Simplified Local Density Model Research Articles

Studies into confined methane adsorption in shale nanopores using a simplified local density model

The large number of nanopores in shale reservoirs provide an effective storage space for gases, which can assist in accurately characterizing the confined adsorption characteristics, including the adsorption amount of fluid in nanopores that is important for a detailed understanding of shale gas storage mechanisms and production prediction. Although the simplified local density (SLD) model has been widely used to describe the behavior of confined adsorption in slit-like pores, its application in relation to cylindrical pores has not been studied in detail. In this study, the importance of fluid–fluid interaction and fluid–solid interaction has been analyzed, with the expressions for the distribution of confined attractive parameter in cylindrical pores are derived by combining with the (3/8)σff assumption to establish a new SLD model. The reliability of the new model was verified by the publicly available experimental methane excess adsorption data for shale at different temperatures and the simulation results from the Grand Canonical Monte Carlo (GCMC). Moreover, by comparing with the SLD model with the slit pore structure, it was found that the adsorption isotherms and the confined fluid density distribution pattern characterized by the SLD model with the cylindrical pores were closer to the actual reservoir conditions of shale. In addition, the densities characterized by SLD models with a (3/8)σff assumption and with a (1/2)σff assumption at different Λb have been discussed and analyzed, and it is found that the selection of a suitable Λb would help to improve the accuracy of SLD model. The results might provide new theoretical insights into confined methane adsorption, with the new SLD model providing better engineering applications in shale gas development, gas storage, and pore structure characterization.

Modeling carbon dioxide and methane adsorption on illite and calcite: enhancing the simplified local density model through crystal structure modifications.

The simplified local density (SLD) model has been frequently utilized to describe gas adsorption in porous media. The common assumptions associated with the SLD model are the graphene slit and uniform distribution of atoms. However, these fail to depict the heterogeneous surface of minerals. In this study, the original SLD model was modified by substituting mineral crystal structures for the homogeneous carbon layer when building the slit. The modified model may capture the heterogeneity-induced variation of the fluid-pore interaction potential and adsorbed phase density near the mineral surface. The calculated adsorption isotherms of methane and carbon dioxide on illite and calcite surfaces at 330.15 K were compared with literature experiment data to validate the modified SLD model. For the simulation of gas adsorption isotherms, the modified model predictions agree reasonably well with the previously reported experiment results using the gravimetric method. The calculated density profile in the slit indicates the monolayer adsorption behavior of CH4 and CO2. Based on more precise interaction potentials, the number of regression parameters was reduced to two, and the physical meaning of the model parameters was clarified. Therefore, for estimating hydrocarbon storage in reservoirs, the modified SLD model could be used as an efficient alternative to time-consuming molecular simulation methods.

CO2 storage in organic nanopores with varying widths: Molecular simulation and simplified local density model

Accurately characterizing CO2 adsorption behavior in organic nanopores is a prerequisite for estimating CO2 storage capacity in shale reservoirs with complex pore structures. This study employs grand canonical Monte Carlo (GCMC) molecular simulations to investigate the CO2 adsorption characteristics in organic nanopores with varying widths over a wide range of temperatures and pressures. Based on GCMC simulations, the pore width in the simplified Local-Density (SLD) adsorption model is related to key adsorption parameters, enabling the SLD model to evaluate CO2 storage density rapidly and accurately in organic nanopores under complex reservoir conditions. The research findings suggest that the features of CO2 excess adsorption curves are mainly influenced by temperature and the number of adsorption layers. Higher temperatures and increased adsorption layers result in higher pressure requirements to achieve the CO2 excess adsorption peak. Under high pressures, the number of adsorption layers plays a critical role in enhancing the adsorption capacity. Due to the constraints of pore size, there are fewer adsorption layers in micropores, leading to higher CO2 excess adsorption in mesopores than in micropores under high pressures. In the SLD model, the key parameter Λb decays exponentially with the increase of pore width. The average density of CO2 in the nanopores calculated by the modified SLD model is in good agreement with the simulation results. Finally, the research reveals that smaller organic nanopore widths result in higher CO2 densities, with limited sensitivity to temperature and pressure variations. Low pressure and high temperature reservoir conditions are unfavorable for CO2 storage, but adsorption significantly enhances CO2 storage density in nanopores, particularly in micropores.

