Dynamic Diffusion Coefficient Research Articles

Simulation and time series analysis of responsive active Brownian particles (rABPs) with memory

To realise the goals of active matter at the micro- and nano-scale, the next generation of microrobots must be capable of autonomously sensing and responding to their environment to carry out pre-programmed tasks. Memory effects are proposed to have a significant effect on the dynamics of responsive robotic systems, drawing parallels to strategies used in nature across all length-scales. Inspired by the integral feedback control mechanism by which Escherichia coli (E. coli) are proposed to sense their environment, we develop a numerical model for responsive active Brownian particles (rABP) in which the rABPs continuously react to changes in the physical parameters dictated by their local environment. The resulting time series, extracted from their dynamic diffusion coefficients, velocity or from their fluctuating position with time, are then used to classify and characterise their response, leading to the identification of conditional heteroscedasticity in their physics. We then train recurrent neural networks (RNNs) capable of quantitatively describing the responsiveness of rABPs using their 2D trajectories. We believe that our proposed strategy to determine the parameters governing the dynamics of rABPs can be applied to guide the design of microrobots with physical intelligence encoded during their fabrication.

Dynamic viscosity, interfacial tension and diffusion coefficient of n-hexane, cyclohexane, 2-methylpentane with dissolved CO2

In this work, n-hexane, cyclohexane and 2-methylpentane were selected to represent linear-alkane, cycloalkane and branched-alkane, respectively. Based on the dynamic light method (DLS), the viscosity, interfacial tension and diffusion coefficient of n-hexane/CO2, cyclohexane/CO2 and 2-methylpentane/CO2 systems under saturation condition were measured in order to explore the change trend of thermophysical properties of the systems with the same carbon atom number but different molecular structures. The experiments were conducted at the temperatures of 303, 343 and 383 K and at pressures up to 5.64 MPa. The expanded uncertainties（k = 2）of dynamic viscosity, interfacial tension and diffusion coefficient were 3 %, 3 % and 4.4 % respectively. The experimental results show that n-hexane and 2-methylpentane with similar molecular structure have more similar value of the properties. The effects of different alkane structures on system viscosity, interfacial tension, and diffusion coefficient were explained at the molecular level through radial distribution function, interface thickness, and CO2 coordination number. At 303.15 K and 4 MPa, the peak radial distribution function of CO2/cyclohexane is 1.845, which is greater than that of CO2/n-hexane and CO2/2-methylpentane molecules. It has been proven that the arrangement of CO2/cyclohexane is more orderly, resulting in higher viscosity and lower diffusion coefficient of the system. The interface thickness of CO2/cyclohexane is 6.13 nm, which is smaller than CO2/n-hexane (7.53 nm) and CO2/2-methylpentane (6.3 nm). The smaller the interface thickness, the more compact the structure, the stronger the intermolecular forces, and the greater the interfacial tension. At 303.15 K and 2 MPa, the number of CO2 coordination sites within 1 nm around liquid phase alkanes is 3.96, which is smaller than 4.78 for cyclohexane and 6.62 for 2-methylpentane. Prove that the coordination number is directly proportional to the diffusion coefficient and inversely proportional to viscosity and interfacial tension.

Study on size effect and model optimization of methane desorption-diffusion in high rank coal

ABSTRACT Methane diffusion models are numerous, but their application, pros, and cons need to be summarized urgently, the link between particle size and methane desorption-diffusion is uncertain. Therefore, this paper carries out the methane desorption-diffusion experiments under multi-scale pressure and particle size conditions to study the effect of coal sample particle size on methane desorption-diffusion. Based on MATLAB, different diffusion models were fitted and comparatively analyzed, and the models were improved in view of their deficiencies. The results showed that the cumulative methane desorption amount and rate are inversely related to the particle size of coal. Comparative analysis of the models revealed that diffusion model under the third type of boundary conditions has a low fitting accuracy for full process of methane desorption, whereas it has a high fitting accuracy of 0.9831 for the first 1000 s of desorption data. Unipore diffusion model, bidisperse diffusion model and new model of dynamic diffusion coefficient have high fitting accuracy for the desorption data of high homogeneous coal, reaching above 0.97, but unipore diffusion model has only 0.5434 fitting accuracy for non-homogeneous coal samples. The fitting accuracy of improved classical unipore diffusion model for both homogeneous and non-homogeneous coals reaches 0.99, which is more extensive than that of unipore diffusion model, only take the first term can satisfy the accuracy requirement, so it is more convenient in the practical engineering application, and has certain reference significance for engineering calculations of gas content and prediction of gas protrusion.

