Matrix Permeability Research Articles

Machine Learning-Based Prediction of Oil-Water Flow Dynamics in Carbonate Reservoirs

Because carbonate rocks have a wide range of reservoir forms, a low matrix permeability, and a complicated seam hole formation, using traditional capacity prediction methods to estimate carbonate reservoirs can lead to significant errors. We propose a machine learning-based capacity prediction method for carbonate rocks by analyzing the degree of correlation between various factors and three machine learning models: support vector machine, BP neural network, and elastic network. The error rate for these three models are 10%, 16%, and 33%, respectively (according to the analysis of 40 training wells and 10 test wells).

COUPLING A GEOMECHANICAL RESERVOIR AND FRACTURING SIMULATOR WITH A WELLBORE MODEL FOR HORIZONTAL INJECTION WELLS

Reservoir cooling during waterflooding or waste-water injection results in thermo-poro-elastic stresses that can significantly alter the reservoir stress tensor field. In addition, colloidal particles in the injected water can filter on the borehole and fracture surfaces resulting in matrix permeability reduction. Fractures are likely to initiate and propagate from injectors because of these thermal and filtration effects. These fractures are of great concern for both environmental reasons and their strong influence on reservoir sweep and oil recovery. In this paper, a fully coupled reservoir-fracture-wellbore model was developed. Fluid flow, solid mechanics, energy balance, fracture initiation and propagation, and particle filtration are modeled in the reservoir, fracture, and wellbore domains. The coupled non-linear systems of equations are solved implicitly using the Newton-Raphson method. Simulation results show that water quality and thermal effects control fluid leak-off and fracture growth. While it is difficult to predict the exact location of fracture initiation due to reservoir heterogeneity, we propose a reasonable method to handle fracture initiation and growth without a predefined fracture location. In open-hole completions, "thief" fractures may propagate deep into the reservoir. Thermal stress changes in the injection zone are shown to be significant because of the combined effects of forced convection, heat conduction, and poro-elasticity. Accurate predictions of thermal stress in different reservoir layers allow us to conduct numerical studies on fracture height growth and containment. We show that controlling the injection water temperature and the water quality are an effective way to ensure fracture containment.

A proxy model to predict reservoir dynamic pressure profile of fracture network based on deep convolutional generative adversarial networks (DCGAN)

Tight oil and gas reservoirs with huge development potential are widely distributed all over the world and horizontal well technique is a popular development technology for such kinds of reservoirs. However, the efficiency of conventional horizontal well technology is usually unsatisfying due to the unfavorable flow conditions caused by the nature of tight reservoirs, such as low matrix permeability and narrow pore throat. Multi-stage fractured horizontal well technology is an emerging attractive technology that can greatly improve oil production by generating highly conductive fracture networks in tight reservoirs. and numerical simulation method is generally used to predict the production dynamics of the multi-stage fractured horizontal wells. Nevertheless, the complex geological conditions of reservoirs would greatly increase the difficulties and time required to implement a complete simulation (including model building and calculation). Therefore, in this paper, deep convolution generative adversarial networks (DCGAN) based on U-Net framework was applied to establish the dynamic mapping relationship between fracture pattern and reservoir pressure during the production process, that is, the dynamic reservoir pressure distribution can be obtained by image mapping the fracture distribution details. The results showed that the efficiency of U-Net framework based deep convolution in extracting, dividing and splicing the geometric features of fracture network is significant, and the generative adversarial networks model can effectively predict the reservoir pressure distribution according to the fracture network geometry after being trained with 6000 sets of data. Herein, the training accuracy of the proxy model towards sample data was compared, and the confrontation between the generator and the discriminator in the iterative training process was clarified according to the error function. Furthermore, the prediction accuracy towards pressure distribution at different fracture network geometry scales by the proxy model was compared. Results indicated that the pressure diffusion range predicted by the proxy model is basically consistent with the range obtained from the numerical simulation, with a mean square error (MSE) generally smaller than 0.2. In addition, the relationship between the prediction accuracy of the proxy model and the number of sample data and iterative training times was also studied, which showed that the mean square error of the proxy model kept decreasing with the increasing iteration cycles and sample size, which met the basic law of statistical learning. Moreover, it is worth mentioning that the proposed method may also shed light on the applications of DCGAN in other reservoir-related problems.