Thermodynamic modeling of adsorption of dimethyl sulfide on raw and modified activated carbon by simplified local density model

The simplified local density (SLD) model was employed to analyze the experimental results of the adsorption of dimethyl sulfide (DMS) from a model fuel (n-hexane) on raw and modified walnut shell activated carbon (WSAC) with different impregnated amounts of silver ions (Ag-2, 4, 6, 8, and 10 mass percent). Modified Peng–Robinson equation of state was used in the liquid phase and the 6-12 Lenard Jones (LJ) potential function was implemented to represent the solid-fluid interactions. The LJ parameters for pure DMS and n-hexane were obtained from the Tsonopoulos correlation for the Second Virial coefficient data. Published experimental results of DMS and n-hexane adsorption were used for the physical properties and the molecular parameters needed in SLD model. Excess adsorption amounts of DMS were then calculated and compared with the experimental data. The average absolute deviations (AAD) between the experimental data and calculated results were 0.0072, 0.0727, 0.0377, 0.0601, 0.0605, and 0.0634 mmol/gr adsorbent for WSAC, WSAC-Ag-2, WSAC-Ag-4, WSAC-Ag-6, WSAC-Ag-8, and WSAC-Ag-10, respectively. For the same adsorbents the percent average absolute relative deviation (AARD%) were 14.11, 15.50, 7.70, 15.48, 16.16, and 29.09, respectively. The applicability of the SLD model in liquid-phase adsorption is validated.

Gas adsorptions of geological carbon storage with enhanced gas recovery

Understanding gas adsorptions in porous media is of critical importance to numerous academic research and industrial applications. Here, adsorptions of methane and carbon dioxide, which are primary compositions of natural gas and carbon capture and storage (CCS) processes, on different minerals are specifically investigated and their effects on reservoir productions and carbon storage processes are evaluated. First, an improved simplified local-density (SLD) model is developed to calculate the gas adsorptions by considering the complex porous composition and confinement effects induced phenomena. Then, the improved SLD model is embedded into a self-developed field simulation program to analyse the production processes of a selected large-scale gas reservoir. The proposed improved adsorption model is validated to be accurate for various multiscale minerals at different temperature and pressure conditions. By using the coupling with reservoir numerical simulation, the adsorption model is successfully up-scaled to practical field scale which is efficient and effective for predicting gas productions and analysing relevant influential factors, such as temperature, pressure and reservoir physical properties. The proposed theoretical approach provides strong technical support for future natural gas productions and CCS projects with its capability of calculating gas adsorptions on different minerals and practical gas field productions.

Predicting Adsorption of Methane and Carbon Dioxide Mixture in Shale Using Simplified Local-Density Model: Implications for Enhanced Gas Recovery and Carbon Dioxide Sequestration

Carbon dioxide (CO2) capture and storage have attracted global focus because CO2 emissions are responsible for global warming. Recently, injecting CO2 into shale gas reservoirs is regarded as a promising technique to enhance shale gas (i.e., methane (CH4)) production while permanently storing CO2 underground. This study aims to develop a calculation workflow, which is built on the simplified local-density (SLD) model, to predict excess and absolute adsorption isotherms of gas mixture based on single-component adsorption data. Such a calculation workflow was validated by comparing the measured adsorption of CH4, CO2, and binary CH4/CO2 mixture in shale reported previously in the literature with the predicted results using the calculation workflow. The crucial steps of the calculation workflow are applying the multicomponent SLD model to conduct regression analysis on the measured adsorption isotherm of each component in the gas mixture simultaneously and using the determined key regression parameters to predict the adsorption isotherms of gas mixtures with various feed-gas mole fractions. Through the calculation workflow, the density profiles and mole fractions of the adsorbed gases can be determined, from which the absolute adsorption of the gas mixture is estimated. In addition, the CO2/CH4 adsorption selectivity larger than one is observed, illustrating the preferential adsorption of CO2 over CH4 on shale, which implies that CO2 has enormous potential to enhance CH4 production while sequestering itself in shale. Our findings demonstrate that the proposed calculation workflow depending on the multicomponent SLD model enables us to accurately predict the adsorption of gas mixtures in nanopores based on single-component adsorption results. Following the innovative calculation flow path, we could bypass the experimental difficulties of measuring the multicomponent mole fractions in the gas phase at the equilibrium during the adsorption experiments. This study also provides insight into the CO2/CH4 competitive adsorption behavior in nanopores and gives guidance to CO2-enhanced gas recovery (CO2-EGR) and CO2 sequestration in shale formations.

