Experimental and Numerical Study of Anomalous Imbibition in Shale Gas Reservoirs

Abstract This paper investigates the phenomenon of anomalous imbibition in shale reservoir rocks through a combination of numerical and experimental approaches. Shale gas reservoirs present unique challenges due to their low permeability and complex pore structure, significantly influencing fluid transport mechanisms. Spontaneous imbibition, where water (or fracturing fluids) infiltrates the shale matrix and displaces the gas driven by capillary force, plays a critical role in the recovery efficiency of shale gas reservoirs. Fluid spontaneous imbibition in heterogeneous porous media, such as tight and shale formations, often exhibits anomalous behavior dominated by multiple time-spatial scales. Based on direct experimental evidence of anomalous imbibition process, this work proposes a fractional derivative model to quantitatively analyze the complete early-to-late time dynamics of the anomalous imbibition in shale gas reservoirs. Prior research on the anomalous imbibition process has primarily focused on fractal models and has compared results with indirect indicators, such as the cumulative imbibed volume derived from imbibition experiments. This study introduces direct observations and quantifications of the anomalous imbibition dynamics, utilizing saturation distributions converted from Computed Tomography (CT) numbers. A fractional diffusion model is proposed, and the resulting non-linear fractional differential equations are solved numerically using the finite-difference method. The proposed model solution accurately captures the complete early-to-late time behavior of cumulative recovery volume and the wetting phase front propagations which exhibit anomalous phenomena.