Vapour extraction (VAPEX) has received considerable attention as an enhanced heavy oil recovery process. Like SAGD it relies on significantly reducing the oil viscosity but has the advantage over SAGD that it will be effective in thin or deep reservoirs where thermal methods are impractical due excessive heat losses. Nonetheless field applications of VAPEX have been limited partly due to difficulties in predicting the high oil rates observed in laboratory experiments and thus in upscaling the results to field scale. In this paper, we present a laboratory investigation of the VAPEX process using analogue fluids in a well characterized glass bead pack. The experiments were focused specifically on determining the role of convective dispersion and reservoir thickness on drainage rates. Longitudinal and transverse dispersion coefficients were measured with and without gravity in order to quantify the impact of interstitial velocities and contrasts in the fluids' viscosity and density on the rate of mixing as encountered in VAPEX. The experimental measurements of oil drainage rates were higher than predicted by the standard Butler-Mokrys analytical model assuming diffusion-controlled mass transfer. The use of measured dispersion coefficients however significantly improved the model predictions. In addition, the results found drainage rates to have a higher than square root dependency on model height. The combined effects of the roles of convective dispersion and model height on drainage rates were incorporated into a predictive model that satisfactorily matched measured rates in the laboratory.