Evaluation of Gas Adsorption in Nanoporous Shale by Simplified Local Density Model Integrated with Pore Structure and Pore Size Distribution.

Simplified local density (SLD) model has been widely used to describe the gas adsorption behaviors in porous media. However, the slit pore geometry and constant pore width associated with the SLD model may fail to represent the heterogeneous pore network structure in shale. In this study, a new method to integrate the SLD model with the slit and cylindrical pore structures as well as the pore size distribution (PSD) is proposed and validated by the grand canonical Monte Carlo (GCMC) simulations and the experimentally measured adsorption of methane on shale with complex pore network. Comparison results show that reasonably good agreement is achieved between the SLD model and GCMC simulations for both the gas adsorption isotherms and discrete-density profiles in multiwalled carbon nanoslit and nanotube. The corresponding average absolute percentage deviations (% AADs) are below 0.3 and 9.3 for gas adsorption isotherm and discrete-density profile, respectively. In addition, the SLD model coupled with the PSD of slit and cylindrical pores ranging from micro- to macropores properly characterizes the measured excess adsorption of methane on Wolfcamp shale core sample with % AADs between 1.7 and 3.6. It is found that when the pore volume is fixed, the gas adsorption isotherm and gas density profile are heavily dependent on the pore geometry and pore size. Furthermore, integrating the PSD into the SLD model can guarantee the valid identification of the adsorbed- and free-gas regions in flow channels with different sizes based on the gas density profiles. The findings of this study shed light on the effects of pore structure on gas adsorption in nanopores and enable us to precisely evaluate and predict the gas adsorption behaviors in slit and cylindrical pores over a wide range of pore sizes.

Methane adsorption on shale under in situ conditions: Gas-in-place estimation considering in situ stress

Gas-in-place (GIP) is one of the essential indices for the resource evaluation of shale gas storage capacity. In this study, based on the simplified local density (SLD) theory, the shale adsorption capacity was investigated considering the effect of burial depth on the shale pore structure. Shale isotherm adsorption experiments under triaxial conditions were performed with a homemade adsorption test device, and CH4 adsorption isotherms under different shale reservoir conditions representative of different burial depths were obtained. By establishing the relationship between the SLD model regression parameters and burial depth, a shale GIP estimation model considering the influence of in situ stress was established. In situ stress controls the pore structure of shale and consequently affects the gas storage capacity of shale. The conventional method does not consider the influence of in situ stress, resulting in overestimation of the free gas content, underestimation of the adsorbed gas content, and overall overestimation of the GIP by 1.12–1.26 times. Taking into account the influence of the stress state, the contribution of the free gas content to GIP is weakened. In contrast, the adsorbed gas content plays a key role in GIP. The distribution of the shale reservoir GIP concentrates at depths of 2500–4500 m. These findings will be helpful in the future evaluation of shale gas reserves and improvement in shale gas content evaluation methods.

Prediction of high-pressure adsorption of CH4 and CO2 in shale

The study of CH4 and CO2 adsorption behavior in shale under high-pressure is critical for the estimation of gas content and CO2 sequestration in deep shale gas reservoirs. However, it is very difficult for the adsorption experiment pressure to reach the high pressure of the deep shale gas reservoirs. This paper aims to study the feasibility of Langmuir model, supercritical Dubinin-Redushckevich (SDR) model and Simplified Local-Density (SLD) model to predict the high-pressure adsorption based on the low-pressure adsorption data. The results showed that the Langmuir model, SDR model and SLD model can fit the adsorption isotherm of CH4 and CO2 in shale well. In the ranges of pressure (0-12 MPa) and temperature (308.15-328.15 K), the adsorption phase densities obtained by the Langmuir model and the SDR model are fixed values, but the adsorption phase density obtained by the SLD model is a function of temperature and pressure, which makes the SLD model more predictive. The high-pressure adsorption data in four literature sources were used to compare the prediction capabilities of the Langmuir model, the SDR model and the SLD model, and average absolute percent error (%AAD) predicted are 11.56%, 6.15%, and 3.05%, respectively. When predicting the absolute adsorption at higher pressures, it is unreasonable to use a fixed adsorption phase density. Compared with the SLD model, the Langmuir and SDR models slightly underestimated the CH4 absolute adsorption capacity and seriously overestimated the CO2 absolute adsorption capacity. The results can help evaluate shale gas production and the potential for CO2 sequestration.

