A comparative analysis of two approaches for pool evaporation modeling: Shrinking versus nonshrinking pool area



Prediction of pool evaporation rates in the event of liquid spills is an important topic in the area of emergency response and has been actively studied by many researchers. The modeling of pool evaporation involves the vaporization, spreading, and shrinking of spilled liquids. Even though there are several well-established evaporation models for calculating the evaporation flux from a pool, the dynamics of the pool spreading and shrinking phases is not well established. The challenge with these models is due to an intractable solution to the full conservation equations to establish the pool dynamics. Therefore, the problem has been solved by order-of-magnitude estimates of the forces involved: gravity, drag, viscous, and surface tension. Researchers have recognized three different spreading regimes for the expansion of the pool: (1) gravity–inertia, (2) gravity–viscous, and (3) viscous–surface tension. The main driving force for the pool spreading phase is gravity, which is dominant in the early stages of pool expansion.

The issues that have not been addressed satisfactorily in the literature are: (a) the maximum radius a pool can expand to; (b) minimum height it can reach before a homogenous pool breaks up into patches of liquids; and (c) the mechanism for the shrinking phase of the pool.

In this article, two separate mechanisms are demonstrated for the spreading phase based on the boiling point of the liquid. A pool consisting of nonboiling or low evaporating liquid is allowed to spread up to a minimum height, which is estimated by minimizing the potential energy of the pool. The boiling liquid pool is allowed to spread up to a minimum height of 1 cm as the liquid may not have enough time to spread to their minimum height estimated by minimizing the potential energy because of the higher evaporation rates.

In addition, the shrinking phase of the pool evaporation model for liquid spills on solid surfaces in unconfined settings has been broadly categorized into two approaches: (1) a shrinking radius approach (i.e., shrinking pool area) and (2) a shrinking height approach (i.e., nonshrinking pool area). Shrinking radius approach, for both instantaneous and continuous spills, allows the pool radius to expand as long as the height of the pool is equal to the minimum height. After the pool depth reaches the minimum height, this constraint is maintained and the radius is allowed to shrink until the liquid is completely evaporated. On the other hand, the shrinking height approach maintains the pool radius as a constant as soon as the pool depth is equal to the minimum height. From there, the pool height decreases due to evaporative mass losses, while the pool radius remains constant.

Furthermore, we try to present arguments on the merit of the shrinking height approach versus the shrinking radius approach for the shrinking phase of pool evaporation on solid surfaces. The results from the two approaches (shrinking radius and constant height vs. shrinking height and constant radius) are compared for various single and binary component spills of varying boiling point ranges for continuous/instantaneous spill scenarios. In particular, pool evaporation rates, pool temperature, pool radius, and total evaporation time are compared for various spill scenarios. Overall, we found that the proposed shrinking height approach methodology represents a more realistic approach than shrinking radius approach for the pool shrinking phase. © 2012 American Institute of Chemical Engineers Process Saf Prog, 2012