Single phase flow simulation in porous media by physical-informed Unet network based on lattice Boltzmann method

•A PI-Unet-BGK network is established based on the LBM-BGK.•The PI-Unet-BGK network is used to simulation the steady-state and dynamic flow.•The average error of predicted dynamic flow field are mostly less than 10−3. The simulation of flow in porous media holds significant importance in investigating various phenomena, but current simulation methods are time-consuming. Recently developed physics-informed neural network employs physical constraints during training, enabling the learning of a more generalized model with limited data samples. This substantially reduces the learning cost and introduces a novel approach to solving flow calculations in porous media. To simulate steady-state and dynamic flow processes of single-phase flow in complex porous media, a physical-informed Unet network (PI-Unet-BGK) is established based on the lattice Boltzmann method with the Bhatnagar-Gross-Krook (BGK) collision model. This research demonstrates that the PI-Unet-BGK network outperforms the conventional Unet network in predicting steady-state flow fields for multiple Berea sandstone slices. Its coefficient of determination is 0.2788, it has improved by 0.06 compared to the Unet network. The relative error of permeability of carbonate rock and shale slices are 64% and 117%. Regarding dynamic single-phase flow simulation, the PI-Unet-BGK network exhibits favorable performance in simulating the flow process within Berea sandstone slices. However, it has some errors at initial stage. When test on a carbonate rock and shale slices, it can only simulate the trend of fluid transport, our model exhibits limited transfer learning ability.