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we developed a novel approach for designing and fabricating depth-varied reservoir-on-a-chip micromodels using the silicon-based multi-depth fabrication strategy and on-chip random generation algorithm. Depth-varied reservoir-on-a-chip micromodels can mitigate confinement of uniform depth and maintain the wide range of pore size distribution similar to natural-occurring 3D porous media. The imbibition experiments performed in the single-depth and multi-depth reservoir-on-a-chip micromodels show the complex interaction between depth variation, capillary number Ca, and wettability (contact angle) θ on multiphase flow dynamics. The combination of micromodel experiments and direct numerical simulations enabled us to purify the complex capillarity as snap-off and by-pass phenomena. A theoretical model was proposed for suppressing or triggering these unstable imbibition phenomena. Phase diagrams predicted by the models were theoretically analyzed and numerically verified, they show that for θ≤45°, increasing Ca stabilizes the imbibition front by suppressing the snap-off mode; for contact angle θ<90°, increasing θ stabilizes the imbibition front by inhibiting the by-pass mode, but increasing depth variation destabilizes the imbibition front as snap-off or by-pass or their combined effect. Our findings extend the classical understanding of forced imbibition in 2D micromodels. The results have potential applications in predicting or manipulating CO2 capillary trapping and enhanced gas/oil displacement efficiency.