Jun Zhang

Amathematical model was derived in this study to reveal the mechanism of CO2 imbibition in shale formations considering the combined effects of capillary force and viscous force in concave curved triangle pore channels surrounded by different solid materials with different wettability. The model reveals that CO2 imbibition depth is proportional to the square root of CO2 soaking time, square root of the pore size determined by grain size, square root of interfacial tension and cosine of contact angle, and inversely proportional to the square root of CO2 viscosity. Up to three solid wall materials with different contact angles can be considered in the model. Using the average contact angle for the three materials over-estimates the imbibition distance. CO2 imbibition is faster in concave curved triangle pores than in equivalent circular-shaped pores. The dimensionless geometry correction factor is less than unity (α = 0.81). The newly developed imbibition model can be used for predicting the maximum time of imbibition between parallel fractures in multi-fractured shale formations. Document Type: Original article Cited as: Zhang, J., Guo, B., Amponsah, V. N. B. A more rigorous mathematical model for capillary imbibition of CO2 in shale gas formations. Capillarity, 2025, 14(3): 63-71. https://doi.org/10.46690/capi.2025.03.01

Multi-stage hydraulic fracturing is a key technology adopted in the energy industry to make shale gas and shale oil fields profitable. Post-frac fluid soaking before putting wells into production has been found essential for enhancing well productivity. Finding the optimum time to terminate the fluid-soaking process is an open problem to solve. Post-frac shut-in pressure data from six wells in two shale gas fields were investigated in this study based on pressure transient analysis (PTA) to reveal fluid-soaking performance. It was found that pressure-derivative data become scattering after 1 day of well shut in. The overall trend of pressure-derivative data after the first day of well shut in should reflect the effectiveness of fluid soaking. Two wells exhibited flat (zero-slope) pressure derivatives within one week of fluid soaking, indicating adequate time of fluid soaking. Four wells exhibited increasing pressure derivatives within one week of fluid soaking, indicating inadequate time of fluid soaking. This observation is consistent with the reported well’s Estimated Ultimate Recovery (EUR). This study presents a new approach to the assessment of post-frac fluid-soaking performance with real-time shut-in pressure data.