Equilibrium Model Research Articles

General properties of the response function in a class of solvable non-equilibrium models

Abstract We study the non-equilibrium response function $R_{ij}(t,t')$, namely the variation of the local magnetization $\langle S_i(t)\rangle$ on site $i$ at time $t$ as an effect of a perturbation applied at the earlier time $t'$ on site $j$, in a class of solvable spin models characterized by the vanishing of the so-called {\it asymmetry}.
This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio $X_{ij}(t,t')=\beta R_{ij}/(\partial G_{ij}/\partial t')$, where $G_{ij}(t,t')=\langle S_i(t)S_j(t')\rangle$ is the spin-spin correlation function and $\beta$ is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal form
$X_{ii}(t,t') = (t+t')/(2t)$, whereas $
\lim _{t\to \infty}X_{ij}(t,t')=1/2$ for any $ij$ couple. The specific case of voter models with long-range interactions is thoroughly discussed.

Capital Investment, Equity Returns, and Aggregate Dynamics in Oligopolistic Production Economies

Abstract We analyze effects of tacit collusion in a dynamic general equilibrium model of oligopolistic sectors with capital investment and real frictions. Through their effects on equilibrium- and off- equilibrium stock prices, fundamental shocks affect incentives for defection from tacit collusion, amplifying the interaction between the real economy and financial markets as well as firms‘ risk exposure. The model implies ambiguous relationship between industry concentration and equity returns depending on operating leverage, which helps reconcile conflicting evidence in the literature. We find quantitative and empirical support for novel theoretical predictions regarding the effects of concentration on returns and investment. (JEL G12, G31, D43)

Alkali metal depletion in the deep Jovian atmosphere: The role of anions

The Juno Microwave Radiometer has allowed observation of Jupiter's atmosphere down to previously inaccessible depths, although the complexity of the atmospheric dynamics has complicated analysis. The longest-wavelength channel (600 MHz) is sensitive to pressure levels of hundreds of bars, and has observed opacity sources other than the known gaseous and cloud components, likely caused by thermally ionized free electrons from alkali metal vapor. We extend previous analysis of limb darkening at these wavelengths, using radiative transfer and thermal equilibrium modeling, by considering the effect of anions in the deep Jovian atmosphere, which act as a sink for free electrons and will thus decrease opacity for a given alkali metal abundance. We show that MWR observations are consistent with a sodium and potassium abundance on the order of 0.1× solar around the 1-kilobar level, higher than previously estimated but still substantially depleted compared to other heavy elements, a value that would be within the range of observed alkali metal abundances on giant exoplanets; alternatively, MWR observations may be consistent with 3× solar sodium abundance, but only if potassium is even more strongly depleted. Such depletion may be the result of either chemical processes yet deeper in the atmosphere, such as in the silicate clouds, or of a long-lived stable layer shallower than the alkali salt clouds.

Synergistic regulation of microstructure, properties, and abrasive wear mechanism of a medium carbon dual phase steel for plowshares

In this study, a new medium carbon dual phase (DP) steel for plowshares is prepared. The quenching and partitioning process of the medium carbon steel is designed and optimised using the constrained carbon equilibrium model. The optimised process parameters are quenching temperature of 880 °C, quenching bath temperature of 190 °C and partitioning temperature of 350 °C. The microstructure of the acicular martensite matrix with 13% retained austenite was prepared, so that the good mechanical properties of tensile strength of 2007 MPa, yield strength of 1689 MPa, elongation of 11% and impact energy of 12 J are obtained. The multi-scale characterisation and abrasive wear experiments are carried out to investigate its microstructural evolution and wear mechanism under simulated working conditions. The results show that the coordinated deformation of retained austenite and martensite, as well as the trip effect, endows it with ultra-high strength and good plasticity. The recurring process of formation and spalling of the hardened layer is the main wear pattern of this medium carbon DP steel. The synergism of twinning formation and (Ti, Mo)C precipitation enhances wear resistance of this medium carbon DP steel.

Gasification of mixed plastic-biomass pellets in an updraft fixed bed reactor: A simplified dynamic model

In the context of materials recycling, updraft gasifiers are promising small and middle-scale reactors to obtain building blocks and/or energy from waste plastic and biomasses. To this aim, these kinds of materials can also be mixed and reduced into pellets, while the needed heat enters the process with a heated carrier gas. In order to preliminarily design a gasifier to check its feasibility with an available feedstock, currently available models are inadequate. Thermodynamic ones are useless for the purposes of sizing, while too detailed rate-based models (e.g. based on fluid-dynamic modelling) are too substrate specific, need detailed input data and are extremely time consuming. A dynamic model of a fixed-bed reactor for biomass gasification is presented here. The gasifier is loaded continuously from the top with solid pellets and fed with counter-current air flow. The model considers: i) a one-step gasification kinetics, yielding a product spectrum which matches experimental data from the literature; ii) dynamic gas and solid energy balances and iii) steady-state energy balance for the furnace. The model has been applied to describe a tubular furnace (Ø 40 cm) which gasifies 500–1000 kg day−1 of mixed wastes using air heated up to 1200 °C: on the basis of the produced chemicals, the energy consumption was estimated as ca. 2 MJ per kg of solid feedstock. This simplified approach proved robust in describing the overall yields and start-up dynamics, showing higher reliability than equilibrium models in addressing the temperature profiles, at the cost of a simplified reaction kinetic and pellet description with respect to more complex simulation models. The model validation was done by comparison between the calculations results and available pilot-plant data. An overall good fit of the data can be concluded. The solid-gas heat transfer and the bed packing are the main computational criticalities to achieve a reliable process description.

