This paper considers the development of a computationally fast model for simulation of multiphase flow in porous media for a heterogeneous reservoir with the unlimited number of wells characterized by a different type of completion. This fast solution has been obtained by means of replacing the differential equation governing the flow in porous media by approximate governing equations which are parametrized by convolutional neural networks. The matching of the dynamic properties of the original and reduced models is ensured by conservation of spatial invariance property of the equations. The suggested approach is characterized by the minimal number of limitations and shortcomings related to geological-hydrodynamical structure and size of the original model. Also, there is no necessity of additional model training for reservoirs not included in a training dataset. Suggested approach has been evaluated on the synthetic benchmark test model SPE10, where a significant decrease in computational time has been demonstrated comparing to a traditional commercial reservoir simulator. Based on the results of all demonstrated test case scenarios, it could be noted that hybrid hydrodynamic modeling leads to a significant reduction in computational cost (by a factor of few hundreds), maintaining at the same time required accuracy of calculations.