Research Article | Open Access
Qing Chen, Yuanyuan Tian, Peng Li, Changhui Yan, Yu Pang, Li Zheng, Hucheng Deng, Wen Zhou, Xianghao Meng, "Study on Shale Adsorption Equation Based on Monolayer Adsorption, Multilayer Adsorption, and Capillary Condensation", Journal of Chemistry, vol. 2017, Article ID 1496463, 11 pages, 2017. https://doi.org/10.1155/2017/1496463
Study on Shale Adsorption Equation Based on Monolayer Adsorption, Multilayer Adsorption, and Capillary Condensation
Shale gas is an effective gas resource all over the world. The evaluation of pore structure plays a critical role in exploring shale gas efficiently. Nitrogen adsorption experiment is one of the significant approaches to analyze pore size structure of shale. Shale is extremely heterogeneous due to component diversity and structure complexity. Therefore, adsorption isotherms for homogeneous adsorbents and empirical isotherms may not apply to shale. The shape of adsorption-desorption curve indicates that nitrogen adsorption on shale includes monolayer adsorption, multilayer adsorption, and capillary condensation. Usually, Langmuir isotherm is a monolayer adsorption model for ideal interfaces; BET (Brunauer, Emmett, Teller) adsorption isotherm is a multilayer adsorption model based on specific assumptions; Freundlich isotherm is an empirical equation widely applied in liquid phase adsorption. In this study, a new nitrogen adsorption isotherm is applied to simultaneously depict monolayer adsorption, multilayer adsorption, and capillary condensation, which provides more real and accurate representation of nitrogen adsorption on shale. In addition, parameters are discussed in relation to heat of adsorption which is relevant to the shape of the adsorption isotherm curve. The curve fitting results indicate that our new nitrogen adsorption isotherm can appropriately describe the whole process of nitrogen adsorption on shale.
Shale gas has attracted much attention in United States, China, Canada, and so forth, because of the gas storage mechanism and recovery potential of shale gas reservoirs [1, 2]. To investigate gas adsorption capacity and pore size distribution of shale rocks, high-pressure methane adsorption and low-pressure nitrogen or carbon dioxide adsorption experiments are conducted, respectively. Many researches have been done to find and modify adsorption equations suitable for describing methane adsorption. Considering methane adsorption as monolayer adsorption, Langmuir equation, L-F (Langmuir-Freundlich) equation, and M-L (modified Langmuir) equation are successfully applied to evaluate methane adsorption [3–5]. Furthermore, D-R (Dubinin-Radushkevich) equation, D-A (Dubinin-Astakhov) equation, and S-D-R (supercritical Dubinin-Radushkevich) equation are also used with consideration of methane adsorption as micropore filling [6–8]. For carbon dioxide adsorption, to take into account the monolayer adsorption property, both Langmuir equation and L-F equation are applied to depict variations of the adsorption capacity with pressure [9–11]. On the contrary, it is hard to find an equation to depict low-pressure nitrogen adsorption because of the complicated adsorption mechanism. On the basis of BDDT (Brunauer-Deming-Deming-Teller) adsorption isotherm classification, nitrogen adsorption belongs to type IV, which indicates that it includes three processes: monolayer adsorption, multilayer adsorption, and capillary condensation. Unfortunately, the majority of adsorption equations are developed based on only one kind of adsorption mechanism, and they can be categorized into three aspects: monolayer adsorption, multilayer adsorption, and micropore filling.
In terms of monolayer adsorption, a widely accepted one is Langmuir adsorption equation which assumed only one type of adsorption sites on the surface of adsorbent [12, 13]. When extending the Langmuir equation for gas-liquid-phase adsorption studies, two types of sites are considered and the relationship between equilibrium concentration and amount of adsorbate is obtained [14–19]. Because the Langmuir equation describes adsorption on homogeneous surface, Gaussian energy distribution is used to adjust monolayer adsorption theory to heterogeneous surface [20–22]. To study multicomponent, monolayer adsorption of multicomponent gas, the assumption that the saturated amount of adsorption for each component is equal based on Langmuir equation was derived [23, 24].
In the aspect of multilayer adsorption, BET (Brunauer, Emmett, and Teller) equation is the most popular one, and it proposes a multilayer adsorption model which assumes that the interaction on adsorbent surface is much larger than that between neighboring adsorbate molecules [25–27]. The theory is appropriate for adsorption on solid surfaces with homogeneous chemical properties, which is frequently applied to calculate specific surface area for porous media. To extend BET equation to multicomponent adsorption, three kinds of n-component BET equations were proposed considering that adsorbed layers have evaporation-condensation characters for liquid mixture, supposing that the adsorbed layer of gas mixture is an ideal solution according to statistic thermodynamics and assuming gas mixture is immiscible liquid [28–31].
Micropore filling is also a common adsorption mechanism, which is introduced on the basis of Polanyi adsorption potential theory . According to thermodynamics, adsorption potential is transferring unit mass of adsorbate from gas phase to adsorbent surface. On account of thermodynamics, D-R and D-A equations were generated [33–36]. Changing micropore filling to surface coverage and keeping feature of Gaussian distribution of energy, D-R-K (Dubinin-Radushkevich-Kaganer) equation was built [37, 38]. For micropore filling on nonregular porous media, D-R equation was modified by fractal dimension function . Furthermore, for supercritical fluid adsorption, S-D-R equation was built .
In fact, most adsorbents are heterogeneous porous media. Combination of adsorption equations is a solution to build equation for heterogeneous adsorbent. In studies of methane adsorption, empirical Freundlich equation was combined with Langmuir equation to obtain the L-F equation which is widely used in depicting CBM (coal bed methane) adsorption successfully [40, 41]. Moreover, heterogeneity of adsorbent surface has been taken into account, and an adsorption equation was built to express the relationship between equilibrium concentration and mass of adsorbate by combining Freundlich adsorption isotherm with Langmuir adsorption isotherm [42, 43].
It is clear that these adsorption equations only focus on one adsorption mechanism and cannot be applied to interpret monolayer adsorption, multilayer adsorption, and capillary condensation simultaneously. In addition, it is well known that shale consists of clay minerals (kaolinite, illite, chlorite, etc.), detrital minerals (quartz, feldspar, etc.), and some characteristic minerals (such as pyrite) [44–48], each with its specific adsorption property. On the other hand, pore size distribution in shale is irregular , which results in an uneven distribution of adsorption potential. Compared with homogeneous materials used in other interfacial phenomenon studies, shale is an extremely heterogeneous adsorbent. However, most of current adsorption models assume that adsorbent is homogenous. Hence, our research is aiming at building a new adsorption equation for shale which enables us to depict complex adsorption including monolayer adsorption, multilayer adsorption, and capillary condensation.
Adsorption and desorption data of shale measured by nitrogen at low temperature (77 K) is a fundamental method to analyze pore structure of shale. Samples were collected from Yanchang formation (Triassic, Ordos), Pingliang formation (Ordovician, Ordos), Wulalik formation (Ordovician, Ordos), Xujiahe formation (Triassic, Sichuan), Niutitang formation (Cambrian, Sichuan), and Doushantuo formation (Ediacaran, Sichuan). Properties of samples are described in Table 1. All samples were ground to pass a sieve size of 60 mesh (250 μm). For outgassing, the pulverized samples were dried and vacuumized at 80°C for 12 hours.