Characterization of adsorption isotherm and density profile in cylindrical nanopores: Modeling and measurement

Gas adsorption behavior in shale kerogen may not be fully described using the Simplified Local-Density (SLD) model with a slit-shaped pore. In this study, an extension of the SLD model is proposed to characterize the adsorption isotherm and density profile in shale nanopores with a circular pore geometry. Such an extension enables the pore structure associated with the SLD model to be comparable with the cylindrical micro- and mesopores in shale kerogen. To examine the accuracy and reliability of the extended SLD model, adsorption isotherms and density profiles of methane and carbon dioxide in single-walled carbon nanotubes (SWCNTs) calculated by the extended SLD model were compared with the corresponding quantities determined via the grand canonical Monte Carlo (GCMC) simulations. In addition, the extended SLD model was used to evaluate the measured adsorption of methane on the Marcellus shale core sample to demonstrate its practicability. The results of this study indicate that the adsorption isotherm and density profile calculated by the extended SLD model are in reasonably good agreement with those determined via the GCMC simulation. Moreover, the extended SLD model can properly characterize the measured adsorption isotherm of methane on shale. These findings illustrate that the extended SLD model is a robust engineering model, which is capable of predicting the adsorption isotherm and density profile in cylindrical nanopores. More significantly, the extended SLD model serves as a link to convey the microscopic details from the GCMC simulations to the interpretation of experimental measurements through rapid computations.

Modeling High-Pressure Methane Adsorption on Shales with a Simplified Local Density Model.

Shale gas has attracted increasing attention as a potential alternative gas in recent years. Because a large fraction of gas in shale formation is in an adsorbed state, knowledge of the supercritical methane adsorption behavior on shales is fundamental for gas-in-place predictions and optimum gas recovery. A practical model with rigorous physical significance is necessary to describe the methane adsorption behavior at high pressures and high temperatures on shales. In this study, methane adsorption experiments were carried out on three Lower Silurian Longmaxi shale samples from the Sichuan Basin, South China, at pressures of up to 30 MPa and temperatures of 40, 60, 80, and 100 °C. The simplified local density/Elliott–Suresh–Donohue model was adopted to fit the experimental data in this study and the published methane adsorption data. The results demonstrate that this model is suitable to represent the adsorption data from the experiments and literature for a wide range of temperatures and pressures, and the average absolute deviation is within 10%. The methane adsorption capacity of the Longmaxi shale exhibited a strong linear positive correlation with the total organic carbon content and a linear negative correlation with increasing temperature. The rate of decrease in the methane adsorption capacity with swing temperature increased with the total organic carbon content, indicating that the organic matter is sensitive to temperature.

Modeling pore proximity using a modified simplified local density approach

Unconventional oil and gas resources have gained remarkable interest, as their production is expected to grow significantly in the coming decades. However, among these resources, the shale formations feature extremely small nanopores, imposing considerable challenges in characterizing and modeling fluid pressure-volume-temperature (PVT) property and fluid phase behavior. The fluid phase behavior was reported to deviate from its bulk phase when confined in nanopores. This is often referred to as pore proximity effect. Herein, we present a systematic study using a modified simplified local density (SLD) approach to investigate the pore proximity effect. Phase envelopes have been constructed for two typical synthetic hydrocarbon mixtures representing volatile and black oils as well as two real-life crude oil samples extracted from an unconventional reservoir in Canada. This work is the first report applying the SLD model on real-life crude oil samples. With decreasing pore size, the confined fluids all exhibit shrinking two-phase envelopes, where the pore proximity effect becomes notable for pore size smaller than 10 nm. Furthermore, the SLD model has been demonstrated on the case where the crude oil sample is confined in a literature reported shale sample with a realistic pore size distribution. This work serves as an important building block towards better understanding of the pore proximity effect and practical implementaion into real-life reservoir simulators to guide production activities.