Experimental Investigation on the Gas Seepage Behavior in Shale Gas Reservoirs Under Different Pore Pressures and Core Matrix Permeability

Experimental Investigation on the Gas Seepage Behavior in Shale Gas Reservoirs Under Different Pore Pressures and Core Matrix Permeability

Approach Couples Reservoir Simulation With Wellbore Model for Horizontal Wells

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203977, “Coupling a Geomechanical Reservoir and Fracturing Simulator With a Wellbore Model for Horizontal Injection Wells,” by Shuang Zheng, SPE, and Mukul Sharma, SPE, The University of Texas at Austin. The paper has not been peer reviewed. Reservoir cooling during waterflooding or waste-water injection can alter the reservoir stress field significantly by thermoporoelastic effects. Colloidal particles in the injected water decrease the matrix permeability and build up the injection pressure. Fractures may initiate and propagate from injectors. These fractures are of great concern for environmental reasons and are a strong influence on reservoir sweep and oil recovery. The complete paper introduces methods to fully couple reservoir simulation with wellbore flow models in fractured injection wells. Introduction In this study, a fully integrated 3D geomechanical thermal reservoir simulator is presented. This simulator is fully coupled with a wellbore model and allows fracture propagation. The model accounts for multiphase flow, solid mechanics, thermal stresses, filtration, and fracture growth in coupled reservoir- fracture-wellbore domains and can be used for simulations in both conventional and unconventional reservoirs. The simulator allows study of induced fracture propagation in cased- and openhole injectors while fully accounting for thermoporoelastic and particle-filtration effects. It also allows study of hydraulic fracture propagation in unconventional reservoirs considering the complex wellbore dynamics. The complete paper provides a practical simulation tool to maximize well injectivity while minimizing environmental risks, and to analyze and optimize the completion design in unconventional reservoirs.

Calculation of matrix permeability from velocity and attenuation of ultrasonic S-wave

AbstractPreviously, hydrogeologists and petroleum engineers use seepage experiments to measure permeability. This paper develops a novel method to calculate matrix permeability from velocity and attenuation of an ultrasonic S-wave. At first, permeability is derived as a function of frequency when an S-wave scans a fluid-saturated rock. Substituting the permeability into a previous S-wave model gives theoretical velocity and attenuation, in which the nexus parameter is the average distance of aperture representing pores. Fitting the predicted velocity and quality factor against the measured counterparts yields permeability in the full frequency range. For Berea sandstone, the inverted permeability at low frequency (0.0376 Darcy) is comparable to Darcy permeability (0.075 Darcy), confirming that Berea sandstone is homogenous. For Boise sandstone, the inverted permeability at low frequency is 0.0457 Darcy, much lower than Darcy permeability (1 Darcy). When S-wave scans the rocks, its velocity and attenuation are dominated by matrix pore throats and the inverted permeability represents matrix permeability. Unlike Berea sandstone, Boise sandstone has fractures and widely distributed grain diameters. The fractures and the large pores (due to large grain diameter) are preferential pathways that increase Darcy permeability far more than matrix permeability.

The influence of microscale lithological layering and fluid availability on the metamorphic development of garnet and zircon: insights into dissolution–reprecipitation processes

AbstractThe response of garnet and zircon to prograde amphibolite-facies metamorphism in late Proterozoic mica schists from the Scottish Highlands has been investigated. Spatial analysis of zircon populations using scanning electron microscopy was undertaken in Dalradian Schists that have undergone a sequence of prograde garnet growth and localised breakdown reactions involving coupled dissolution–reprecipitation. Fluid availability and matrix permeability strongly control this metamorphic response and different generations of garnet contain radically different populations of metamorphic micro-zircon and associated changes in the detrital zircon population. Micro-zircon abundance increases during garnet growth, whereas that of detrital zircon decreases. The mineralogy of the matrix influences zircon abundance in porphyroblast phases, where garnet overgrows a micaceous matrix zircon-rich garnet forms and where it overgrows a quartzofeldspathic matrix the result is zircon-poor garnet. Following garnet growth, micro-zircon abundance decreases at each stage of the prograde reaction history, with sillimanite-zone schists containing the lowest abundance, suggesting micro-zircons are texturally less stable at staurolite- and sillimanite-grade metamorphism. Micro-zircons are distributed evenly across host minerals in the matrix, with the exception of retrograde chlorite where micro-zircons are absent due to fluids removing Zr before new zircon can precipitate. There is an overall decrease in the mode of zircon at each stage of the reaction history, indicating that zircon is a highly reactive phase during amphibolite-facies metamorphism and is very sensitive to individual prograde and retrograde reactions.