Method of Lines for flexible coupling of the Single Particle Model for Lithium-Ion Batteries demonstrated by thermal modelling

Electrochemical models like the Pseudo-two-dimensional (P2D) model and the Single Particle Model (SPM) are widely used in the field of battery simulation. The SPM provides accurate results for small currents with low computational costs. However, commonly used solving strategies limit the applicability of the SPM to certain physical effects. This work introduces a universal solving strategy using Method of Lines (MOL) that allows the integration of several electrochemical and thermal effects without changing the basic mathematical model structure. The model can be easily extended, which was demonstrated by including thermal effects and dynamic diffusion coefficients. The MOL-SPM is compared to a P2D model and experimental data of galvanostatic discharges and a dynamic current profile. The MOL-SPM calculates up to 400 times faster than the P2D model for the dynamic current profile while producing a similar small model error with an RMSE difference of only 0.9 mV compared to the P2D model.

MR-Guided Transurethral Ultrasound Ablation of Prostate Cancer: Initial Experience of Monitoring Tumor Response by Dynamic Apparent Diffusion Coefficient Measurements at 3.0 T

Introduction: Diffusion-weighted imaging (DWI) as part of multiparametric magnetic resonance imaging (mpMRI) is an important sequence for the detection of prostate cancer (PCa). The objective of this retrospective analysis was to evaluate changes in apparent diffusion coefficient (ADC) measurements in biopsy-proven PCa undergoing TULSA-PRO (MR-guided transurethral ultrasound ablation of the prostate) at 3.0 T after 1, 3, and 6–12 months posttreatment. Methods: Nineteen patients underwent follow-up examinations after 1, 3, and 6–12 months including mpMRI at 3.0 T and urological-clinical examinations with quantitative analysis of ADCs. Results: In PCa, a significant increase of ADC values after 6–12 months was measured after TULSA-PRO treatment by 29.1% (pre-TULSA: 0.79 ± 0.16 × 10−3 mm2/s, 6–12 months: 1.02 ± 0.35 × 10−3 mm2/s), while the corresponding value in the reference tissue decreased by 48.5% (pre-TULSA: 1.20 ± 0.15 × 10−3 mm2/s, 6–12 months: 0.91 ± 0.29 × 10−3 mm2/s). The mean ADC values in the early follow-up groups at 1 and 3 months did not change significantly. Conclusion: DWI with ADC as part of mpMRI can serve as a biomarker to dynamically monitor the follow-up after TULSA after 6–12 months. For early posttreatment progression, it is not suitable due to too many confounding variables.

Electrodeposition model with dynamic ion diffusion coefficients for predicting void defects in electroformed microcolumn arrays.

Due to the confined mass transfer capability in microchannels, void defects are easily formed in electroformed microcolumn arrays with a high depth/width ratio, which seriously affects the life and performance of micro-devices. The width of the microchannel constantly decreases during electrodeposition, which further deteriorates the mass transfer capability inside the microchannel at the cathode. In the traditional micro-electroforming simulation model, the change of the ion diffusion coefficient is always ignored, making it difficult to accurately predict the size of void defects prior to electroforming experiments. In this study, nickel ion diffusion coefficients in microchannels are tested based on the electrochemical experiments. The measured diffusion coefficients decrease from 4.74 × 10-9 to 1.27 × 10-9 m2 s-1, corresponding to microchannels with a width from 120 to 24 μm. The simulation models of both constant and dynamic diffusion coefficients are established, and the corresponding simulation results are compared with the void defects obtained using micro-electroforming experiments. The results show that when the cathode current densities are 1, 2 and 4 A dm-2, the size of void defects obtained with the dynamic diffusion coefficient model is closer to the experimental results. In the dynamic diffusion coefficient model, the local current density and ion concentration distribution proves to be more inhomogeneous, leading to a big difference in the deposition rate of nickel between the bottom and the opening of a microchannel, and consequently a larger void defect in the electroformed microcolumn arrays. In brief, the ion diffusion coefficient inside microchannels with a different width is tested experimentally, which provides a reference for developing reliable micro-electroforming simulation models.

