Numerical Simulation Based on the Canister Test for Shale Gas Content Calculation

The accurate determination of the gas in place in shale reservoirs is a basic but challenging issue for shale gas evaluation. Conventional canister gas desorption tests on retrieved core samples and subsequent data analyses (via linear or polynomial regression)—originally developed for coalbed methane, where gases are mainly stored in the adsorbed phase—is unadvisable for shale gas, which is stored as an appreciable amount of free gas in shale reservoirs. In the present study, a mathematical model that simultaneously takes into account gas expansion, adsorption/desorption, and the gas flow in shale is proposed to simulate gas release from a core sample retrieved from the Lower Silurian Longmaxi Formation of the Fuling shale gas field, Sichuan Basin. The results indicate that, compared with the value of 2.11 m3/t rock estimated with the traditional United States Bureau of Mines (USBM) method, the total gas in place within the studied Longmaxi Shale estimated with our mathematical model under reservoir pressure conditions is up to 5.88 m3/t rock, which is more consistent with the result from the new volumetric approach based on Ambrose et al. According to our mathematical model, the content of free gas is 4.11 m3/t rock at true “time zero”, which accounts for 69.9% of the total gas. On the other hand, the lost gas portion is determined to be up to 4.88 m3/t rock (~85% of the total gas). These results suggest that the majority of the free shale gas is actually trapped within the pore space of the shale formation.

Phase Behavior and Composition Distribution of Multiphase Hydrocarbon Binary Mixtures in Heterogeneous Nanopores: A Molecular Dynamics Simulation Study

In this study, molecular dynamics (MD) simulation is used to investigate the phase behavior and composition distribution of an ethane/heptane binary mixture in heterogeneous oil-wet graphite nanopores with pore size distribution. The pore network system consists of two different setups of connected bulk and a 5-nm pore in the middle; and the bulk connected to 5-nm and 2-nm pores. Our results show that nanopore confinement influences the phase equilibrium of the multicomponent hydrocarbon mixtures and this effect is stronger for smaller pores. We recognized multiple adsorbed layers of hydrocarbon molecules near the pore surface. However, for smaller pores, adsorption is dominant so that, for the 2-nm pore, most of the hydrocarbon molecules are in the adsorbed phase. The MD simulation results revealed that the overall composition of the hydrocarbon mixture is a function of pore size. This has major implications for macro-scale unconventional reservoir simulation, as it suggests that heterogenous shale nanopores would host fluids with different compositions depending on the pore size. The results of this paper suggest that modifications should be made to the calculation of overall composition of reservoir fluids in shale nanopores, as using only one overall composition for the entire heterogenous reservoir can result in significant error in recovery estimations.

Activity coefficient models for accurate prediction of adsorption azeotropes

In this study seven adsorption azeotropes involving binary systems and zeolite-based adsorbents were systematically investigated. Pure component isotherms and mixed-gas adsorption data were taken from published literature except for the benzene–propene system on silicalite, which is newly presented in this work using molecular simulations. Experimental adsorbed phase composition and total amount adsorbed of the azeotropic systems were compared with the predictions of several models including: the ideal adsorbed solution theory (IAST), the heterogeneous ideal adsorbed solution theory (HIAST) and the real adsorbed solution theory (RAST) coupled with the 1-parameter Margules (1-Margules) and the van Laar equations. In the latter two models an additional loading parameter was incorporated in the expression of the excess Gibbs energy to account for the reduced grand potential dependency of the activity coefficients in the adsorbed phase. It was found that the HIAST and RAST–1-Margules models were able to predict the azeotropic behaviour of some systems with good accuracy. However, only the RAST–van Laar model consistently showed an average relative deviation below 3% compared to experimental data for both the adsorbed phase composition and the total amount adsorbed across the systems. This modified van Laar equation is therefore preferable in those engineering applications when the location of adsorption azeotropes is required with great accuracy and when there is lack of detailed characterization of the adsorbent that is needed to carry out molecular simulations.

Absolute Adsorption Isotherms for Ethylbenzene + n-Octane + Zeolite NaX System: Determination of the Activity Coefficients of the Adsorbed Phase (Изотермы абсолютной адсорбции для системы этилбензол + н-октан+ цеолит NaX: определение коэффициентов актив

Адсорбция из растворов неэлектролитов микропористыми адсорбентами, такими как цеолиты, представляет не только практический интерес. Благодаря четко определенной внутренней структуре цеолита, он может служить хорошей модельной системой, что дает возможность измерить абсолютную адсорбцию в прямом эксперименте. Такие данные могут привести к лучшему пониманию свойств жидкого раствора в микропорах. В то время как избыточная изотерма адсорбции может быть легко измерена, точное определение абсолютной изотермы адсорбции требует весьма кропотливого и трудоёмкого эксперимента. Поэтому основная проблема заключается в преобразовании данных по избыточной адсорбции в абсолютную изотерму адсорбции. Учитывая данное обстоятельство, нами ранее был предложен метод оценки изотермы абсолютной адсорбции бинарного раствора на микропористом адсорбенте. Метод основан на уравнении Дубинина-Радушкевича, модифицированном для адсорбции из растворов. Уравнение дает концентрационную зависимость абсолютной адсорбции раствора и включает три неподгоночных параметра: предельные величины адсорбции чистых компонентов, которые намного легче измерить, чем изотерму абсолютной адсорбции раствора, и значение равновесной концентрации, соответствующей максимальной избыточной адсорбции. Целью данной работы было изучение физико-химических характеристик адсорбционной фазы на основе данных по абсолютной адсорбции адсорбционной системы этилбензол+н-октан+цеолит NaX. Изотермы избыточной адсорбции измерены при температурах 303.15, 338.15 и 363.15 К с использованием общепринятого статического метода. Предельные (абсолютные) величины адсорбции чистых компонентов измерены пикнометрическим методом. Показано, что измеренные избыточные изотермы адсорбции относятся к II типу по классификации Шая и Надя. Это указывает на сильную адсорбцию этилбензола во всей области концентраций. Рассчитаны по указанному выше методу изотермы абсолютной адсорбции раствора и предпочтительно адсорбируемого компонента. Эти данные позволили рассчитать для адсорбционной фазы избыточный объем смешения, плотность раствора и коэффициенты активности компонентов раствора. На основе последних рассчитаны избыточные термодинамические функции смешения для адсорбционной фазы: свободная энергия, энтропия и энтальпия. Полученные данные позволяют сделать некоторые выводы об адсорбционном растворе. Отрицательное значение величины избыточного объема смешения свидетельствует о сжатии объема. Коэффициенты активности указывают на значительное отрицательное отклонение от идеальности, что означает доминирование межмолекулярного взаимодействия между различными молекулами. Об этом же свидетельствует отрицательная величина избыточной свободной энергии смешения.

