Experimental study on influence of adsorption equilibrium time on methane adsorption isotherm and Langmuir parameter

Highlights

• Pore structures of coal sample with different particle sizes are investigated.

• The impact of equilibrium judgment criteria on adsorption test is investigated.

• The equilibrium judgment criteria affects the calculation of Langmuir parameters.

• The disequilibrium adsorption data satisfies the Langmuir equation.

Abstract

The aim of this work was to examine the impact of equilibrium judgment criteria on adsorption test of samples with different adsorption kinetics and determine how long it takes for different particle size samples to attain equilibrium adsorption data. The adsorption data of coal samples with three different particle sizes was obtained by manometric method at the different time intervals. High pressure CH₄ adsorption equilibrium measurements and low pressure N₂ and CO₂ adsorption measurements were carried out for coal samples of eight various particle sizes. The results demonstrated that both the equilibrium and disequilibrium adsorption data satisfied the Langmuir equation. The Langmuir volume (V_L) increased on the equilibrium time increase and it became more remarkable with increasing particle size. The Langmuir pressure (P_L) showed an opposite and more obvious trend. When the particle size of the coal sample decreased from 2 to 4 to <0.074 mm, the adsorption equilibrium time (AET) required for the adsorption isotherm testing declined rapidly from 389 to 5 h. This research is of some enlightening significance for comparing the adsorption characteristics of samples with different adsorption kinetics (adsorbent, temperature, particle size, etc.).

Introduction

Coalbed methane (CBM), as a clean and high–efficiency energy source, is composed primarily of methane [1]. The energy released in the combustion of 1 m³ of methane is 35.9 million Joules, which is equivalent to the combustion of 1.2 kg of standard coal [2]. For the primary gas production in CBM reservoirs, understanding the adsorption characteristic of CBM is of great importance, and the storage capacity is among important parameters for the coal reservoir's evaluation. Over the few past decades, the Langmuir parameters ($V_L$ and $P_L$) obtained by fitting the adsorption data using the Langmuir equation were extensively used to describe the occurrence of the CBM [3], [4], [5], [6].

As is widely known, the manual grinding and mechanical crushing can damage the complex pore structure of coal [7], [8], [9], [10], [11], [12], which means that such coal particle samples cannot represent the adsorption characteristics of coal and the occurrence regularity of CBM under in situ conditions. On the other hand, the bigger the particle size, the slower the adsorption process occurs and the adsorption equilibrium time is longer [13], [14], [15]. Therefore, an important problem related to the adsorption measurements on coal samples is the particle size selection for the experiments. In recent years, it is remarkable that various equilibrium judgment criteria were used to measure the adsorption isotherms of different samples in previous publications (see Table 1) [13], [16], [17], [18], [19], [20], [21], [22], [23], and, particularly, the random or same equilibrium time was used in the adsorption test for coal samples of different particle sizes. In this case, the bigger the sample, the more representative it is for the natural in situ conditions [24], [25], [26]. It also means that it is more difficult for large particle samples to obtain realistic adsorption data [12], [13], [14], [27].

The adsorption isotherm of coal sample is composed of a series of isothermal adsorption points. These adsorption data points can be measured by gravimetric or manometric methods. With the gravimetric method, a high precision balance is used to measure the change in the sample’s weight when the sample adsorbs gas [28], [29]. With the manometric method, the adsorbed volume of gas can be calculated by subtracting the volume of gas occupying the free volume after adsorption equilibrium is reached from the total volume of gas which was present in the reference cell [24]. In adsorption measurement, there are many factors that may affect the measurement of the adsorbed volume of gas. Lutynski [24] divided them into three categories: intrinsic properties, extrinsic properties, and other factors. The intrinsic properties mainly include content of organic and mineral matter, type of clay minerals, macerals content, and so on [30], [31], [32], [33], [34], [35], [36]. The extrinsic properties mainly include temperature of the sample under analysis, moisture content and particle size of the sample [8], [37], [38], [39]. There are also other factors that may affect the measurement, such as the accuracy of the setup, the compressibility factor, and the time to attain adsorption equilibrium [4], [23], [40]. Among the intrinsic and extrinsic properties, many achievements were made in the previous study [30], [31], [32], [33], [34], [35], [36], [37], [38], [39]. However, the effects of equilibrium time on the adsorption measurement have not received much attention, which determines whether the measured adsorption data are equilibrium or disequilibrium adsorption data. The equilibrium adsorption isotherm is the cornerstone for studying adsorption characteristics and it plays a particularly important role. Scholars found that the adsorption capacity of large particle samples is always low when studying the adsorption properties of samples with different particle sizes [24], [41], [42]. Lutynski [24] thought that this phenomena can be attributed to the fact that the adsorption kinetics is the fastest for fine particles and the complete adsorption may not have occurred for coarser particles. However, it was only a conjecture and no further study was conducted on the effect of equilibrium time on the adsorption capacity of large particle samples.

To attain equilibrium adsorption is the key for the adsorption test of different particle size samples. It is widely known that methane migration within the coal can be generally categorized into three processes, i.e., seepage, diffusion, and adsorption [43], [44]. The diffusion rate restricts the rapid attaining equilibrium adsorption [45]. This study does not look at the kinetics of adsorption. It only considers the influence of equilibrium time on the measured adsorption data from the perspective of adsorption measurement, and how long it takes for different particle size samples to attain equilibrium adsorption data. Therefore, the adsorption isotherms of coal samples with three different particle sizes (0.2–0.25, 0.5–1.0 and 2.0–4.0 mm), which all consisted of six isothermal adsorption points, were obtained at different time intervals (6, 8, 12, 24, 48 and 144 h) to explore the influence of the equilibrium time on the Langmuir parameters. The adsorption equilibrium tests of coal samples with eight various particle sizes were performed to determine the adsorption equilibrium time (AET) which is the shortest adsorption contact time (ACT) that allows the methane molecules to fully enter the coal matrix. The measured results may have a certain significance in the actual adsorption test.