Numerical Modeling of Gas Migration through Cement Sheath and Microannulus.

Cement sheath is considered an important barrier throughout the life cycle of the well. The integrity of the cement sheath plays a vital role in maintaining the integrity of wells. Cement’s ability to seal the annular space or a wellbore, also known as cement sealability, is an important characteristic of the cement to maintain the well integrity. It is believed that placing cement in the annular space or wellbore can totally prevent any leakage; however, that is debatable. The reason why cement cannot completely prevent fluid leakage is that cement is considered as a porous medium, and also flaws in cement, such as microannuli, channels, and fractures, can develop within the cement sheath. Furthermore, the complexity of casing/cement and cement/formation interaction makes it very difficult to fully model the fluid migration. Hence, fluid can migrate between formations or to the surface. This article presents a numerical model for gas flow in cement sheath, including the microannulus flow. A parametric study of different variables and their effect on the leakage time is carried out, such as the microannulus gap size, cement matrix permeability, cement column length, and cement porosity. In addition, it presents leakage scenarios for different casing/liner overlap length with the existence of microannulus. The leakage scenarios revealed that the cement matrix permeability, microannulus gap size, and cement length can highly impact the leakage time; however, cement porosity has a minimal effect on the leakage time. In addition, modeling results revealed that the casing/liner overlap length should not be less than 300 ft, and the casing pressure duration should be beyond 30 min to detect any leak.

Interfacial layer thickness is a key parameter in determining the gas separation properties of spherical nanoparticles-mixed matrix membranes: A modeling perspective

The existing traditional models cannot accurately predict the gas permeability of spherical nanoparticle-mixed matrix membranes (SP-MMMs) due to ignoring the physical and chemical characteristics of the SP/matrix interface. In this paper, first, a new model is derived for the prediction of thermal conductivity of SP-polymer composites according to multiple scattering theory. Then, a new theoretical model for gas permeability of SP-MMMs is developed based on the analogy with the derived model for the prediction of thermal conductivity. The significant feature of the new model is its ability to quantify the crucial role of SPs/matrix interface in gas permeability by introducing a new dense interfacial layer thickness (aint) parameter, which increases with increasing the strength of interfacial interactions. It is demonstrated that the value of aint is independent of the nature of gas molecules and mathematically correlated to the strength of SPs/matrix interfacial interactions. Finally, the gas permeability of SP-MMMs is accurately predicted by inserting the values of non-adjustable aint parameter, obtained from the correlation, diameter of SPs as well as the gas permeability of matrix into the new model, without using any adjustable parameter. Moreover, this technique can be utilized to determine the dense interfacial layer thickness in SP-polymer composites using gas permeation data.

Controls on compactional behavior and reservoir quality in a Triassic Buntsandstein reservoir, Upper Rhine Graben, SW Germany

The main reservoir quality controls in Triassic Buntsandstein deposits in the Upper Rhine Graben and surrounding outcrops in Germany and France are discussed to be authigenic mineral precipitates and the vicinity to structural elements (faults and fractures). To better understand reservoir quality controls in this lithology, a detailed diagenetic study based on petrographic methods (optical and SEM) in combination with petrophysical measurements (porosity and permeability) on core material (1133–1591 m TVD) was initiated. This case study highlights that large detrital grain sizes and low compactional porosity loss in association with blocky authigenic cements such as quartz and dolomite are beneficial to reservoir quality, whereas variable illite textures have a dual, but opposite effect on reservoir qualities. Grain coating illite (tangential and radial) may preserve intergranular porosity by inhibition of syntaxial quartz precipitation, while at the same time, if present at grain contacts, tangential illite enhances chemical compaction and reduces the available intergranular volume. The presence of early diagenetic carbonate cemented nodules is also beneficial for reservoir quality in stabilizing the grain framework against compactive porosity loss. Overall, detrital grain size and the intergranular volume, as a result of compaction and cementation, are derived as the main reservoir quality controls. The formation of hydrothermally mineralized veins prior to hydrocarbon charging does not show a distinct impact on porosity and permeability in the sandstone matrix. Fractures and interstices between vein minerals such as barite, galena, tetrahedrite, and siderite are equally covered in hydrocarbon residue, as are all present detrital and authigenic minerals in the sandstones indicating that vein precipitates, if not pervasive, do not alter the overall reservoir quality. This study may indicate additional potential to identify high reservoir quality intervals in the studied succession.

