The detection of trace explosives in the subsurface is an active area of research for landmine detection. Understanding the air-water flow and heat transport phenomena in the subsurface plays an important role in improving chemical vapor detection. Implementing a finite element method that accurately captures water vapor transport in the vadose zone is still an open question. A non-equilibrium, pressure-pressure formulation has been implemented based on Smits, et al [22]. This implementation consists of four equations: a wetting phase (water) mass balance equation, a non-wetting phase (air) mass balance equation, a water vapor transport equation, and a heat transport equation. This work will compare two implementations, a fully coupled approach and an operator splitting approach for the water vapor and heat transport equations. The formulation of the methods will be presented and the methods will be tested using collected data from physical experiments.