A semi-analytical model for fractured horizontal wells production considering imbibition during shut-in periods

After hydraulic fracturing in tight oil reservoirs, part of the fracturing fluid is retained in the formation. Therefore, it's essential to investigate the pressure and saturation distributions during and after fracturing to further understand the impact of fluid loss on productivity. Concerning the capillary pressure, fracture propagation, and fracture volume changes, a semi-analytical model was established innovatively. Comparisons between the model's calculations and actual measurements demonstrate a high level of agreement, validating the model's accuracy. Furthermore, the impacts of capillary pressure, shut-in time, injection rate, initial reservoir pressure, and initial water saturation on actual production performance were investigated. The results show that the effect of capillary pressure on production in the tight reservoir cannot be ignored. A reasonable shut-in operation should be carried out according to the actual situation. A smaller injection rate should be selected to achieve a larger fracture length and imbibition area. The proportion of oil produced by capillary pressure decreases with the increase of initial pressure. The initial water saturation is positively correlated with oil production and negatively correlated with water production. The imbibition effect of shut-in operation is more obvious in tight reservoirs with low initial pressure and low water saturation.