Countercurrent spontaneous imbibition (SI) is an important flow mechanism for oil recovery in fractured reservoirs during waterflooding. SI plays a key role in the mobilization of oil in the matrix because it facilitates water infiltration by capillarity even when the matrix permeability is low, which limits fluid transport by advection. However, the modeling of SI in fractured media under dynamic conditions has been insufficiently studied. Most imbibition models assume conventional exponential functions and empirical constants based on experimental results of oil recovery under static conditions. Thus, the modeling of water distribution in the fracture and the matrix has been ignored which may lead to incorrect estimates of the efficiency of countercurrent SI to recover oil. Using the classic fractional flow equation, we present a semi-analytical solution to model countercurrent SI in a water-wet fractured medium by including a transfer function to account for continuous fluid exchange between the fracture and the matrix. The model is numerically solved using finite differences by including an effective imbibition time as a function of water advance in the fracture, which overcomes the difficulty of solving iterative numerical summations as shown in other imbibition models. The novelty of the presented solution is that it enables the modeling of water infiltration in the matrix under dynamic conditions. We verified the semi-analytical model against 2D numerical simulations and validated against experimental data to demonstrate that the model accurately predicts oil recovery and water infiltration in the matrix.

逆流自吸（SI）是注水过程中裂缝性油藏采油的重要流动机理。SI在基质中的油动员中起关键作用，因为即使基质渗透率较低，它也可以通过毛细管作用促进水渗透，从而限制了对流流体的输送。但是，在动态条件下对裂隙介质中SI的建模还没有得到足够的研究。基于静态条件下采油的实验结果，大多数吸水模型均采用常规的指数函数和经验常数。因此，裂缝和基质中水分布的模型已被忽略，这可能导致对逆流SI采油效率的错误估计。使用经典的分数流方程，我们提出了一种半解析解决方案，通过包括传递函数来解释裂缝和基质之间的连续流体交换，从而在水湿裂隙介质中模拟逆流SI。通过在裂缝中加入有效吸水时间作为进水的函数，使用有限差分对模型进行数值求解，从而克服了求解其他吸水模型所示的迭代数值求和的难题。提出的解决方案的新颖性在于，它可以对动态条件下基质中水的渗透进行建模。我们针对2D数值模拟验证了半分析模型，并针对实验数据进行了验证，以证明该模型可以准确预测基质中的油采收率和水渗透率。