Absolute Adsorption of CH4 on Shale with the Simplified Local-Density Theory

Summary Using a thermogravimetric (TGA) method, the excess methane (CH4) adsorption of four organic shale samples is measured at temperatures of 303.15 to 383.15 K and pressures of 0 to 15.0 MPa. Simplified-local-density (SLD) theory is used to calculate the density distribution of CH4 in nanopores, which is then used to obtain the adsorbed CH4 density on four shale samples. Such density is applied to obtain the absolute CH4 adsorption by correcting the measured excess CH4 adsorption. SLD theory shows that the adsorbed CH4 density is strongly affected by temperature and pressure, as well as the pore size, which is in line with the previous findings from molecular simulations. SLD theory captures the density of the adsorbed phase of CH4 in the presence of CH4/pore-wall interactions. However, the SLD theory is more efficient than molecular simulation methods in determining the adsorbed CH4 density considering that only two parameters in the SLD model are adjusted to match the excess adsorption of CH4 on shale. It is observed that the corresponding absolute adsorption of CH4 is higher than the excess adsorption; this suggests that it is not reasonable to use the measured excess adsorption to estimate the storage of CH4 on shale. This study applies the SLD theory to investigate the adsorption behavior of CH4 in organic pores at different pressure/temperature conditions, and, more importantly, it yields a more-efficient approach (i.e., SLD theory) in determining the absolute adsorption than the sophisticated molecular simulations tools.

Modified SLD model for coalbed methane adsorption under reservoir conditions

In the process of coalbed methane (CBM) mining, with the decreasing of reservoir pressure, stress sensitivity and matrix desorption shrinkage, which could be called self-regulating effect comprehensively, possess great effect on the gas adsorption due to the changing of pore volume. Therefore, it is necessary to modify the simplified local density (SLD) model to investigate the gas adsorption under reservoir conditions for an accurate prediction of CBM production. For the utilization of SLD adsorption model, assume the pores as slit pore. When pressure is lower than critical desorption pressure and keeps falling, the deformations of specific surface area (SSA) and pore width could be studied by the chosen Shi and Durucan (S&D) model. Furthermore, based on the variation relationship and the modification of SLD model, a new adsorption predicting model could be derived with the consideration of stress sensitivity, and matrix desorption shrinkage. In the absence of stress sensitivity and matrix desorption shrinkage, the calculated consequence is relatively smaller than the actual field adsorption data. What’s more, the sensitivity analyses of Poisson’s ratio, pore volume compressibility and critical desorption pressure are conducted with the application of this new model. At the same reservoir pressure, Poisson’s ratio possesses negative relationship with modified adsorption, while pore volume compressibility and critical desorption pressure both possess positive influence on modified adsorption. The main reason is that Poisson’s ratio affects matrix desorption shrinkage negatively, while pore volume compressibility and critical desorption pressure affect matrix desorption shrinkage positively. In spite of the opposite effect of stress sensitivity and matrix desorption shrinkage on pore deformation, matrix desorption shrinkage exhibits a dominant role in self-regulating.

Simplified local density model for gas adsorption in cylindrical carbon pores

Abstract Carbon materials, coal-bed methane and shale gas reservoirs contain various carbon pore geometries like slit and cylinder. Simplified local density (SLD) model is a beneficial and widely recognized method for gas adsorption in slit-like carbon pore, and hasn't been completely extended from slit-like carbon pore to cylindrical carbon pore, which restricts its actual application. Herein, a SLD-cylinder model is established by obtaining the key parameters (i.e. attractive parameter and co-volume parameter in adsorbed phase) with the introduction of dummy attractive potential and the validation with clean energy gas (i.e. H2 and CH4) computational adsorption results. Meanwhile, for this model, the effect of carbon layers and the sphere of application are fully discussed here. Furthermore, based on SLD-cylinder model, isobars and isotherms of H2 and CH4 at a temperature ranging from 213 to 413 K and a pressure ranging from 1 to 10 MPa are investigated in 2.7 nm and 1.35 nm cylindrical pores. We find that carbon layer number is an essential factor for gas adsorption calculation in a cylindrical pore. Also, the SLD-cylinder model is applicable for the pressure higher than ambient one and the pore size larger than 1 nm. Moreover, owing to the significant effect of bulk fluid density (BFD) on excess adsorption, for CH4 especially, the shapes of isobar and excess isotherm vary mightily with pressure and temperature, respectively. This understanding could be applied to the storage of clean energy gas and the recovering of coal-bed methane (CBM) and shale gas. Therefore, the new developed SLD-cylinder model is as useful as the original SLD-slit model in the applications of gas storage, unconventional gas reservoirs recovering and pore structure characterization.

