Mathematical Models for Pneumatically Induced Sewer Overflow and Geysering

Pneumatically induced overflow and geysering through vertical shaft in storm sewer systems can lead to flooding, sewage overruns and threats to public safety or welfare. Air can be trapped due to surcharge, especially when poor venting exists, during the transition from free surface flow to pressurized flow under wet weather conditions. Entrapped air pockets may be then compressed continuously in the system. When air reaches vertical structures like a vent tower or a dropshaft, it moves upward and may push water out, generating overflow and geysers. The evolution process and its association with air release from the pressurized pipe were still limitedly investigated. Therefore, there is a necessity to develop mathematical models for such a system, through which further understanding of the mechanism can be delivered.

In the present study, mathematical models were built for the air-water flow through a straight vertical shaft, and the main focus considered the cases of release of large air pockets or continuous air release. Two stages were characterized in the overspilling/geysering process and the models involve a system of nonlinear equations incorporating the ideal gas law for air phase. They were validated by experimental data and numerical modelling results, and suggested to compute air-water movements and to estimate geyser heights as a first approximation. It is shown that geyser heights can be associated with different parameters including the driving pressure head, pipe size and the density of air-water mixture. The influence of the downward film flow around the pipe wall was also evaluated through the comparison between the models.