Experimental Study on Sweep Characteristics of Gas Gravity Drainage in the Interlayer Oil Reservoir

Stable gas gravity drainage is considered an effective method to enhance oil recovery, especially suitable for deep buried, large dip angle, and thick oil reservoirs. The influence of reservoir heterogeneity on controlling the gas–oil interface and sweep characteristics of injected gas is particularly important to design reservoir development schemes. In this study, according to the interlayer characteristics of Donghe carboniferous oil reservoirs in the Tarim Basin, NW China, 2D visual physical models are established, in which the matrix permeability is 68.1 mD and average pore throat radius is 60 nm. Then, hydrocarbon gas gravity drainage simulation experiments are carried out systematically, and a high-speed camera is used to record the process of gas–oil flow and interface movement. In this experiment, the miscible zone of crude oil and hydrocarbon gas is observed for the first time. The interlayer has an obvious shielding influence, which can destroy the stability of the gas–oil interface and miscible zone, change the movement direction of the gas–oil interface, and reduce the final oil recovery after gravity drainage. The remaining oil mainly is distributed near the interlayers. The higher displacement pressure leads to increased stability of the gas–oil displacement front and later gas breakthrough, which leads to higher oil recovery. The lower gas injection rate contributes to a slower front velocity and wider miscible zone, which could delay gas breakthrough. For the immiscible gas gravity drainage, there is a critical gas injection rate, with which the oil recovery factor is the highest.

Electrochemical devices based on conducting surfaces modified with smart hydrogels: Outlook and perspective

AbstractThe unique properties of smart hydrogels combined with conducting surfaces opened new possibilities in the construction of novel electrochemical devices. Electrodes modified with thin gel layers demonstrate the properties that are usually unachievable for bare electrodes. Usually a thin gel layer provides a highly permeable matrix for analytes, and can also serve as an immobilizing/impermeable matrix for larger molecules. Hydrogel barriers/layers are able to protect the electrode surface against the unwanted influence of the environment and to isolate the environment from the usually metallic, stiff, and hard electrode surfaces. A layer of hydrogel attached to the electrode surface can also serve as solid electrolyte, buffer and a reservoir for electroactive probes. In addition, the ability of smart gel materials to undergo a reversible volume phase transition related to significant changes in their volume and shape is very interesting from the point of view of the construction of switchable electrochemical systems. Such properties are strongly desired for the construction of various electrochemical devices. This review is focused on recent progress in the above field.

Hydro-mechanical effects of seismic events in crystalline rock barriers

Abstract. Under ideal conditions, owing to its extremely low matrix permeability, crystalline rock can constitute a suitable hydro-geological barrier. Mechanically, its high strength and stiffness provide advantages when constructing a repository and for long-term stability. However, crystalline rock usually occurs in a fractured form, which can drastically alter hydromechanical (HM) barrier functions due to increased permeability and decreased strength. Seismic events have the potential to alter these HM properties by activating faults, increasing their transmissibility, creating new fractures or altering network connectivity (De Rubeis et al., 2010). Therefore, it is of high importance to build computational models to allow assessment of the HM effects of seismic events in a Deep Geologic Repository (DGR) in crystalline rock, as illustrated in Fig. 1. For this purpose, we consider a DGR in Russia (Yeniseysky site) for high-level waste in crystalline rock (Proterozoic and Archaean gneiss complexes) that is located close to a potentially seismically active area (Jobmann, 2016). Here, we present a coupled HM simulation, using OpenGeoSys (Kolditz et al., 2012), of a large-scale, three-dimensional finite-element model of the Yeniseysky site to assess the consequences of seismically induced stress-field changes on the local stress field and the fluid flow. This research also provides an outlook of current model development geared towards a more detailed assessment of seismically induced hydro-mechanical processes in porous and fractured rocks.

