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A one-fluid, or algebraic slip, model has been developed to simulate two-dimensional, two-phase flow in a kettle reboiler. The model uses boundary conditions that allow for a change in flow pattern from bubbly to intermittent flow at a critical superficial gas velocity, as has been observed experimentally. The model is based on established correlations for void fraction and for the force on the fluid by the tubes. It is validated against pressure drop measurements taken over a range of heat fluxes from a kettle reboiler boiling R113 and n-pentane at atmospheric pressure. The model predicts that the flow pattern transition causes a reduction in vertical mass flux, and that the reduction is larger when the transition occurs at a lower level. Before transition, the frequently-used, one-dimensional model and the one-fluid model are shown to predict similar heat-transfer rates because similar magnitudes of mass flux are predicted. After transition, the one-dimensional model significantly over-predicts the mass fluxes. The average heat-transfer coefficient predicted by the one-fluid model is consequently about 10% lower. The one-fluid model shows that tube dryout can be expected at much lower heat fluxes than previously thought and that the fluid kinetic energy available to induce tube vibrations is significantly smaller.

Shell and tube heat exchangers are widely used in the process industry. One of the most commonly used designs is the kettle reboiler, which consists of a horizontal tube bundle placed in a shell. The heating fluid flows inside the tubes while the heated fluid boils outside the tubes, Fig. 1.The design problem is essentially a three-dimensional one. Fluid is moved axially from the inlet end of the shell to the weir, as well as vertically and horizontally in cross sections perpendicular to the shell axis. The latter motion is the predominant one, and, once determined, can be incorporated into a fully three-dimensional design solution. The motion is due to natural circulation resulting from the difference in densities between the two-phase mixture flowing in the tube bundle and the liquid flowing between the tube bundle and the shell wall. To determine the circulation flow rate, different modelling approaches have been proposed. The simplest approach is the one-dimensional model, [1], [2], [3] and [4], where saturated liquid is assumed to enter the bundle from the bottom and to evaporate while it moves vertically upwards. The two-phase pressure drop in the tube bundle is assumed equal to the static head of the liquid between the tube bundle and the shell wall. Since the two-phase pressure drop has gravitational, acceleration and frictional components, the void fraction and a two-phase friction multiplier are required to complete the model. Several investigators have proposed void fraction correlations, e.g. Schrage et al. [5], Dowlati et al. [6] and Feenstra et al. [7]. For the two-phase multiplier, various investigators have applied the Lockhart and Martinelli method, [8], represented by a simple correlation designed by Chisholm and Laird [9]. Barmardouf and McNeil, [10], studied a range of available experimental data, mostly for pure fluids at atmospheric pressure, and concluded that the Feenstra et al. [7] void fraction correlation and the Ishihara et al. [11] two-phase multiplier correlation provided the best empirical information for the range of conditions likely to occur in a kettle reboiler.

This paper describes a two-dimensional model of a kettle reboiler. The model is based on information for void fraction and tube wall force that has been established by many investigators. It also uses boundary conditions that are consistent with the experimental evidence. However, in the implementation of the boundary condition it was assumed that the maximum deviation from the static liquid case would be sought. This forces the east boundary to be at or below the transition superficial gas velocity. The agreement with the measured pressure drops, Fig. 4, Fig. 5, Fig. 6, Fig. 7 and Fig. 8, suggests that this is reasonable, but it may not extrapolate to higher heat fluxes. Also, the boundary conditions are not the natural ones of no slip on the shell wall. After transition, the boundary condition on the tube bundle should result from the interaction of the fluid flowing from the bundle and the geometrical configuration between the tube bundle and the shell wall. In this study, it is probably the case that this space was sufficiently large to ignore this. This is supported by the predicted pool pressures, Fig. 15, and the observed phase distributions, Fig. 5, Fig. 7, Fig. 9 and Fig. 11. However, this may not be true of all geometries. The transition criterion from bubbly to intermittent flow was established using two fluids, R113 and n-pentane. The main difference between these two fluids is the liquid density, 1507 kg/m3 for R113 and 610 kg/m3 for n-pentane: the vapour–liquid density ratios being similar. Only one tube bundle geometry was used. Further work is therefore required with other fluids and mixtures at a range of pressures and for other tube bundle geometries. Despite the shortcomings, the model predicts all of the observed phenomena in a kettle reboiler. The constant pressure drops at low heat fluxes and their corresponding decay at larger heat fluxes, the increasing heat-transfer coefficient at low heat flux and the maximum turning value at the larger values. This is a significant step forward. To overcome the remaining difficulties a two-fluid model is needed. With a true extrapolation of the one-dimensional data now complete, this should prove more tractable and will be the focus of future work.