The aim of this paper is to study the imbibition phenomenon in Kirkuk tertiary reservoir (which is a dual-porosity system) and to isolate the individual effects of various parameters on imbibition's recovery. It also addresses the importance of characterizing the imbibition mechanism for analyzing the reservoir performance. A surrounded matrix block by the wetting phase is presented for the purpose of better understanding spontaneous imbibition characteristics. Numerous parametric studies have been performed within the scope of this research. Results showed that the temperature in Kirkuk tertiary reservoir crude oil have a substantial effect on the imbibition recovery mechanism, and the wettability index at the reservoir temperature is 0.24, which indicates that this formation has a very weak water-wet characteristics.