The use of supercritical CO2 in deep geothermal reservoirs as a working fluid: Insights from coupled THMC modeling

A coupled THMC (thermal-hydrological-mechanical-chemical) model is developed and applied to explore the potential feasibility of using scCO 2 (supercritical carbon dioxide) as a working fluid in geothermal reservoirs . This is achieved by examining the evolution of the kinetics of mineral precipitation-dissolution and its associated impact on the evolution of the rock permeability and porosity. The pH of the reservoir rapidly reduces from 7 to ∼4.5–5 due to the fast dissolution of calcite . Chemical reactions and mineral dissolution and precipitation near the injector are suppressed by the plug-flow penetration of anhydrous scCO 2 displacing the original pore fluid . A conceptual three-zone model is proposed to illustrate the kinetic process of feldspar dissolution and precipitation depending on timing. The initial high concentration of K + prompts feldspar to precipitate in the first stage by consuming K + until 1 y , Feldspar were dissolved into precipitations of illite , smectite , and siderite at 1-6 y , with albite , muscovite and kaolinite mostly precipitated in the last stage 6–10 y . The precipitations of secondary clay minerals and quartz serve to maintain the integrity of caprock sealing. Continuous scCO 2 injection under fully coupled THMC model shows a 1.4-times enhancement of fracture permeability and 1.2-times enhancement of matrix permeability dominated by chemical dissolution and thermal unloading process. The pronounced thermal drawdown is the principal factor in enhancing permeability and porosity near injection well. Furthermore, the expansive capability of CO 2 provides extra benefits in enhancing formation pressure to ensure consistent high flow rates, while achieving a higher thermal energy extraction efficiency and preventing scaling issues in wellbore . The mass concentration of scCO2 in the production well increased to 0.82 after 1.2 × 10 8 s also leads to the enhancement of fluid enthalpy up to 6.5 × 10 5 J/kg, due to the high heat capacity of scCO 2 . The injected CO 2 are sequestered at ∼2 × 10 7 kg at t = 2 × 10 8 s (6.34 y ) as the solubility trapping mechanism.

The impact of permeability heterogeneity on water-alternating-gas displacement in highly stratified heterogeneous reservoirs

Availability of gases at the field level makes attractive to water-alternating-gas (WAG) process for low viscosity and light oils carbonate reservoir. However, impact of reservoir heterogeneity on WAG performance is crucial before field application. In general, ramp carbonates have heterogeneity due to variation of permeability and porosity. However, WAG performance significantly affected by permeability variations. This article investigates merits and demerits of WAG displacement due to permeability heterogeneities such as permeability anisotropy, high permeability streaks (HKS), matrix permeability, dolomite and thin dense stylolite layers. High-resolution compositional simulations with tuned equation of state (EoS) were carried out using 2D and 3D sector models. The study focuses on WAG performance in terms of oil recovery, vertical sweep, solvent utilization, gas oil ratio (GOR), water cut (WCT), WAG response time, gravity override, hysteresis, un-contacted oil saturation and economics. The results of simulation show that the heterogeneous reservoir provides initially faster WAG response, lower expected ultimate recovery (EUR), faster gas breakthrough, higher GOR and WCT production compared to homogeneous reservoir. The gas gravity override at smaller wells spacing is less in homogeneous reservoir as compared to heterogeneous reservoir, but it is reverse in case of larger well spacing. In heterogeneous reservoir, the HKS shows significant gas override resulting in poor vertical sweep due to capillary holding, and the high permeability dolomite layer shows early water breakthrough. This reservoir has higher solvent utilization in initial stage, and then, it becomes nearly equal to homogeneous reservoir. Simulation in both reservoirs overestimates incremental recovery of 2–3% OOIP at one pore volume injection because of not involving un-contacted oil saturation as predicted in core flood. The findings of this study will help to understand WAG performance and design in highly heterogeneous reservoirs for field applications.Graphical abstract

CO2 EOR Performance Evaluation in an Unconventional Reservoir through Mechanistic Constrained Proxy Modeling

