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Adsorption models for methane in shales: review, comparison and application Xu Tang, Nino Ripepi, Kray Luxbacher, and Eleanor Pitcher Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01948 • Publication Date (Web): 31 Aug 2017 Downloaded from http://pubs.acs.org on September 3, 2017
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Energy & Fuels
Adsorption models for methane in shales: review, comparison and application Xu Tang*1 , Nino Ripepi1,2 , Kray Luxbacher2 , Eleanor Pitcher3 (1 Virginia Center for Coal and Energy Research, & 2 Department of Mining and Minerals Engineering Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24060, U.S; 3 GeoEnergy Research Center, University of Nottingham, Nottingham NG7 2RD, UK) Highlights Adsorption models are reviewed for methane adsorption in shales. Three criteria are proposed to compare available methane adsorption models in shale. The dual-site Langmuir model is recommended for engineering applications. Some inappropriate concepts and methods routinely used in shale gas community are clarified. Abstract: Finding an optimized adsorption model to estimate the true adsorbed quantity of methane in shale at reservoir conditions is fundamental for estimating the gas-in-place (GIP), and developing an accurate shale gas transport model. However, describing true methane adsorption behavior in shale is challenging because the density or volume of the adsorbed phase cannot be measured directly using current technology. There are several models available to describe the observed adsorption isotherms and extrapolate the true adsorbed quantity of methane, but a consensus model has not been reached by researchers. This work first revisits available absolute and Gibbs excess adsorption models for describing methane in shales. It then compares nine available adsorption models to assess the efficacy of each model in describing both high pressure and low pressure methane adsorption isotherms in shales. Three aspects of the adsorption model are compared: (1) the goodness-of-fit of each adsorption model, (2) interpretation of the observed test phenomena, and (3) predicted isotherms beyond test data. Comparison results show that even though the goodness-of-fit for each model is comparable, the dual-site Langmuir model is still superior to other available models in interpreting observed phenomena and extrapolating adsorption isotherms beyond test data. The successful application of the dual-site Langmuir model therefore lays the foundation for accurately estimating and extrapolating the deep gas resource and differentiating the accurate ratio of the adsorbed phase to bulk gas for use in shale gas transport models. This study also clarifies some inappropriate concepts and methods routinely used by the shale gas community. Key words: Methane, adsorption, shale, Langmuir model, high pressure
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1 Introduction Shale gas has been considered as one of the most important energy resources in the world and countries have launched different programs to estimate shale gas resources and develop new techniques to enhance shale gas recovery [1-3]. Shale gas, the most significant component of which is methane, exists in three different states in the subsurface: free gas, adsorbed gas and dissolved gas. Current studies have shown the adsorbed gas accounts for 20-85% of the total shale gas-in-place (GIP) [4]. Therefore, it is important to understand the adsorption behavior of methane in shale in order to accurately estimate shale gas resources in shale formations. Knowing the exact ratio between the adsorbed and free gas is also fundamental to understand shale gas transport behavior, and predict shale gas well production behavior [5, 6]. Since most shale formations are at depths from 1000m to 3000m the reservoir pressure of some deep shale formations can go up to 27MPa [4]. This in situ characteristic of shale formations requires high pressure methane adsorption studies for shales. Unfortunately, because of instrument limitation, there is limited high quality data for high pressure methane adsorption in shale [7-11] which makes investigation and characterization of methane adsorption in shale challenging. In order to understand methane adsorption behavior in shale under reservoir conditions it is essential to have an accurate model for methane adsorption in shale. The challenge is to describe observed adsorption isotherms showing Gibbs excess phenomenon [12, 13]. Some researchers use the molecular simulation approach to simulate methane adsorption behavior in shale and synthetic materials [14-26]. These studies are important to understanding the methane adsorption mechanism at a molecule scale. However, since the simplified, homogeneous pore structure of the computational approach does not represent the heterogeneous properties of shale and the computation costs are high, the molecular simulation method has not been widely used in engineering applications. In addition, molecular simulation has not been used to interpret the adsorption phenomenon such as the crossover of the isotherms under different temperatures observed in experimental data. Other researchers have attempted to build a physical model from observed adsorption isotherms based on either known constant density (density of liquid methane) or constant volume assumptions of the adsorbed methane phase [5, 10-13, 27-35]. Unfortunately, most of the proposed adsorption models in literature do not provide satisfactory interpretation