Spontaneous imbibition is a crucial process for oil recovery from fractured and unconventional reservoirs. Herein, with the assumption of capillaries being independent, a new mathematical model for spontaneous imbibition is proposed and solved using a numerical method. The simulated results show that the wetting phase preferentially enters smaller capillaries where the advancement velocity is higher than that in larger ones, while the non-wetting phase can be displaced out in the larger capillaries. In addition, the effect of fluid viscosity ratio on counter-current imbibition is analyzed. The results show that imbibition velocity becomes higher with the increase in the viscosity ratio. When the viscosity of the non-wetting phase is larger than that of the wetting phase, the end pressure gradually increases as the imbibition front advances. In contrast, when the viscosity of the non-wetting phase is less than that of the wetting phase, the end pressure decreases with the infiltration. With a higher viscosity ratio of non-wetting and wetting phase, the heterogeneity of the interface advancement among different capillaries increases.

This paper proposed a general physics-based data-driven framework for numerical modeling and history matching of reservoirs that achieves a good balance of flow physics and actual field data. Underground reservoir is easily discretized in this framework as a flow network composed of one-dimensional connection elements, each of which is defined by two flow characteristic parameters. Each one-dimensional connection element is divided into some grids, and the cross-sectional area and permeability of the grids on the same connection element are equal. The fully implicit scheme of flow equations and the Newton iteration nonlinear solver concurrently solve all unknown quantities. Then, using actual field data, the simultaneous perturbation stochastic approximation algorithm is used to invert flow characteristic parameters of each connection element, and the unequal constraint that the volume of connection elements should not exceed the total reservoir volume is added to control the data-driven process. To demonstrate the unequal constraint is physical, a test case of a waterflooding reservoir with a high permeability zone is given. A waterflooding reservoir example with five injectors and four producers is used to demonstrate that this framework outperforms earlier techniques, and another case with single-phase depletion development is used to demonstrate that this framework has a high generalization for flow models. In addition, this data-driven framework based on physics is expected to serve as a reference for other fields of science and engineering.