Assessing the carbon footprint of soybean transportation in Brazil: a network equilibrium model approach.

Brazil has historically invested few resources in its transport infrastructure, leaving gaps and reducing its efficiency. The country presents a high dependence on road transport, which results in increased operational costs and higher greenhouse gas (GHG) emissions. Consequently, the performance of cargo transportation in Brazil has been deteriorating, accompanied by a rise in the consumption of fossil fuels and noteworthy levels of GHG emissions. This article assesses the carbon intensity of soybean transport operations within Brazil. Utilizing a network equilibrium model, this study estimated the soybean transportation flows that minimize the total cost of transporting this product across the origins and destinations within the grain handling system. The modeling also calculated the GHG emissions in transportation. The results show that the transportation of soybeans produced 2.74 million tonnes of CO2 equivalent annually, with road transport accounting for 81.7% of these emissions. The state of Mato Grosso, responsible for 44.08kg CO2 equivalent per tonne of soybeans transported, contributed almost 49% of the total emissions due to the extensive distances involved. In contrast, states like Paraná and Rio Grande do Sul, located closer to southern ports, exhibited the lowest emissions, with rates of 11.55kg CO2 eq/t and 12.52kg CO2 eq/t, respectively. The analysis highlights the significant potential for reducing GHG emissions by increasing the use of rail and barge transport, particularly in high-emission regions such as Mato Grosso.

Two-stage multi-objective distributionally robust operation optimization and benefits equalization of an off-grid type electric-hydrogen-ammonia-methanol coupling system

As the proportion of renewable energy has increased significantly, electric-hydrogen coupling technology has emerged as a pivotal strategy for optimizing the utilization of renewable energy resources. In particular, within the power and chemical sectors, the preparation of ammonia and methanol using electric-hydrogen coupling technology has emerged as the two principal avenues for the utilization of hydrogen energy. However, as a nascent technology, the preparation of ammonia and methanol by electric-hydrogen coupling is confronted with a multitude of challenges, including the considerable uncertainty surrounding the generation of renewable energy, the dearth of economic benefits, and the need to ensure a fair allocation of benefits among the various stakeholders. To enhance the risk resistance of the electric-hydrogen-ammonia-methanol coupling system (EHAMCS), improve the economic benefits, ensure the environmentality and stability of the system, and realize the fair distribution of benefits among the energy participants, this paper constructs a multi-objective distributionally robust optimization (DRO) and multi-dimensional benefits equilibrium model for the EHAMCS and performs a numerical analysis with an off-grid type EHAMCS as an example. The results demonstrate that: 1) The cooperative operation of the EHAMCS offers notable economic advantages. When compared with only pursuing economic benefits, under multi-objective optimization, the economic benefits of the coupling system can be reduced by 1.49 %, but the carbon emission can be reduced by 10.06 %, and the instability is reduced by 0.02, which can create derivative benefits. 2) The two-stage DRO model is an effective means of addressing the impact of system operation uncertainty and the affine strategy enables the rapid adjustment of the day-ahead dispatching plan, thereby balancing the power deviation. 3) The multi-dimensional factor benefit balancing scheme is more conducive to the participation of clean energy and downstream ammonia and methanol energy subsystems in cooperative operation and promotes the consumption of clean energy while improving the energy conversion value of the EHAMCS to increase economic benefits. 4) EHAMCS operators should adjust their operational strategies in time with market and policy signals, and select historical samples reasonably, so as to realize the balance of the DRO model in terms of economy, robustness, and practicality. The effectiveness of the model and the superiority of the EHAMCS are thus verified.

Vertical specialization, global expansion of supply chain, and convergence

Abstract In this paper, we construct an elaborate general equilibrium model with a continuum of production fragments for an intermediate good, then incorporate it in a growth model to address the effects of global production fragmentation, vertical specialization, and trade on growth and inequality for a small developing country. Among other things, we show that a small developing economy grows faster than the rest of the world as a result of global fragmentation and trade in intermediates if it is skilled-labor scarce. We further address the effects of such a trade opening on wage inequality.

