Abstract
This paper presents a mathematical model for the pressure inside the vapor space of an underground storage tank (UST). Using mass balances based on dispensing activities, vapor recovery, evaporation, leaks, and the safety vent, the model resulted in a system of nonlinear differential equations with unknown parameters, leak rate and evaporation rate. Given the leak rate and evaporation rate, the pressure inside the UST can be obtained by solving the system of differential equations numerically. Given the pressure inside a UST over a period of time, one can find the evaporation and leak rates such that the calculated pressure from our model best fits the given pressure data. This optimal value of leak rate can allow us to determine whether the UST system is leaking and if the leak rate is above the EPA standard. Numerical results and statistical analysis of our model are also presented.
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