AC Back Surface Recombination Velocity as Applied to Optimize the Base Thickness under Temperature of an (n<sup>+</sup>-p-p<sup>+</sup>) Bifacial Silicon Solar Cell, Back Illuminated by a Light with Long Wavelength

The bifacial silicon solar cell, placed at temperature (T) and illuminated from the back side by monochromatic light in frequency modulation (ω), is studied from the frequency dynamic diffusion equation, relative to the density of excess minority carriers in the base. The expressions of the dynamic recombination velocities of the minority carriers on the rear side of the base Sb1(D(ω, T); H) and Sb2(α, D(ω, T); H), are analyzed as a function of the dynamic diffusion coefficient (D(ω, T)), the absorption coefficient (α(λ)) and the thickness of the base (H). Thus their graphic representation makes it possible to go up, to the base optimum thickness (Hopt(ω, T)), for different temperature values and frequency ranges of modulation of monochromatic light, of strong penetration. The base optimum thickness (Hopt(ω, T)) decreases with temperature, regardless of the frequency range and allows the realization of the solar cell with few material (Si).

Experimental study of the radial multi-scale dynamic diffusion model for gas-bearing coal

Purpose. The purpose of this paper is to solve the scientific problem that the classical diffusion model in columnar coal cores cannot accurately describe the whole process of gas diffusion. Methods. The diffusion-percolation experiments were carried out using the laboratory’s homemade experimental equipment with standard ϕ 50mm×100 mm columnar raw coal cores under different air pressures. Findings. The classical diffusion model was used to fit the experimental data. The experiment has found that the classical diffusion model of the columnar coal core can only partially describe the gas diffusion process. The longer the experimental time, the larger the error between the model and the experiment, and the analysis has found that the apparent diffusion coefficient shows decay changes with time. The dynamic diffusion coefficient concept is then proposed in order to con-struct a radial multi-scale dynamic prominent diffusion-percolation model for columnar coal cores. The theoretical curve of the new model nearly coincides with the experimental curve, and the new model can describe the gas diffusion-percolation process of columnar coal cores more accurately. The multi-scale dynamic diffusion-percolation model covers the classical diffusion model. It explains the mechanism of gas diffusion-percolation in multi-scale pores, i.e., at the beginning of the flow, gas flows out from the large external pores first, from the surface inwards. Over time, the pore size through which gas flows gradually becomes smaller, the diffusion resistance gradually increases, and the apparent diffusion coefficient slowly decreases. Originality. This paper proposes a new multi-scale dynamic diffusion-percolation model to compare the old and new model analysis, as well as carefully studying the mechanism of gas flow in coal. Practical implications. This research has important engineering significance for the accuracy of measuring the gas content of coal seams, as well as predicting coal and gas content.

Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example.

The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.

Modeling Subsurface Hydrogen Storage With Transport Properties From Entropy Scaling Using the PC‐SAFT Equation of State

AbstractHydrogen is a promising alternative to carbon based energy carriers and may be stored in large quantities in subsurface storage deposits. This work assesses the impact of static (density and phase equilibria) and dynamic (viscosity and diffusion coefficients) properties on the pressure field during the injection and extraction of hydrogen in the porous subsurface. In a first step, we derive transport properties for water, hydrogen and their mixture using the Perturbed‐Chain Statistical Associating Fluid Theory equation of state in combination with an entropy scaling approach and compare model predictions to alternative models from the literature. Our model compares excellently to experimental transport coefficients and models from literature with a higher number of adjustable parameters, such as GERG2008, and shows a clear improvement over empirical correlations for transport coefficients of hydrogen. In a second step, we determine the effect of further model reduction by comparing our against a much simpler model applying empirical transport coefficients from the literature. For this purpose, hydrogen is periodically injected into and extracted out of a dome‐shaped porous aquifer under a caprock. Our results show that density and viscosity of hydrogen have the highest impact on the pressure field, and that a thermodynamic model like the new model presented here is essential for modeling the storage aquifer, while keeping the number of coefficients at a minimum. In diffusion‐dominated settings such as the diffusion of hydrogen through the caprock, our developed diffusion coefficients show a much improved dependence on temperature and pressure, leading to a more accurate approximation of the diffusive fluxes.

Experimental Research on the Influence of Microwave Radiation on Coal Permeability and Microstructure.