There are multiple parameters including reservoir characteristics, hydraulic fracture design, injection solvent selection, and the enhanced oil recovery (EOR) operational design, etc., that are directly and indirectly involved in the unconventional reservoir development. And due to the lack of field data availability, the key performance indicators for such complex reservoirs are not well defined, therefore, reservoir engineers end up with a huge volume of numerical simulation scenarios to find an optimum field development plan. This approach makes the field development planning process complicated and time-consuming.In this study, a smart unconventional EOR performance evaluation tool is presented utilizing intelligent modeling strategies through proxy modeling approach with mechanistic constraints. The mechanistic constraints incorporate physics-based numerical simulation dataset. Key reservoir and hydraulic fracture topographies including average reservoir pressure and the matrix & hydraulic fracture permeability contrast are used as some of the key input parameters for the Deep Neural Network (DNN) modeling. Total four DNN models are generated for primary and EOR cases presenting the recovery performance prediction at two different timelines. The trained and validated DNN models are finally found well qualified to be applied for the development of the unconventional reservoirs with identical reservoir and hydraulic fracture characteristics for the EOR application forecasting.

Adaptation of Crushed Rock Analysis to Intact Rock Analysis To Improve Assessment of Water Saturation and Fast Pressure Decay Permeability

Summary Legacy crushed rock analysis, as applied to unconventional formations, has shown great success in evaluating total porosity and water saturation over the previous three decades. The procedure of crushing rock into small particles improves the efficiency of fluid recovery and grain volume measurements in a laboratory environment. However, a caveat to crushed rock analysis is that water and volatile hydrocarbons evaporate from the rock during the preparatory crushing process, causing significant uncertainty in water saturation assessment. A modified crushed rock analysis incorporates nuclear magnetic resonance (NMR) measurements before and after the crushing process to quantify the volume of fluid loss. The advancements improve the overall total saturation quantification. However, challenges remain in the quantification of partitioned water and hydrocarbon loss currently derived from the NMR spectrum along with its uncertainty. Furthermore, pressure decay permeability from crushed rock analysis has been reported to have two to three orders of magnitude difference between different laboratories. The calculated pressure decay permeability of the same rock could even vary by several orders of magnitude with different crushed sizes, which questions the quality of the crushed pressure decay permeability. In this paper, we introduce an intact rock analysis workflow on unconventional cores for improved assessment of water saturation and enhanced quantification of fast pressure decay matrix permeability from intact rock. The workflow starts with acquisition of NMR T2 and bulk density measurements on the as-received state intact rock. Instead of crushing the rock, the intact rock is directly transferred to a retort chamber and heated to 300°C for thermal extraction. The volumes of thermally recovered fluids are quantified through an image-based process. The grain volume measurement and a second NMR T2 measurement are performed on post-retort intact rock. The pressure decay curve during the grain volume measurement is then used for calculating the pressure decay matrix permeability. Total porosity is calculated using the bulk volume and grain volume of the rock. Water saturation is quantified using the total volume of recovered water. In addition, the twin as-received-state rocks are processed through the crushed rock analysis workflow for an apple-to-apple comparison. Meanwhile, the pressure decay permeability of the post-retort intact sample is cross-validated against the steady-state gas permeability of the same post-retort sample. The introduced workflow has been tested successfully on different formations, including Bakken, Bone Spring, Eagle Ford, Cotton Valley, and Niobrara. The results show that total porosities calculated from intact rock analysis are consistent with total porosities from crushed rock analysis, while water saturations from the new workflow are an average 8% saturation unit (SU) [0.2 to 0.7% porosity unit (PU) of bulk volume water (BVW)] higher than those from the prior crushed rock workflows. The study also indicates that for some formations (e.g., Bone Spring), the fluid loss during the crushing process is dominated by water; however, for some other formations (e.g., Bakken), the hydrocarbon loss is significant. Pressure decay permeability quantified using intact rock analysis is also confirmed within an order of magnitude of steady-state matrix permeability.

