A Quasi-Steady Diffusion-Based Model for Design and Analysis of Fuel Tank Evaporative Emissions 2019-01-0947
Emad Ghadirian, Jonathan Brown, and Syed Wahiduzzaman
Gamma Technologies, LLC, 601 Oakmont Ln, Suite 220, Westmont, IL 60559
In this paper, a fuel tank evaporation and condensation model was developed, which was suitable for calculation of evaporative emissions in a fuel tank. The model uses a diffusion-controlled mass transfer approach in the form of Fick's second law in order to calculate the average concentration of fuel in the carrying gas and its corresponding evaporation rate. The partial differential equation of transient species diffusion was solved using a separation of variables technique with the appropriate boundary conditions for a fuel tank. In order to simplify the solution, a quasi-steady assumption was utilized and justified. The fuel vapor pressure was modeled based on American Petroleum Institute (API) procedure 5A1.19  using either a distillation curve or a Reid Vapor Pressure (RVP) as an experimental input for the specific fuel used in the system. The advantage of this model compared to other published models is the fact that it is a non-equilibrium model that takes into account the effects of mass transfer between phases.
The model is comprised of a two volume system with liquid fuel and a mixture of fuel vapor and air. The two volumes interact through an interface area. As the volume of liquid changes due to evaporation or condensation the liquid-to-wall heat transfer area and vapor-to-wall heat transfer area change dynamically. There are vapor and liquid ports provided in the model for integration with other evaporative emissions component models. There is a vapor port for modeling the flow and diffusion of fuel vapor from the fuel tank to the carbon canister and canister purge valve. A fuel line port is provided to transport liquid fuel to a pickup line and fuel pump, or for fuel returning to the tank from the fuel rail return line.
The model was validated for steady-state and transient conditions. The experimental data of Reddy  was compared to the steady-state fuel vapor generation of the fuel tank model. The transient drive cycle experimental data of Lavoie et al  was used to validate the transient diffusion and evaporation rate. In addition evaporation and condensation cycling simulations were performed.
 American Petroleum Institute, Technical Data Book, June, 1993.
 Reddy, S. R., "Prediction of Fuel Vapor Generation from a Vehicle Fuel Tank as a function of Fuel RVP and Temperature," SAE Paper 892089, 1989.
 Lavoie, G. A., Imai, Y. A., and Johnson, P. J., "A Fuel Vapor Model (FVSMOD) for Evaporative Emissions System Design and Analysis," SAE Paper 982644, 1998.
Emad Ghadirian, Jonathan Brown, Syed Wahiduzzaman