to prevent the domino effect originating from this source tank, under fire, to the target fuel storage tanks in a tank farm. A simple one dimensional model has been developed from the steady state energy balance to simulate the safe distances (i.e. rim–rim distance) between fuel storage tanks containing class-I fuel (e.g. gasoline), both in presence and absence of a water-shield under no-wind and cross-wind conditions. The model predictions have shown that the maximum safe inter-tank separation distance of 28.42 m is anticipated at a wind velocity of 6 m/s, compared to 16.34 m in no-wind condition, beyond which the centroid of the parallelepiped (a solid-flame geometry) falls outside the base of the tilted flame geometry causing flattening of flame and a very sluggish increase in the flame tilt angle as the inverse of the Richardson number in the presence of wind velocity vector increases. Furthermore, the present one dimensional mathematical model has also been extended to show that introduction of a water-shield with an appropriate thickness (δ_opt) is able to prevent the propagation of radiation heat flux under both no-wind and cross-wind conditions to a much lower distance close to 8.34 m between tanks (measured from the centre of the source tank), than those predicted from the existing empirical models; viz. Point Source model and Shokrie-Beyler’s model.

Appendix

Within radiative regime, i.e. transfer of heat transport fluxes from the flame-front surfaces at x and x + ∆x (refer Fig. 1b) are dominantly by radiation; while the heat losses from the other surfaces of the elemental control volume can still be via convection and radiation (Sects. 2.1 and 2.2), the flame can be optically thick or thin depending on the pool diameter [33]. For pool diameter > 1 m with radiative flame give rise to optically thick flame [33]. Koseki [29] via experiments on large pool fires had concluded that large unconfined pool fires are predominantly in radiative regime. In the present scenario, we have considered a large 10 m diameter pool fire which is therefore, assumed to be in the radiative regime. The mean optical thickness of a flame is defined in terms of κβ, where κ is the absorption extinction coefficient and β is the mean beam length corrector [26, 27, 33]. While κ value for most of the fuel is documented in literature for pool fires with D ≥ 0.2 m, it had been argued that a “common β value does not emerge” for a given fuel and pool diameter and therefore, the κβ value is not unique [33]. Hence, while Babrauskas [33] reported the κβ value for gasoline pool fires of D ≥ 0.2 m to be 2.1 m⁻¹; Sudheer et al. [26] reported κβ = 1.5 m⁻¹. So we have calculated the κβ value for the present pool fire of D = 10 m containing gasoline; using the following relation, where $\dot{m}^{\prime \prime }$ is the mass burning rate of the fuel (which can be obtained from pool diameter relationship [4, 27, 29, 33]) and $\dot{m}_{\infty }^{\prime \prime }$ is a constant for a given fuel [33].

$$ \dot{m}^{\prime \prime } = \dot{m}_{\infty }^{\prime \prime } (1 - \exp ( -\upkappa \upbeta {\text{D))}} $$

(32)

For gasoline ($\dot{m}_{\infty }^{\prime \prime } = 0.055\;{\text{kg/m}}^{ 2} / {\text{s}}$, κ = 2 m⁻¹ [33]) we have reported the κβ and the β values in Table 5 under both no-wind and windy conditions. The mass burning rate for each of the cases are also reported in the same table and are obtained from pool diameter relationship given in literature [27] under the no-wind condition; or by using Eq. (8) for windy conditions. Furthermore, the calculation of the optical depth (τ) have been performed using the Equation (33) [27, 44] and these values are also reported in Table 5:

$$ \tau = \upkappa \upbeta \left( {\frac{{3.6V_{f} }}{{A_{f} }}} \right) $$

(33)

where V_f is the volume of the flame geometry and A_f is the surface area of the flame geometry. It is noted that the κβ value and the optical depth under no-wind condition for the present case is 0.1595 m⁻¹ and 1.595, respectively. Following the argument on radiative regime pool fires with D > 1 m [33], τ = 1.595 is taken to be the optical thin limit for the gasoline pool fire and we also observe that for all windy conditions considered the corresponding optical depth values are greater than this limit. Therefore, the flame surface temperatures of the pool fires have been used to estimate the safe inter-tank distance in a gasoline tank farm for both no-wind and windy conditions. We also note an increase in the τ value with the increasing wind speed.

Table 5 Effect of Wind Velocity on Optical Thickness of Pool Fires in the Fuel Storage Tanks with 10 m Diameter and Containing Gasoline