At present, there is limited information available about the effects of microwave radiation on desorption characteristics, microstructures, and functional groups of coal. This research focuses on the influence of microwave radiation on coal sample desorption and examines the changes in pore structures and oxygenic groups of different coal samples using liquid nitrogen adsorption, nuclear magnetic resonance, and X-ray photoelectron spectroscopy. Results prove that the methane desorption capacity and desorption rate are proportional to the increase in microwave energy; the initial dynamic diffusion coefficient is also proportional to microwave energy but negatively proportional to the attenuation coefficient. As a result of microwave radiation, the Brunauer–Emmett–Teller (BET) surface area, pore size, and Barret–Joyner–Halenda (BJH) pore volume decreased. The specific surface area of BET decreased and then increased as microwave energy increased, while the average pore size increased and then decreased. However, the change in the BJH cumulative adsorption pore volume was complicated. The microwave radiation decreases the volume and number of micropores while increasing the volume and number of medium pores. With the increase in microwave energy, the number and volume of micropores continue to decrease, while the number and volume of medium pores continue to increase. An increase in microwave energy increased the surface area of oxygenic groups with the increasing relative content of COO–, C–O, and C=O bonds; however, the relative content of C–C/C–H bonds decreased. These findings deepen the understanding of the antireflection effects of microwaves on coal.

Experimental study on methane adsorption and time-dependent dynamic diffusion coefficient of intact and tectonic coals: Implications for CO2-enhanced coalbed methane projects

CO2-enhanced coalbed methane (CO2-ECBM) technology can be applied not only to extract coal seam gas, but also to geologically store a large amount of CO2 produced in various industries, thus reducing the CO2 concentration in the atmosphere and protecting the earth’s environment from the adverse effects of climate change. For CO2 injection and methane recovery from coal seams, the differences in the gas adsorption and diffusion characteristics due to the properties of the coal seam are crucial. In this study, first, intact and tectonic coals were collected to conduct a proximate analysis and high-pressure methane adsorption/desorption tests. Subsequently, the adsorption characteristics of the intact and tectonic coals with different particle sizes were analyzed. A time-dependent dynamic diffusion coefficient was introduced to investigate the diffusion characteristics of the two coals. The results showed that the intact and tectonic coals have higher adsorption capacity for CO2 than methane under the same particle size, demonstrating the potential for storing a large amount of CO2 in coal seams. The time-dependent dynamic diffusion coefficient decreased significantly in the initial stages and then tended to stabilize as the desorption progressed. To better explain the gas diffusion characteristics of the coal, a gas diffusion mechanism model was established to analyze the variation in the diffusion coefficient over time. In addition, a new method for reducing the pressure difference was proposed to maximize CO2 storage and methane recovery. Finally, the environmental implications and safety of CO2 storage in coal seams during the implementation of a CO2-ECBM project was analyzed.

Influence rules and mechanisms of mechanical vibration at different frequencies on dynamic process of gas diffusion from coal particles

To study the influence of vibration on gas desorption and diffusion in particle coal, gas desorption experiments on soft coal with outburst risk under different frequency vibrations were carried out by using a self-designed gas adsorption and desorption platform under vibration conditions, and the influence of different frequency vibrations on the diffusion kinetic parameters was quantitatively analyzed by using a dynamic diffusion coefficient model. The influence mechanism of vibration on gas desorption and diffusion in coal was further analyzed from the three aspects of gas molecules, energy conversion and pore structure through theoretical analysis and mercury injection experiments. The results showed that with increasing vibration frequency, the gas desorption of the coal samples first increases and then decreases. The initial diffusion coefficient of gas in the coal samples increases linearly with increasing vibration frequency, but the attenuation coefficient of the diffusion coefficient decreases first and then increases with increasing vibration frequency. The "throwing effect" and thermal effect of vibration on the gas molecules are both conducive to the desorption of gas molecules. In addition, vibration causes changes in the pore structure in coal, increasing gas diffusion paths and reducing diffusion resistance.

“In Silico” Seawater

Many important processes affecting the earth’s climate are determined by the physical properties of seawater. In addition, desalination of seawater is a significant source of drinking water for the human population living in coastal areas. Since the physical properties of seawater governing these processes depend on the molecular interactions among its components, a deeper knowledge of seawater at the molecular level would contribute to a better understanding of these phenomena. However, in strong contrast with the situation in other areas such as biomolecules or materials science, molecular simulation studies reporting the physical properties of seawater are currently lacking. This is probably due to the usual perception of the seawater composition being too complex to approach. This point of view ignores the fact that physical properties of seawater are dependent on a single parameter representing the composition, namely the salinity. This is because the relative proportions of any two major constituents of seasalt are always the same. Another obstacle to performing molecular simulations of seawater could have been the unavailability of a satisfactory force field representing the interactions between water molecules and dissolved substances. However, this drawback has recently been overcome with the proposal of the Madrid-2019 force field. In this work we show for the first time that molecular simulation of seawater is feasible. We have performed molecular dynamics simulations of a system, the composition of which is close to the average composition of standard seawater and with the molecular interactions given by the Madrid-2019 force field. In this way we are able to provide quantitative or semiquantitative predictions for a number of relevant physical properties of seawater for temperatures and salinities from the oceanographic range to those relevant to desalination processes. The computed magnitudes include static (density), dynamical (viscosity and diffusion coefficients), structural (ionic hydration, ion–ion distribution functions), and interfacial (surface tension) properties.

