A mathematical model for co-current spontaneous water imbibition into oil-saturated tight sandstone: Upscaling from pore-scale to core-scale with fractal approach

Abstract

Spontaneous Imbibition (SI) is an important mechanism of enhancing oil recovery in tight oil reservoirs. Predicting core-scale oil flow rate by water imbibition from the pore-scale SI modelling is challenging due to the wide distributions of nano- and micro-pores in tight sandstone and huge amount of calculation of upscaling pore-scale modelling results for core-scale prediction. A semi-analytical mathematical model of characterizing co-current SI of water into oil-saturated tight sandstone has been proposed in this paper based on the capillary tube model and fractal theory. The non-uniform of water imbibition front due to the different imbibition rate in different sizes of pores can be dynamically characterized. Connate water and residual oil are considered and treated as immovable boundary-layers and coupled into the tortuous capillary tube model. The proposed model has been validated with the experiments results of core imbibition tests from literature. The key parameters of pore structures and fluid properties influencing imbibition flow rate have been quantitatively analyzed and identified.