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Tortuous pores are ubiquitous in natural porous media; however, the linear effects of tortuosity on the liquid flow behaviors are usually considered through capillary bundle models, which lead to inaccurate permeability prediction. Additionally, in the nanopores, due to the existence of heterogeneous viscosity and boundary slip, the effects of tortuosity on nanoconfined liquid flow behaviors are more complicated. In this paper, we comprehensively use the theoretical models and a nanoscale multi-relaxation-time lattice Boltzmann method (MRT-LBM) to characterize water flow behaviors in the tortuous nanopores, where heterogeneous viscosity and boundary slip are considered. The results show that the increase of tortuosity causes more negative effects, which results in a decreasing apparent permeability. The conventional model of the influence of tortuosity on the apparent permeability is linear$k_{\mathrm{\text{app}}}=\frac{k_{\mathrm{\text{ini}}}}{\tau }$, which greatly underestimates the effect of tortuosity on apparent permeability. Then, a new fractal apparent permeability model $k_{\mathrm{\text{app}}}=\frac{k_{\mathrm{\text{ini}}}}{A+Bln(\tau -C)}$ based on modified tortuous effects is obtained by fitting the results from the MRT-LBM simulations. Based on the new fractal apparent permeability models, the results show that with an increasing fractal tortuosity dimension, the apparent permeability decreases rapidly first and then this trend becomes moderate. Our works can provide a more accurate basic model for studying liquid flow in porous media based on the capillary bundle model or pore network model.