Gas seepage laws based on dual porosity and dual permeability: Numerical simulation and coalbed methane extraction practice

AbstractCoalbed methane (CBM) is the very important unconventional energy resource. Enhancing extraction is the main method to improve the utilization of CBM and prevent coal mine gas disasters. To reveal the laws of gas migration during the underground gas extraction, the paper established the solid‐gas coupling model, regarding coal as the homogeneous elastic medium with dual pore‐fracture structure and dual permeability and considering the gas dynamic diffusion coefficient. Then, the regulations of gas migration in the in‐seam borehole were simulated by the COMSOL Multiphysics software and verified via the field trials of gas extraction. The results revealed that the permeability increased with time due to the coupling of matrix shrinkage and volume compression of coal, in which the matrix shrinkage played a leading role. The gas seepage velocity at the observation points can be divided into three stages: the rapid rise stage, the stable decline stage, and the stable and invariant stage. The gas extraction rate continued decreasing with time and finally tended to a fixed value. In the coal seam #4 of Zhongxing coal mine, the measured flow rates of three in‐seam drilling holes were in good agreement with the simulation results, which verified the correctness of the theoretical coupling model.

Pore-Scale Lattice Boltzmann Simulation of Gas Diffusion–Adsorption Kinetics Considering Adsorption-Induced Diffusivity Change

The diffusion–adsorption behavior of methane in coal is an important factor that both affecting the decay rate of gas production and the total gas production capacity. In this paper, we established a pore-scale Lattice Boltzmann (LB) model coupled with fluid flow, gas diffusion, and gas adsorption–desorption in the bi-dispersed porous media of coalbed methane. The Knudsen diffusion and dynamic adsorption–desorption of gas in clusters of coal particles were considered. Firstly, the model was verified by two classical cases. Then, three dimensionless numbers, Re, Pe, and Da, were adopted to discuss the impact of fluid velocity, gas diffusivity, and adsorption/desorption rate on the gas flow–diffusion–adsorption process. The effect of the gas adsorption layer in micropores on the diffusion–adsorption–desorption process was considered, and a Langmuir isotherm adsorption theory-based method was developed to obtain the dynamic diffusion coefficient, which can capture the intermediate process during adsorption/desorption reaches equilibrium. The pore-scale bi-disperse porous media of coal matrix was generated based on the RCP algorithm, and the characteristics of gas diffusion and adsorption in the coal matrix with different Pe, Da, and pore size distribution were discussed. The conclusions were as follows: (1) the influence of fluid velocity on the diffusion–adsorption process of coalbed methane at the pore-scale is very small and can be ignored; the magnitude of the gas diffusivity in macropores affects the spread range of the global gas diffusion and the process of adsorption and determines the position where adsorption takes place preferentially. (2) A larger Fickian diffusion coefficient or greater adsorption constant can effectively enhance the adsorption rate, and the trend of gas concentration- adsorption is closer to the Langmuir isotherm adsorption curve. (3) The gas diffusion–adsorption–desorption process is affected by the adsorption properties of coal: the greater the pL or Vm, the slower the global gas diffusivity decay. (4) The effect of the gas molecular adsorption layer has a great impact on the kinetic process of gas diffusion–adsorption–desorption. Coal is usually tight and has low permeability, so it is difficult to ensure that the gas diffusion and adsorption are sufficient, the direct use of a static isotherm adsorption equation may be incorrect.

Diffusive process under Lifshitz scaling and pandemic scenarios

We here propose to model active and cumulative cases data from COVID-19 by a continuous effective model based on a modified diffusion equation under Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is rich enough to capture different aspects of a complex virus diffusion as humanity has been recently facing. The model being continuous it is bound to be solved analytically and/or numerically. So, we investigate two possible models where the diffusion coefficient associated with possible types of contamination are captured by some specific profiles. The active cases curves here derived were able to successfully describe the pandemic behavior of Germany and Spain. Moreover, we also predict some scenarios for the evolution of COVID-19 in Brazil. Furthermore, we depicted the cumulative cases curves of COVID-19, reproducing the spreading of the pandemic between the cities of São Paulo and São José dos Campos, Brazil. The scenarios also unveil how the lockdown measures can flatten the contamination curves. We can find the best profile of the diffusion coefficient that better fit the real data of pandemic.

