## 2 Materials and Methods  
### Coal Samples  
Ordos Basin is a large stable craton basin, which is rich in coal, oil, gas, and other energy sources formed in marine facies, marine-terrigenous/continental facies, and continental facies. The geological structure is relatively simple in this basin. The outcrops are Archean, Erathern, Cambrian, Ordovician, Carboniferous, Permian, Trias, Neogene, and Quaternary from the east to the west [23; 24].  
The main coal-bearing strata are the strata of the Carboniferous-Permanian, and the thickness of the Carboniferous-Permanian coal-bearing strata are approximately 764 m on average. The formations of Benxi, Taiyuan, Shanxi, Lower Shihezi, Upper Shihezi, and Shiqianfeng are the main coal-bearing formations, which consist principally of coal, limestone, siltstone, and sandstone. The Formations of Shanxi and Taiyuan are mainly concentrated economic coals and coalbed methane resources [25]. The coal seams of the Shanxi Formation, No. 5 and Taiyuan Formation, No. 8 are the main mined coal seams and have large thickness, stable distribution, and low to medium coal rank. The total thickness of the coal seams in the Carboniferous-Permanian strata increases from east to west and varies from 5 to 22.8 m.  
The pore structure of coal is determined by the coal rank [7; 8; 26], and is affected by the geological structure [27]. To investigate the influence of coal rank to Sc-CO\({}_{2}\) extraction and avoid the influence of geological structure, five samples that were evenly distributed around the second coalification jump were collected from undeformed Permian coal seams at the southeast margin of Ordos Basin (Figure 1). The physical properties of the coals that were used are shown in Table 1. The maximum vitrinite reflectance under oil immersion (\(R_{\rm o,max}\)) of the coals varies from 0.79% to 1.80%. For the vitrinite, it varies from 56.84% to 78.40%; for the inertinite, it varies from 14.87% to 37.71%; for the exinite, it varies from 2.36% to 5.48%; as for minerals, it varies from 1.25% to 10.0%. The proximate analysis showed that the equilibrated moisture varies from 0.83% to 4.34%, the ash yields varies from 6.57% to 11.36%, and the volatile matter varies from 20.31% to 31.05% for the five coal samples.  
To avoid oxidation during the transportation of specimens and the time required to carry out Sc-CO\({}_{2}\) extraction, the coal samples were stored in vacuum packaged, sealed plastic bags. Theoretically, bigger size coal samples are better for simulating Sc-CO\({}_{2}\) extraction in situ conditions, but bigger size coal samples require a long time to reach the equilibrium of extraction and solution. On the other hand, smaller size coal samples induce difficulty for pore structure with mercury intrusion. So, to mediate the limitations of the two extreme sizes, coal samples were sieved into grain size (20\(-\)60 mesh) using a SPARTAN pulverisette before the experiment. After that, coal samples were sorted into two parts. One part was dried in an air oven at 80 \({}^{\circ}\)C for 12 h and then used for mercury intrusion measurements. The other part was exposed to Sc-CO\({}_{2}\) extraction followed by the same drying and mercury intrusion measurement applied to the first part of the coal samples.