of the experimental data, and the assumptions used are still uncertain. For example, the crossover of the observed adsorption isotherms at high pressures has not been reasonably explained. In addition, none of the models can be used to extrapolate adsorption isotherms beyond test data without using empirical relationships. Therefore, an optimized model is needed for accurately describing the adsorption behavior of methane in shale. The authors previously applied the dual-site Langmuir model for accurately estimating high pressure shale GIP resource in deep shale formations. This supports the fact that the true adsorbed amount of shale gas has been underestimated, while the total GIP has been historically overestimated [5]. This model is also able to determine the behavior of the adsorbed phase of methane in shale. However, whether the same method can be extended for low pressure shale formations is still unclear since this method in general requires a larger 2 ACS Paragon Plus Environment
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experimental data set. Under low pressure conditions, the Gibbs excess adsorption phenomenon is not observed, where the measured adsorbed amount always increases with increasing pressure. Whether the behavior of the adsorbed phase can be obtained from low pressure adsorption data for methane in shales still remains unknown. This work first reviews the adsorption models for both absolute and Gibbs excess adsorption isotherms. Then, nine current available models are compared to present the specific characteristics of each model using three data sets (two low pressure data sets and one high pressure data set). These were chosen to provide a clearer picture of the strengths and weaknesses of each model. Through this comparison the best adsorption model can be obtained for engineering applications. Some inappropriate concepts and methods routinely used for shale gas development are also clarified. This study reviews and compares adsorption models used for engineering applications, especially for the shale gas industry; therefore, molecular simulation for methane adsorption in shale is not part of this work. 2. Concept of Gibbs excess adsorption In the laboratory, adsorption measurements made using either manometric (volumetric) or gravimetric approaches cannot measure the true adsorbed quantity. This is because it is observed that the measured adsorption uptake increases up to a maximum and then decreases with increasing pressure. This observation contradicts the fact that the true adsorbed amount monotonically increases with pressure. In order to solve this issue, Josiah Willard Gibbs introduced the concept of “excess sorption” (also called “Gibbs excess sorption,”) where he gives a simple geometric explanation of the measured adsorbed quantity by considering the finite volume of the adsorbed phase [36],
ne = na −Va ⋅ ρg
(1)
where ݊ is the Gibbs excess adsorbed amount, ݊ is the true adsorbed amount (absolute
adsorbed amount), ܸ is the volume of adsorbed phase, and
ρa is the density of adsorbed phase,
ρg is the bulk gas density. Derivation of equation (1) based on manometric measurement
method is shown in Supplemental Material. The Gibbs excess sorption concept is illustrated in Figure 1, which shows a simplified equilibrium sorption system with a single component gas adsorbed on the porous solid at pressure (ܲ) and temperature (ܶ). The density of “gas” (also called “adsorbed phase”) near the solid surface is higher than the bulk gas density and decreases the farther the distance away from the solid surface. At a certain distance, the surface can no longer influence the bulk gas, and the density is equal to the bulk gas density.
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Figure 1 Concept of Gibbs surface excess sorption for gas adsorption on solid. Vtot is the sum of Va*and Vgas*, which can be measured by non-adsorbed gas (Helium) intrusion test but both Va*and Vgas* cannot be measured separately. The density figure shows the hypothetical density profile near the solid surface. According to Gibbs excess concept, if the volume of the adsorbed phase is extremely small or the density of adsorbed phase is much higher than the bulk gas under low pressure, the Gibbs excess adsorbed amount is almost equivalent to the true adsorbed amount,
ne ≈ na
(2)
Equation (2) is the standard approach to obtain isotherm adsorption curves in the laboratory using either the manometric approach or the gravimetric approach. However, under highpressure conditions (>15 MPa), the volume of the adsorbed layer, Va ) cannot be ignored (equation-1), and there is a significant difference between Gibbs excess adsorption content ( ne ) and true (absolute) adsorption content ( na ). In this scenario, equation (2) is no longer true.In the laboratory we can only measure Gibbs excess adsorption content. Therefore, we have to build an appropriate adsorption model using Gibbs excess concept (equation-1) to simulate the Gibbs excess adsorption isotherms and then obtain the absolute adsorption content. 2 Adsorption model review In order to model gas adsorption behavior, a large collection of adsorption models have been proposed by previous researchers to model adsorption isotherms such as Henry’s model, Langmuir’s model, BET model and pore-filling model [37-41]. Here, an overview of these original models and their revised forms will be presented, and the scopes of their applicability are discussed in detail. Many of the recently developed models have only been fit to a few sets of low pressure (