Evolution of gas transport pattern with the variation of coal particle size: Kinetic model and experiments

Gas desorption laws varies with coal particle size. Their proper description is of great importance to natural gas engineering. This paper tries to summarize the internal links in commonly used models and combine them into a more general form. The combined general model is capable of describing fracture flow, matrix diffusion and surface sorption processes in pores with shapes like flat plates, cylinders and spheres. It can also be simplified into a power function which can be readily implemented into simulation of sorption and calculation of dynamic Fickian diffusion coefficients. Experiments including low-temperature liquid N2 adsorption, proximate analysis, isothermal methane sorption and desorption experiments with different particle sizes were conducted to validate the model. Other sorption data from literature were also collected for validation. The fitting results can help explain the size dependence of desorption characteristics and show the flow type evolutions during the damage of pore system.

Experimental investigation of the constant and time-dependent dynamic diffusion coefficient: Implication for CO2 injection method

Gas diffusion in coal is an important transport mechanism that plays a crucial role in carbon dioxide (CO2) storage in and methane (CH4) extraction from coal seams. Studies on coal diffusion are largely based on experimental work on different coal particles and the establishment of uni-pore or bidisphere theoretical models. However, problems remain in both experimental and theoretical analyses. Therefore, the initial desorption time of adsorbed gas, something that is not done using conventional experimental devices, was revealed in this study. The initial desorption time was obtained by calculating the relationship between the amount of gas collected and the theoretical amount of free gas. An improved diffusion model considering lost gas was established based on the initial desorption time of adsorbed gas. The mpdel provides diffusion coefficients for different equilibrium pressures and particle sizes on the basis of a unipore diffusion model. By correlating diffusion coefficient and time, an empirical time-dependent diffusion model was established to solve the dynamic diffusion coefficient under different conditions. Finally, in order to substantiate that the variation in diffusion length is the primary cause of the variation of diffusion coefficients with time, the variation of diffusion length with desorption time was obtained. As a result, a stepwise pressure-rasing method was proposed. This new injection method can effectively improve CO2 storage and CH4 recovery from coal seams. The study has a certain guiding significance in engineering practice.

Determination of the Diffusion Coefficient of Supercritical CO2 in Low-Permeability Formation Cores

CO₂ diffusion in the oil phase in the presence of porous media is of great importance to forecast the performance of enhanced oil recovery and carbon dioxide capture and storage. When CO₂ is brought into contact with an oil phase, diffusion occurs. The indirect pressure-decay methodology has been applied successfully to determine the mutual diffusion coefficients of supercritical CO₂ and crude oil at temperature of 65 °C. Theoretically, a one-dimensional double-way mass transfer model incorporating the capillary and adsorption effects of porous media has been constructed to quantify the mutual dynamic diffusion coefficients. The crude oil has been characterized into five pseudo-components for the accurate description of the phase behavior of CO₂ gas and oil phases. An optimization method along with the PR equation of state is employed to determine each component’s diffusion coefficients in the gas and oil phases for the purpose of minimization of the difference between the experimental data and calculated results. Satisfactory agreements are obtained with a merely 0.97% pressure difference when a variable diffusion coefficient is implemented. The short-time experimental test and a long-time-duration calculation are recommended for further diffusion investigation. The capillary analysis gave a regressed fractal dimension of 2.7049 with the average absolute deviation of 0.602%. The adsorption phenomenon can be greatly influenced by the existence of heavy components. The heavier the components, the greater their impact on adsorption. Furthermore, a faster and enhanced diffusion process is observed at high pressure and temperature. The combination of several complex mechanisms leads to the initial gradual increase of the diffusion coefficient with time, and then, it arrives at a plateau, which is slightly different from the previous diffusion coefficient changing tendency mentioned in the literature. In the presence of a low-permeability formation core, the determined diffusion coefficients of CO₂ in the gas and liquid phases are increased from 4.38 × 10–⁹ to 6.21 × 10–⁹ and 6.16 × 10–¹⁰ to 9.21 × 10–¹⁰ m²/s when the system pressure is decreased from 18.2 to 12.11 MPa, respectively. In addition, the capillary effect can lead to a reduction of the diffusion coefficient in the oil phase but has little effect on the diffusion coefficient in the gas phase.