Prediction of methane adsorption content in continental coal-bearing shale reservoir using SLD model

Shale gas, as an important unconventional resource, has drawn global attention. It is mainly composed of adsorption gas and free gas. Adsorption gas content could play an important guiding role on both the selection of favorable perspective area and the exploration and exploitation of shale gas resources. In order to accurately measure adsorption gas content, a new approach was established to predict the adsorption isotherm of methane on shale. Based on the simplified local-density (SLD) method, both the adsorption isotherms of illite, illite/smectite mixed-layer, cholorite and type III kerogen and the total shale rock could be well fitted. The fitting results show good coincidences with the true experimental test data, which proves the method is reasonable and dependable and the prediction results are effective and credible. In addition, the good simulation results show that the SLD parameters can reflect the pore structure characteristics and corresponding adsorption characteristics of the shale samples, which can be used for the quantitative characterization of shale pore system.

Measurements and modeling of high-pressure adsorption of CH4 and CO2 on shales

The Simplified Local Density (SLD) model has been widely used to study the adsorption of gases on activated carbon, coal and shale. However, previous studies mainly focused on the experimental data fitting and the adsorption prediction based on model regression parameters. Few studies have been conducted to investigate the fluid distribution in the pores, which is of great significance for the study of the adsorption mechanism. In this study, high pressure adsorption experiments coupled with SLD model were impressed on the study of adsorption characterizations of shales from Sichuan Basin, China. The results showed that the SLD model could fit the adsorption of gas on shale well, and the average absolute deviations were within 10%. The gas was adsorbed around the pore wall when the pore size was large. As the pore size decreased, the gas molecules in the pore center also began to be adsorbed and finally all the gas in the pores were in an adsorbed state when the pore size was decreased to a certain value. According to the adsorption potential energy curves of CH4 and CO2 gas, CO2 was preferentially adsorbed relative to CH4 when the pore size was larger than 0.42 nm, which was consistent with the experimental results; while when the pore size is less than 0.42 nm, CH4 was preferentially adsorbed. This may be due to that in smaller pores, the repulsion of the pores to CO2 was greater than CH4, making it more difficult for CO2 to enter the pores. The adsorbed phase density was a function of temperature, pressure and pore size. The temperature only changed the magnitude of the adsorbed phase density, while the pore size not only changed the magnitude, but also changed the tendency of the adsorbed phase density with pressure. A temperature dependency model was finally established. Adsorption at a wider range of temperatures can be predicted basing on the model.

Experimental measurement and analytical estimation of methane absorption in shale kerogen

Gas storage in shale (organic-rich mudstone) consists of three different states: free gas in pores and natural fractures; adsorbed gas on organic and inorganic pore walls; and absorbed gas into organic matter (kerogen). Since it is difficult to differentiate absorbed gas from adsorbed gas, most current studies combine the adsorbed gas with absorbed gas and call the combination as gas sorption. In this study, a conceptual model of gas sorption is proposed to account for the contributions from adsorption and absorption to gas storage in shale, respectively. Methane sorption capacity of Barnett and Eagle Ford shale core samples is measured by magnetic suspension sorption system. Regression analysis is performed on the measured data by Simplified Local-Density model coupled with modified Peng-Robinson Equation of State (SLD-PR). Absolute sorption capacity of these two shale core samples is estimated based on the density profile of SLD-PR model. Additionally, the absorbed gas, which is regarded as the gas molecules dissolving/diffusing into the bulk of solid kerogen, is distinguished from the adsorbed gas through interpreting the results of gas expansion measurements using Fick’s law of diffusion. Moreover, methane diffusion coefficients for the two shale core samples are determined, which range from 10−22 m2/s to 10−21 m2/s. The percentage of absorbed gas accounting for total sorbed gas increases with pore pressure. When the pore pressure increases, more gas molecules attempt to adsorb on the surface of kerogen and create a larger gas concentration gradient for gas diffusing into the kerogen. The gas molecules, which adsorb on the pore walls of kerogen and then diffuse into the solid lattice of kerogen, may lead to the swelling of kerogen and thus reduce the pore width for free gas transportation. Therefore, the accurate prediction of the gas absorption capacity of kerogen is significant to understand gas storage mechanism and characterize original gas in place (OGIP) in shale gas reservoirs.

