“…Despite PNM simplifications, it is still interesting due to the low computational cost, especially with the Fig. 1 Network structure of the previous single PNMs and D-PNMs compared to the presented T-PNM, a single PNM (Blunt 2001;Fatt 1956), b D-PNM with meso-pores coupled to a lattice micro-pores (Bekri et al 2005), c dual with meso-pores and parallel micro-pores and throats (Bauer et al 2012), d a fully twoscale PNM with micro-and meso-pores (Jiang et al 2013), e dual with extra micro-throats to connect the meso-pores (Bultreys et al 2015), f dual with meso-pores and fractures with variable aperture (Hughes and Blunt 2001), g dual with meso-pores and fractures with fixed aperture (Erzeybek and Akin 2008), h D-PNM with extra bypassing fracture links (Liu et al 2017), i dual with unstructured network and variable geometry of fracture (Jiang et al 2017), j the presented T-PNM which includes meso-and micro-pores, meso-and micro-throats, fracture nodes, and fracture links have been accomplished by researchers to enhance the capability and reliability of PNMs (Baychev et al 2019) to realistically simulate and predict the properties of porous materials (Garboczi 1990;Joekar-Niasar and Hassanizadeh 2012;Xiong et al 2016), from hydraulic permeability (Dong and Blunt 2009) and mass diffusivity (Burganos and Sotirchos 1987;Erfani et al 2019) to electrical (Friedman and Seaton 1998) and thermal conductivities (Plourde and Prat 2003).…”