Measurement and interpretation of unary supercritical gas adsorption isotherms in micro-mesoporous solids

Gas adsorption at high pressures in porous solids is commonly quantified in terms of the excess amount adsorbed. Despite the wide spectrum of adsorbent morphologies available, the analysis of excess adsorption isotherms has mostly focused on microporous materials and the role of mesoporosity remains largely unexplored. Here, we present supercritical CO2 adsorption isotherms measured at $$T=308$$ T = 308 K in the pressure range $$p=0.02{-}21$$ p = 0.02 - 21 MPa on three adsorbents with distinct fractions of microporosity, $$\phi_2$$ ϕ 2 , namely a microporous metal-organic framework ($$\phi_2=70$$ ϕ 2 = 70 %), a micro-mesoporous zeolite ($$\phi_2=38$$ ϕ 2 = 38 %) and a mesoporous carbon ($$\phi_2<0.1$$ ϕ 2 < 0.1 %). The results are compared systematically in terms of excess and net adsorption relative to two distinct reference states–the space filled with gas in the presence/absence of adsorbent–that are defined from two separate experiments using helium as the probing gas. We discuss the inherent difficulties in extracting from the supercritical adsorption isotherms quantitative information on the properties of the adsorbed phase (its density or volume), because of the nonuniform distribution of the latter within and across the different classes of pore sizes. Yet, the data clearly reveal pore-size dependent adsorption behaviour, which can be used to identify characteristic types of isotherm and to complement the information obtained using the more traditional textural analysis by physisorption.

Adsorption Modeling of CO2 and CH4 in Nanopores Using Simplified Local Density Model: Application in Enhanced Hydrocarbon Recovery in Unconventional Reservoirs

Adsorption isotherms of methane and carbon dioxide adsorption isotherms on shale samples are measured and the simplified local density (SLD) model is used to match the experimental data. The SLD equation also has the generic modeling capabilities to draw the deviation from bulk properties as a function of fluid-solid interaction energies. Still, compared to other available techniques such as molecular simulation, SLD has an advantage of mathematical simplicity and being run at shorter time interval. The model also has satisfactory potential to paint the underlying mechanisms for adsorption preference of one fluid component over the other. The higher adsorption preference of carbon dioxide is reflected in the measurement data and the adsorption model is successfully used to fit the data. In addition to different critical properties of carbon dioxide compared to methane, the main important factor that may describe the high adsorption affinity of carbon dioxide is the fluid-solid potential energy. As shown in this work, the potential energy function shows deeper well depth, the deeper the well depth, the stronger the interaction between the fluid particles and solid surface. By storing gas in high density, liquid like adsorbed phase, the adsorption mechanism can enhance the overall storage capacity of CO2 in deep reservoir rock relative to if there were a free phase alone.

Performance Evaluation of an Adsorption Heat Pump System Using MSC-30/R1234yf Pair with the Impact of Thermal Masses

In this study, we evaluated the performance of low Global Warming Potential (GWP) refrigerant R1234yf on the activated carbon (MSC-30) for adsorption heating applications. The adsorption isotherms of MSC-30/R1234yf were measured using a constant-volume–variable-pressure (CVVP) method from very low relative pressure to the practical operating ranges. The data were fitted with several isotherm models using non-linear curve fitting. An improved equilibrium model was employed to investigate the influence of dead thermal masses, i.e., the heat exchanger assembly and the non-adsorbing part of the adsorbent. The model employed the model for the isosteric heat of adsorption where the adsorbed phase volume was accounted for. The performance of the heat pump was compared with MSC-30/R134a pair using the data from the literature. The analysis covered the desorption temperature ranging from 60 °C to 90 °C, with the evaporation temperature at 5 °C and the adsorption temperature and condensation temperature set to 30 °C. It was observed that the adsorption isotherms of R1234yf on MSC-30 were relatively lower than those of R134a by approximately 12%. The coefficient of performance (COP) of the selected pair was found to vary from 0.03 to 0.35 depending on the heat source temperature. We demonstrated that due to lower latent heat, MSC-30/R1234yf pair exhibits slightly lower cycle performance compared to the MSC-30/R134a pair. However, the widespread adaptation of environmentally friendly R1234yf in automobile heat pump systems may call for the implementation of adsorption systems such as the direct hybridization using a single refrigerant. The isotherm and performance data presented in this work will be essential for such applications.

Adsorption of an Ideal Gas on a Small Spherical Adsorbent

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs’ surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics.