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Coalbed methane (CBM) is produced before coal mining at the Qinshui Basin in China to utilize CBM and reduce CH4 volume fraction for coal mining. However, the volume fraction of CH4 often reaches the range between lower and upper explosion limits after CBM production, which is a great threat to coal mining safety. In previous work, we analyzed the feasibility of injecting CO2 into coalbeds to control CH4 volume fraction for mining safety and simultaneously enhancing CBM recovery. In this paper, we extended our work to propose a model to calculate the critical CO2 volume fraction for CO2 injection. We simplified the gas mixture during coal mining as the CO2/CH4/air mixture. The model of the critical CO2 volume fraction was then built based on the explosion limit formula for the CO2/CH4/N2 mixture. The formula for the critical CO2 volume was derived using the critical CO2 volume fraction. The model of the critical CO2 volume fraction was applied in a CBM reservoir at the South Shizhuang Block in the Qinshui Basin. The CO2 injection rate for this block was optimized to obtain the highest CBM recovery using the reservoir simulation method. Results show that the critical CO2 volume fraction is 7.97%, which makes the CH4 volume fraction out of the explosion limits. The optimum CO2 injection rate for this block is 8000m3/d which improves the CBM recovery up to 86.24%.

Many chemical and physical equilibrium conditions can be determined from minimizing the Gibbs free energies of the system. Efficient analytical representations of the entropy and Gibbs free energy of carbonyl sulfide remain elusive in the communality of science and engineering. Here, we report two analytical representations of the entropy and Gibbs free energy for carbonyl sulfide, and the prediction procedures only involve six molecular constants of the carbonyl sulfide molecule. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values of carbonyl sulfide from the National Institute of Standards and Technology database are arrived at 0.150 and 0.189%, respectively.

We first report three reliable analytical expressions of the entropy, enthalpy and Gibbs free energy of carbon dioxide (CO2) and perform predictions of these three thermodynamic quantities on the basis of the proposed analytical expressions and in terms of experimental values of five molecular constants for CO2. The average relative deviations of the calculated values from the National Institute of Standards and Technology database over the temperature range from 300 to 6000 K are merely 0.053, 0.95, and 0.070%, respectively, for the entropy, enthalpy, and Gibbs free energy. The present predictive expressions are away from the utilization of plenty of experimental spectroscopy data and are applicable to treat CO2 capture and storage processes.

The analysis of numerical dispersion in reservoir simulation usually focuses on its impacts on liquid saturation and component concentration profiles. However, the production of coalbed methane (CBM) reservoirs is highly sensitive to the pressure diffusion owing to its unique gas storage and flow mechanism. The effect of numerical dispersion on pressure diffusion during gas production has not been studied yet. In this work, the numerical dispersion term of pressure diffusion equation is derived using finite difference scheme to determine the influence of numerical dispersion on pressure diffusion. Simulation examples are then performed to evaluate the effect of numerical dispersion on pressure diffusion and gas production in CBM reservoirs. Finally, a field case is presented to study numerical dispersion impacts on gas rate, using the production history of two wells in Ordos Basin, China. The numerical dispersion term of pressure diffusion equation, derived in this paper, illustrates that the numerical dispersion is controlled by pressure diffusivity, grid size, time step and finite difference scheme. The simulation results indicate that both coarse grid and low permeability contribute to dramatic numerical dispersion and significant errors in simulation. Once the permeability is lower than 200 mD, there is a dramatic effect of grid size on numerical dispersion. A slight deviation of pressure still results in an unacceptable error in CBM production simulation. The simulation results and field example show that the numerical dispersion of pressure may overestimate the dewatering efficiency and gas production rate. An effective way to diminish the numerical dispersion in CBM reservoir simulation is to apply the fine grid system.

This paper presents a field-development case study of a tight gas sandstone reservoir in China. The gas production well JK1 in the Linxing-Shenfu Gasfield in Eastern Ordos Basin is concurrent producing from three separate layers, and experienced interlayer interference stage in which gas production dropped to 0 rapidly. The purpose of this study is to investigate the influence of interference between different layers on concurrent production, to explore a reasonable adjustment plan, and finally to enhance the productivity of well JK1. The production history of this well was analyzed and a three-dimensional geological model for it was constructed. The interlayer interference of pay zones and zones combination optimization were simulated for field application. The simulation results show that the interlayer interference is obvious when the three layers have commingled production, the fluids even flow backward to the Upper layer. When the Middle layer is produced with other layers, it is the main water production layer with less gas. The Lower layer has always been the main gas production layer with less water. The optimization results indicate that only the Lower formation produces separately, the gas production is the highest. The optimization of field operational practices was based on the introduction of numerical simulation results enabled a gas production increase from vanishingly low to almost 4500 m3/d in the following year. This study can provide an insight on interlayer interference and a good guidance for a production strategy on full field development.

Nitrogen (N2) is widely used in oil and gas industry. We report two new efficient closed-form representations for the molar entropy and Gibbs free energy of pure gaseous substances. A comparison of the predicted and experimental values shows that the molar entropies and Gibbs free energies of N2 can be excellently predicted in the temperature range of 100–6000 K. The present entropy and Gibbs free energy prediction models only require the experimental values of three molecular constants and are away from the utilization of a great number of experimental spectroscopy data.

We develop a new closed-form representation for the molar Gibbs free energies of gaseous substances. The predicted molar Gibbs free energies are in excellent agreement with the experimental data in a wide temperature range for three gases under consideration, and the average absolute deviations of the predicted results from the experimental data are 0.06155%, 0.0708% and 0.16696% for the gases Cl2, Br2, and HCl, respectively. The proposed model is away from the need of a large amount of experimental spectroscopy data, and only related to the dissociation energy, equilibrium bond length, and equilibrium vibration frequency.

The methane from two coal seams are usually produced in the same production well, and the commingled production process is of low efficiency. In order to enhance the methane recovery from the two c...

We report a new efficient analytical representation of the molar enthalpy for gaseous substances. The predicted molar enthalpy values are in good agreement with the experimental data in a wide temperature range for the gases Cl2, Br2, and gaseous BBr. The present enthalpy prediction model does not need of a great number of experimental spectroscopy data, and requires only three molecular constants, for which the experimental values can be easily obtained in the literature.

We present a universal efficient closed-form representation for the molar enthalpy of gaseous substances. The predicted molar enthalpy values show excellent agreements compared to the experimental data in a wide temperature range for the gases CO, HCl, and BF. The proposed model is away from the need of plenty of experimental spectroscopy data, and depends on only four molecular constants, for which the experimental values can be easily found in the literature.

Nonpharmaceutical interventions (NPIs), particularly contact tracing isolation and household quarantine, play a vital role in effectively bringing the Coronavirus Disease 2019 (COVID-19) under control in China. The pairwise model, has an inherent advantage in characterizing those two NPIs than the classical well-mixed models. Therefore, in this paper, we devised a pairwise epidemic model with NPIs to analyze COVID-19 outbreak in China by using confirmed cases during February 3rd–22nd, 2020. By explicitly incorporating contact tracing isolation and family clusters caused by household quarantine, our model provided a good fit to the trajectory of COVID-19 infections. We calculated the reproduction number R = 1.345 (95% CI: 1.230 − 1.460) for Hubei province and R = 1.217 (95% CI: 1.207 − 1.227) for China (except Hubei). We also estimated the peak time of infections, the epidemic duration and the final size, which are basically consistent with real observation. We indicated by simulation that the traced high-risk contacts from incubated to susceptible decrease under NPIs, regardless of infected cases. The sensitivity analysis showed that reducing the exposure of the susceptible and increasing the clustering coefficient bolster COVID-19 control. With the enforcement of household quarantine, the reproduction number R and the epidemic prevalence declined effectively. Furthermore, we obtained the resumption time of work and production in China (except Hubei) on 10th March and in Hubei at the end of April 2020, respectively, which is broadly in line with the actual time. Our results may provide some potential lessons from China on the control of COVID-19 for other parts of the world.

Transient or sustained permeability transition pore (PTP) opening is important in normal physiology or cell death, respectively. These are closely linked to ${\mathrm{Ca}}^{2+}$ and reactive oxygen species (ROS). The entry of ${\mathrm{Ca}}^{2+}$ into mitochondria regulates ROS production, and both ${\mathrm{Ca}}^{2+}$ and ROS trigger PTP opening. In addition to this feedforward loop, there exist four feedback loops in the ${\mathrm{Ca}}^{2+}$-ROS-PTP system. ROS promotes ${\mathrm{Ca}}^{2+}$ entering (F1) and induces further ROS generation (F2), forming two positive feedback loops. PTP opening results in the efflux of ${\mathrm{Ca}}^{2+}$ (F3) and ROS (F4) from the mitochondria, forming two negative feedback loops. Owing to these complexities, we construct a mathematical model to dissect the roles of these feedback loops in the dynamics of PTP opening. The qualitative agreement between simulation results and recent experimental observations supports our hypothesis that under physiological conditions the PTP opens in an oscillatory state, while under pathological conditions it opens in a high steady state. We clarify that the negative feedback loops are responsible for producing oscillations, wherein F3 plays a more prominent role than F4; whereas the positive feedback loops are beneficial for maintaining oscillation robustness, wherein F1 has a more dominant role than F2. Furthermore, we manifest that the proper increase in negative feedback strength or decrease in positive feedback strength not only facilitates the occurrence of oscillations and thus protects the system against a high steady state, but also assists in lowering the oscillation peak. This study may provide potential therapeutic strategies in treating neurodegenerative diseases due to PTP dysfunction.

Transient or sustained permeability transition pore (PTP) opening is important in normal physiology or cell death, respectively. These are closely linked to Ca^{2+} and reactive oxygen species (ROS). The entry of Ca^{2+} into mitochondria regulates ROS production, and both Ca^{2+} and ROS trigger PTP opening. In addition to this feedforward loop, there exist four feedback loops in the Ca^{2+}-ROS-PTP system. ROS promotes Ca^{2+} entering (F1) and induces further ROS generation (F2), forming two positive feedback loops. PTP opening results in the efflux of Ca^{2+} (F3) and ROS (F4) from the mitochondria, forming two negative feedback loops. Owing to these complexities, we construct a mathematical model to dissect the roles of these feedback loops in the dynamics of PTP opening. The qualitative agreement between simulation results and recent experimental observations supports our hypothesis that under physiological conditions the PTP opens in an oscillatory state, while under pathological conditions it opens in a high steady state. We clarify that the negative feedback loops are responsible for producing oscillations, wherein F3 plays a more prominent role than F4; whereas the positive feedback loops are beneficial for maintaining oscillation robustness, wherein F1 has a more dominant role than F2. Furthermore, we manifest that the proper increase in negative feedback strength or decrease in positive feedback strength not only facilitates the occurrence of oscillations and thus protects the system against a high steady state, but also assists in lowering the oscillation peak. This study may provide potential therapeutic strategies in treating neurodegenerative diseases due to PTP dysfunction.

The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These containment efforts often lead to changes in the contact pattern among individuals of the population. Many existing compartmental epidemic models fail to account for the effects of contact structure. In this paper, we devised a pairwise epidemic model to analyze the COVID-19 outbreak in China based on confirmed cases reported during the period February 3rd--17th, 2020. By explicitly incorporating the effects of family clusters and contact tracing followed by household quarantine and isolation, our model provides a good fit to the trajectory of COVID-19 infections and is useful to predict the epidemic trend. We obtained the average of the reproduction number $R=1.494$ ($95\%$ CI: $1.483-1.507$) for Hubei province and $R=1.178$ ($95\%$ CI: $1.145-1.158$) for China (except Hubei), suggesting that some existing studies may have overestimated the reproduction number by neglecting the dynamical correlations and clustering effects. We forecasted that the COVID-19 epidemic would peak on February 13th ($95\%$ CI: February $9-17$th) in Hubei and 6 days eariler in the regions outside Hubei. Moreover the epidemic was expected to last until the middle of March in China (except Hubei) and late April in Hubei. The sensitivity analysis shows that ongoing exposure for the susceptible and population clustering play an important role in the disease propagation. With the enforcement of household quarantine measures, the reproduction number $R$ effectively reduces and epidemic quantities decrease accordingly. Furthermore, we gave an answer to the public concern on how long the stringent containment strategies should maintain. Through numerical analysis, we suggested that the time for the resumption of work and production in China (except Hubei) and Hubei would be the middle of March and the end of April, 2020, respectively. These constructive suggestions may bring some immeasurable social-economic benefits in the long run.

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π i is proportional not only to k i + A, the sum of the old node i's degree k i and its initial attractiveness A, but also to the aging factor τ i − α , where τ i is the age of the old node i. That is, Π i ∝ ( k i + A ) τ i − α . Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k −γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t i , t) at time t for any node i that is added into the network at time t i scales as k ( t i , t ) ∝ t i − β where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.

The pore volume compressibility of reservoir rock is usually measured by volume method and the relation between compressibility and porosity follows the Hall plot. However, the volume method yields a high pore volume compressibility value and a negative correlation between compressibility and porosity. Both results illustrate that unconventional reservoirs with low porosity has higher elastic energy than conventional reservoirs with high porosity, which disagrees with the production practice. In this paper, volume method of pore volume compressibility is investigated and problems of Hall plot are analyzed. Then a novel analytical model on pore volume compressibility of reservoir rock is derived to resolve these problems. The reason on the improper results using volume method is discussed. The calculated results from our new model are validated by the experimental tests using mercury immersion method for pore volume compressibility measurement. The effects of compressibility on original oil in place and the flow radius are analyzed. The analytical model shows that pore volume compressibility of reservoir rock is related not only to porosity but also to elastic modulus and Poisson’s ratio. There is a positive correlation between pore volume compressibility and porosity. The compressibility value of our model is much lower than that measured using volume method. The reason of the improper results from volume method is the micro interstice in core holder. Without the effects of micro interstice (mercury immersion method or loading and unloading stress treatment before the test), the measured pore volume compressibility shows a relatively low value and a positive correlation between pore compressibility and porosity, which validate the results of our analytical model. The pore volume compressibility calculated by volume method and Hall plot will overestimate the elastic energy of the reservoir and bring substantial errors in evaluation of original oil in place and the flow radius.

We establish an analytical representation for the prediction of the molar Gibbs free energies of gaseous diatomic molecule substances. By comparing the predicted values to the experimental data for the gaseous phosphorus dimer, the availability of the Gibbs free energy calculation model is verified. The present model is related to three molecular constants and away from the need of lots of experimental spectroscopy data.

Based on the improved Rosen-Morse oscillator for describing the internal vibration of a molecule, we establish an explicit representation of molar entropy for gaseous substances. Using the dissociation energy, equilibrium internuclear distance and harmonic vibrational frequency, we calculate the molar entropy values of the gaseous phosphorus dimer. Our calculated results show an excellent agreement compared to the experimental data in a wide variety of temperatures ranging from 298 up to 6000 K.

In the context of epidemic spreading on networks, there are at least three concerns that should be considered. Firstly, the demographic process can change the underlying network structure and thus affect the disease spreading; secondly, the attachment probability of newcomers (namely, newborn or immigrated nodes) to other nodes depends on the degrees and states of existing nodes in the network; and thirdly, newcomers may remove some dangerous contacts once they perceive the risk of disease. In view of these facts, we propose two high-dimensional susceptible-infectious-susceptible (SIS) epidemic models on heterogeneous networks with demographics and risk perception — one that neglects both the degree and state correlations among nodes and the other that reserves the state correlation. Then the log-normal moment closure is adopted to reduce the dimensions of models. The basic reproduction numbers of the two corresponding low-dimensional models are derived. It is found that the basic reproduction numbers of the two models are different. In spite of this, both of them show that increasing recruitment will help to inhibit the disease spreading. In addition, numerical results demonstrate that the extent to which newcomers avoid contacting with infectious nodes can affect both the epidemic threshold and the equilibrium prevalence. Finally, comparisons between numerical and stochastic simulations indicate that the model with state correlation is more accurate.

In tight gas reservoirs, permeability is pressure dependent owing to pore pressure reduction during the life of the reservoir. Empirical models are commonly used to describe pressure-dependent permeability. In this paper, it was discussed a number of issues which centered around tight sandstone pressure-dependent permeability experiment, first to apply core aging on permeability test and then to develop a new semi-analytical model to predict permeability. In tight sandstone permeability test experiment, the microinterstice between core and sleeves resulted in over estimation of dependency of permeability on pressure. Then, a new semi-analytical model was developed to identify the relation between permeability and fluid pressure in tight sandstone, which indicates there is a linear relation between pore pressure changes and the inverse of permeability to a constant power. Pressure-dependent permeability of 8 tight sandstone core samples from Ordos Basin, China, was obtained using the modified procedure, and results were perfectly matched with the proposed model. Meanwhile, the semi-analytical model was also verified by pressure-dependent permeability of 16 cores in the literature and experiment results of these 24 cores were matched by empirical models and the semi-analytical model. Compared with regression result of commonly used empirical models, the semi-analytical model outperforms the current empirical models on 8 cores from our experiment and 16 cores from the literature. The model verification also indicates that the semi-theoretical model can match the pressure-dependent permeability of different rock types. In addition, the permeability performance under reservoir condition is discussed, which is divided into two stages. In most tight gas reservoirs, the permeability performance during production is located in stage II. The evaluation result with proposed experiment procedure and the stress condition in stage II will reduce permeability sensitivity to stress.

We present an explicit representation of molar entropy for gaseous substances. Fortunately, through comparison of theoretical and experimental results, we discover that the molar entropies can be successfully predicted by applying experimental values of only four molecular constants for the carbon monoxide, hydrogen chloride, hydrogen fluoride, deuterium fluoride, gaseous boron monobromide, and nitrogen monoxide. The present entropy calculation scheme provides opportunities for predicting successfully entropy values of other gaseous substances with no use of a large number of experimental spectroscopy data.

For waterflooded tight oil formations, imbibition is a dominant mechanism for oil recovery. Although substantial imbibition experiments have been conducted in lab-on-a-chip systems, few of them have etched patterns with representative pore/throat features of tight rocks and are studied in Liquid-Liquid systems. This study aims to summarize the achievements of pore-scale imbibition experiments and point out the potentials/issues faced in applying micro/nanomodels for studying imbibition mechanisms in tight oil formations. This review first summarizes pore/throat features in tight rocks to provide benchmarks for evaluating micro/nanomodel designs. Then, recent efforts on pore-scale imbibition studies are documented based on pore-scale phenomena, testing materials, and pattern designs. Finally, the challenges and recommendations of applying lab-on-a-chip systems for imbibition studies are discussed from six aspects: the representability of channel designs, wettability issues, surface roughness effects, blocking events, pressure handling, and experiment repeatability.

In tight sandstones from the Sichuan basin, permeability jail is observed. Because tight sandstones in the Sichuan basin have a high water saturation, gas and water exist as discontinuous phases at the pore scale, which could be the cause of permeability jail. In this paper, flow resistance in tight sandstones was studied, and its relationship with permeability jail was investigated. First, a model to characterize flow resistance in discontinuous phase flow was proposed. The model was based on a bundle of capillary tubes with non-uniform radii, which took the capillary pressure difference induced by the Jamin effect, water viscosity force and gas viscosity force into account. Then, a gas-water relative permeability test and NMR experiment were conducted to verify the model. Finally, the flow resistance at a series of water saturation points was calculated to study the relationship between flow resistance and permeability jail. The results show that discontinuous phase flow is affected by the Jamin effect, which induces permeability jail because the capillary pressure difference reaches the maximum and leads to a very high flow resistance in permeability jail. Capillary pressure difference falls, however, when water saturation is outside of permeability jail, which contributes to the drop of the flow resistance and helps recover the flow capability.

We present a closed-form expression of the vibrational partition function for the improved Tietz potential energy model. The vibrational partition functions for the improved Manning-Rosen potential and improved Rosen-Morse potential are easily deduced as two special cases. The obtained results are applicable to many issues in chemical physics and engineering.

Complex heterogeneous reservoir exhibits special characteristics, such as multiple storage types, wide range of storage sizes, complicated storage combinations, and various flow behaviors. Multi-continuum model is needed to rigorously simulate this type of reservoir. However most reservoir simulators use dual porous media model, and the theory of the models is mainly focused on matrix-fracture system. Therefore when porous media is more complex than matrix-fracture system, such software cannot be utilized to simulate these reservoirs directly. Some studies have been proposed to solve the problem, but most of them are either at the theoretical level or cannot been used widely in the simulation softwares. The goal of this paper is not to develop new numerical simulation software, but to obtain appropriate ways to improve performance of current simulation software for complex reservoir. Our approach is theoretically based on multi-continuum seepage theory. By comparing the microscopic seepage model and multi-continuum seepage model, we find that the conventional theory becomes improper because of the absence of an important restriction to the interporosity flow. In the conventional way, an N-multiple flow model always can be established based on N types of continuous media. In fact, one more restrictive condition needs to be added to make it valid: all the crossflow between any two types of continuum can be simplified into a source or sink terms in the seepage model. Consequently, the multiplicity of the seepage model is always less or equal to the number of the continuum types. In addition, because different type of dual-medium has different crossflow, it is required to construct their crossflow models respectively and derive corresponding calculation formula. Several steps developed in this paper are as follows on the basis of multi-continuum theory and the restrictions appended: First, reservoir storage is categorized into continuous and non-continuous media according to storage scale characteristics, distribution and intensity. In general, small cavities, small fractures, and pores in the rock are continuous while large-scale fractures, big cavities or caves are non-continuous. The whole reservoir is therefore classified into continuum region and dis-continuum region. Second, in the continuum region, multi-media model and its multiplicity are determined by using the new theory proposed in this paper. Third, calculation formulae are constructed for each type of crossflow. This research takes fractured vuggy reservoirs as an example. A new calculation for the flux transfer is derived for such fracture-vug dual-porosity system. Forth, in the discrete region, flow in a filled non-continuous medium is described by Darcy's law and free flow in large unfilled cavities or caves follows Navier-Stokes equation and an approximate approach to using Darcy flow simulation is provided. Lastly, this paper introduces the methods how to simplify multi-media into two media and how to simulate the complex reservoir by using the existing simulators. The proposed method is applied to a naturally fractured carbonate reservoir with cavities in the Tarim Basin in China. The simulation results illustrate the production mechanisms of reservoir development using water flooding, including water injection and shut-in, stairs-shaped line of water cut with time, high production with low water cut for long time.

Community structures in complex networks play an important role in researching network function. Although there are various algorithms based on affinity or similarity, their drawbacks are obvious. They perform well in strong communities, but perform poor in weak communities. Experiments show that sometimes, community detection algorithms based on a single affinity do not work well, especially for weak communities. So we design a self-adapting switching (SAS) algorithm, where weak communities are detected by combination of two affinities. Compared with some state-of-the-art algorithms, the algorithm has a competitive accuracy and its time complexity is near linear. Our algorithm also provides a new framework of combination algorithm for community detection. Some extensive computational simulations on both artificial and real-world networks confirm the potential capability of our algorithm.