2. Models and Methodology

2.1 Structure of illite and charged surface chemistry

Kaolinite, illite, chlorite and smectite are the most commonly occurring clay minerals43 with illite being the most common diagenetic product in shales44. Generally, clay-hosted pores in shales are slit-shaped or cylindrical, with few occurrences of oval- and cone- shaped pores45,46. Because slit pores are the most prevalent47, we focus on investigating fluid transport in illite-hosted slit-shaped pores. We refer the readers to our previous work and those of others42,48 for a more detailed description of the illite unit cell with chemical formula, K[Si7Al](Al4)O20(OH)4. In Fig.1, we show one illite layer comprising 20-unit cells. 2 illite layers form the top pore surface and the other two illite layers form the bottom. Each illite pore model has three different basal spacings (5nm, 10nm, and 15nm).
There are generally four illite slit pore structures discussed in literature based on charged clay surface chemistry: potassium-hydroxyl (PH)49, hydroxyl-hydroxyl (HH)50, potassium-potassium (PP)51, and a structure52 between the PH and HH pore systems. The corresponding illustrations are shown in the Fig.S-1 in Supporting Information. This work considers only the PH and HH pore systems and a schematic of both are shown in Figs. 2a-b.