Investigating Gas–Adsorption, Stress–Dependence, and Non–Darcy–Flow Effects on Gas Storage and Transfer in Nanopores by Use of Simplified Local Density Model

Summary As an unconventional rock, shale contains all the features of coalbed and tight sandstone specified as gas-adsorption capacity, microscale and nanoscale porosity, and extremely low permeability. The gas-storage mechanism of shale rocks not only is dominated by free gas in macropores and natural fractures, but also is controlled by adsorbed gas in microporous organic matter (kerogen) and clay minerals. Furthermore, Darcy's law is no longer applicable to describe gas transport in nanopores (Javadpour 2009; Wu et al. 2015). Therefore, developing a reliable model to calculate effective porosity and permeability in nanopores considering the effects of gas adsorption, stress dependence, and non-Darcy flow is crucial to characterize properties of shale-gas reservoirs and explain gas-flow behavior in nanopores. In this study, the simplified local density (SLD) model, which has been successfully applied to analyze gas adsorption on coal, activated carbon, and shale in recent studies, is used to analyze methane-adsorption data measured from five shale-core plugs in the laboratory (Mohammad et al. 2011; Chareonsuppanimit et al. 2012; Clarkson and Haghshenas 2016). A new approach to determine the thickness of adsorbed gas dependent on the density profile of the SLD model is proposed, which in turn provides the correction of methane adsorption to pore volume (PV). Furthermore, stress-dependence effect is incorporated into the gas-adsorption effect to generate an effective porosity function in shale rocks. In addition, non-Darcy-flow effect on gas transfer in nanopores is derived from the slit-shaped pore geometry of the SLD model and is represented by a weighted sum of second-order gas slippage and Knudsen diffusion. Consequently, the effective permeability is established as a function of the effects of gas adsorption, stress dependence, and non-Darcy flow. Moreover, the functions of effective porosity and permeability are incorporated into a numerical simulator to perform history matching for gas-production data from a horizontal well with multistage hydraulic fractures in a Barnett Shale reservoir. The simulation results properly match the gas-production data at the field scale. Finally, sensitivity studies on gas adsorption, stress dependence, and non-Darcy-flow effects are conducted to investigate their contributions to evaluating and estimating gas production from shale-gas reservoirs. The results of this study suggest that gas adsorption and non-Darcy-flow effects are two competitive aspects that have major influences on shale-gas production. The developed model including gas-adsorption, stress-dependence, and non-Darcy-flow effects provides insight into the characterization of rock properties and the description of gas-transport behavior in shale-gas reservoirs.

Experimental and analytical investigation of adsorption effects on shale gas transport in organic nanopores

Gas production from shale gas reservoirs is determined by original gas-in-place and gas transport mechanism in shale. Gas storage in shale consists of three different states: first, free gas in pores and natural fractures; second, adsorbed gas on the organic and inorganic pore walls; and third, absorbed or dissolved gas into formation water and organic matter. On the other hand, gas transport in shale may be dominated by noncontinuum flow in nanopores, which depends on gas slippage, bulk diffusion, Knudsen diffusion and adsorbed surface diffusion. In this study, a gas velocity model involving all of these parameters is proposed to describe the gas adsorption and Non-Darcy flow effects on gas transport behavior in shale gas reservoirs. Adsorption capacity of six shale core samples is measured by the gravimetric method using magnetic suspension sorption system. Regression analysis of the measured data has been performed using the Simplified Local-Density model coupled with modified Peng-Robinson Equation of State (SLD-PR). The presence of the moisture content is taken into consideration to distinguish between gas adsorption on the surface of organic matter and clay minerals. The hydrophilic feature of clay minerals and hydrophobic feature of organic matter result in water molecules preferring adsorbing on the surface of clays, while gas molecules preferring adsorbing on the surface of organic matter. In the developed velocity model, adsorbed gas is treated as mobile gas molecules adsorbing on the surface of organic nanopores, which moves by means of adsorbed surface diffusion. The surface diffusion velocity is characterized by adsorbed surface diffusion coefficient. Simultaneously, bulk gas is governed by second-order gas slippage, which is calculated using Navier-Stokes (N-S) equation associated with second-order slip boundary condition. Finally, the adsorbed surface diffusion is incorporated into bulk gas flow using Langmuir slip model to account for the total gas flow in the organic nanopores. The results of this study indicate that adsorbed surface diffusion contributes to the enhancement or impediment of total gas flow velocity in organic nanopores. Therefore, properly handling the adsorption effect on gas transport in organic nanopores is critical to correctly understand gas production from shale gas reservoirs.