The Devonian Grosmont Formation is a bitumen saturated carbonate unit located in northern Alberta. It is considered to be Canada's second largest unconventional oil resource after the McMurray Formation oil sands. Production from the Grosmont Formation has been tested by a consortium of Unocal, Canadian Superior, AOSTRA, Chevron and other companies between 1970's to 1980's with some success and significant learning. Since 2010, Laricina Energy Ltd. and Osum Oil Sands Corp. have started a new wave of testing thermal recovery processes for the Grosmont Formation using horizontal wells. The Grosmont C carbonate reservoir contains vugs and fractures at multiple scales, and thus has a different porosity and permeability network than the clastic oil sands. This paper describes a numerical simulation approach to history matching the performance of one of the pilot wells in order to better characterize reservoir properties such as fractures and vugs at multiple scales and their interactions with the rock matrix. CMG's STARS dual porosity dual permeability module was used to simulate this complex system. The results of the simulation suggest that small-scale vugs should be combined with the matrix in order to obtain a better history match of the reservoir and production performance. Parameters describing fracture properties have become critical not only in matching the well behavior, but also in matching reservoir thermal responses. Advantages, limitations, and recommendations for using a dual porosity and dual permeability model for understanding a multiple-scale porous and permeability system are also discussed.