Onset of solutal convection in layered sorbing porous media with clogging

The effect of pore clogging on the onset of solute-driven convection in a layered sorbing porous medium consisting of two sublayers with distinct permeabilities is investigated. Solute transport in the medium is described by the nonlinear MIM model involving the Langmuir equation. The solute is divided into two phases. The first one is a mobile phase that drifts with flow and the second one is an immobile phase captured by porous matrix and reducing the total pore space. The model takes into account the saturation concentration, which is a maximal possible amount of solute adsorbed by a unit volume of porous medium. The degree of pore clogging is determined through a clogging coefficient proportional to the saturation concentration. Another coefficient is a sorption parameter including the ratio of adsorption and desorption rates. By varying these coefficients, we obtain the threshold solutal Rayleigh–Darcy number for the onset of convection in the following three types of layered sorbing systems: (1) system with the upper thin highly permeable sublayer, (2) system with the lower thin highly permeable sublayer, and (3) system with equal thick sublayers. The results show that convection onset delays due to the enhancement of clogging effect in all of the three systems. It is more difficult to induce convection here because the pore plugging together with an increase in adsorption rate as compared to desorption rate reduces the mean porosity and permeability of porous matrix. Forward and reverse transitions between the critical convective rolls with different wavelengths are found to occur in the systems 1 and 2 containing the upper or lower thin highly permeable sublayers as the sorption parameter increases. A sequence of “local convection – large-scale convection – local convection” transitions is observed in system 1. There is an opposite sequence of “large-scale convection – local convection – large-scale convection” transitions in system 2. The preferred convective roll width at the onset of convection changes by almost fifth times at the described forward and reverse transitions. It roughly corresponds to the ratio of the total thickness of porous system to that of the thin highly permeable sublayer where local convection generates.

Determination of the Thickness of Interfacial Voids in a Spherical Nanoparticles - Polymer Membrane: Fundamental Insight from the Gas Permeation Modeling

In this work, a new approach is proposed to determine the thickness of interfacial voids in impermeable spherical nanoparticles-containing mixed matrix membranes (SP-MMMs) based on the gas permeation data. The interfacial void thickness, lv, between SPs and polymer matrix is firstly obtained as an adjustable parameter by fitting the modified Maxwell model to the experimental gas permeability data reported in the literature. It is shown that the value of lv parameter is independent of the nature of gas molecules and mathematically related to the strength of SP/matrix interfacial interactions. Then, for the first time in this paper, a universal relationship is established between the SPs/polymer interfacial void thickness and the interfacial interactions at the SPs/polymer interface, which is described by the Flory–Huggins interaction parameter, χ. Finally, the gas permeability of SP-MMMs is predicted using the values of lv parameter, diameter and volume fraction of SPs as well as the gas permeability of polymer matrix. Moreover, according to the obtained relationship, the interfacial void thickness in SP-polymer composites can be directly calculated for a wide range of interaction parameter values.

The effect of salt precipitation on the petrophysical properties and the adsorption capacity of shale matrix based on the porous structure reconstruction

The study of salt precipitation and its effect on the reservoir physical properties and hydrocarbon adsorption capacity is important to the development of the shale reservoir with high salinity brine. In this study, a brine evaporation (static salting-out) is conducted on the shale matrix sample extracted from the Eocene Qianjiang inter-salt hypersaline lacustrine shale formation located in the Qianjiang Depression, Jianghan Basin, mid-eastern China, to prompt the salt precipitation to reach the exacerbation stage. The porous structure reconstruction technology is applied to study the effect of salt precipitation on the petrophysical properties of the shale matrix. The 3D pore networks of the shale matrix before and after brine evaporation are reconstructed based on 2D high-resolution nanoscale focused ion beam scanning electron microscopy (FIB-SEM) images. Pore-throat structural analyses and fluid flow simulations are carried out on the reconstructed pore networks to generate the physical and fluid flow properties. The density function theory (DFT) and the adsorption potential theory (APT) are combined to predict the CH4 adsorption isotherms of shale matrix with salt precipitation at different temperatures based on the pore size distribution (PSD) obtained from the reconstructed pore networks. The results show that salt precipitation can cause a 23.0% reduction in the porosity and a 47.0% reduction in the absolute permeability of the shale matrix. Salt precipitation has a stronger effect on larger pores and throats, which will cause the destruction of the reservoir fluid flow channels and a large change in the pore size distribution. The CH4 adsorption isotherms that are predicted based on the pore size distribution by the density function theory and the adsorption potential theory show that salt precipitation could cause a reduction of approximately 20.4% in the adsorption capacity, and the absolute adsorption capacity could be even smaller when the temperature is increased from the lab temperature to higher temperatures.