Effect of particle size, water saturation, inorganic salt and methane on the phase equilibrium of CO2 hydrates in sediments

Understanding the thermal stability of gas hydrate in complex marine geological environment is of importance to hydrate-based carbon sequestration. In this work, the factors affecting the equilibrium of CO2 hydrate in ocean sediments, including quartz sands, inorganic salts and gas impurities were quantitatively measured in a temperature range from 273 to 283 K and a phase equilibrium model of hydrate was established. To reveal the distribution in pore structure, the micro-morphologies of hydrate-bearing sediments were measured by cryo-SEM. Results showed that reduction of initial water saturation, addition of NaCl and CH4 were found to have inhibitory effect on CO2 hydrate equilibrium. Initial water saturation reduced the equilibrium temperature by the capillary pressure, but only 0.3–0.7 K temperature depression was observed as the water saturation reduced to 5 %. About 5.7 K in the average temperature depression was found by the addition of 10 wt% NaCl and 24 mol% CH4. NaCl and CH4 influenced the hydrate equilibrium by changing the water activity and chemical potential of hydrate water lattice. SEM images showed that the hydrate formed in pores of quartz sand had porous surface and coated the sand particles like a layer of cells which are 5–20 μm in diameter, suggesting the hydrate layer exists between the liquid and gas phase. Based on the van der Waals-Platteeuw model, a hydrate equilibrium model was developed. The model provided a good prediction of the hydrate equilibrium in the presence of quartz sand, NaCl and CH4 with an averaged deviation of ±4.2 %, which had the potential to be applicated in more complexed ocean sedimentary environment.

Infection externalities and social welfare

ABSTRACT This paper investigates the effects of infection externalities on social welfare through constructing several general equilibrium models. The main findings are as follows. When the government increases the degree of controlling infection externalities of the urban skilled sector and the rural sector, social welfare will rise. However, for the urban unskilled sector, the change of social welfare is determined by the elasticity of substitution between unskilled labor and infection rights in this sector.

Paleoproterozoic ultrahigh-temperature metamorphism in the Helanshan Complex, North China Craton: New constraints from chloritized sapphirine-bearing pelitic granulites

Identifying ultrahigh-temperature (UHT) metamorphism in granulite-facies metamorphic terrains and determining its pressure-temperature-time (P-T-t) paths are crucial steps toward elucidating the anomalously hot geodynamic evolution process. This study presents the inaugural identification of chloritized sapphirine-bearing granulites in the Helanshan Complex, located in the western segment of the Khondalite Belt, North China Craton. Three stages of metamorphic evolution were identified based on petrographic analyses, mineral chemistry, and phase equilibrium modelling: the pre-Tmax stage involves the presence of rutile-stable phase assemblage, wherein rutile is partially substituted by ilmenite; the Tmax stage involves the assemblage of garnet + plagioclase + K-feldspar + sillimanite + spinel ± sapphirine + quartz + ilmenite + melt, as evidenced by microscale (<5 μm) blebs of variably chloritized sapphirine within spinel; and the retrograde cooling stage features the solidus assemblage of garnet + plagioclase + biotite + K-feldspar + sillimanite + cordierite + quartz + ilmenite + melt. Phase equilibrium modelling indicates Tmax conditions of 958–1055 °C and 6.4–7.8 kbar, suggesting UHT conditions accompanied by a high geothermal gradient of approximately 150 °C/kbar. Furthermore, a clockwise P-T trajectory was established, involving pre-Tmax decompression and post-Tmax near-isobaric cooling. Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) zircon and monazite U-Pb dating of UHT pelitic granulites produced ages clustering around 1.91 Ga, marking the era of UHT metamorphism within the Helanshan Complex. This discovery broadens the scope of UHT metamorphism and indicates that the entire Khondalite Belt experienced a regional UHT metamorphic event during 1.93–1.91 Ga, which was likely induced by an initial radiogenic heating synergy followed by an augmented mantle heat flux.

Contribution of road transport infrastructure in mitigating the inward–immiserizing growth in Cameroon: An externality approach in computable general equilibrium analysis

The issue of immiserizing growth has been largely discussed in the literature since 1958. It describes a country context contending with high volume of exports relatively to its imports on the international market that benefits from high economic growth but losses in households’ welfare. This study aims to investigate the contribution of transport infrastructure to tackle immiserizing growth in developing countries, focusing on the Cameroon economy, a contending with a significant lack in the development of road transport infrastructure. Further, the study enriches the debate on the wider economic impacts, closely related to immiserizing growth. The loss of welfare is observed upstream to the investigations, as a response to the application of two types of fiscal policies: the import tariff and the capital income tax. Through a dynamic Computable General Equilibrium (CGE) model, the effect of road transport infrastructure is explored, using the externalities approach. This is an innovative methodology recently applied to access the economic impacts of infrastructure investment making a difference between productive and non-productive infrastructure investments. The findings reveal that productive transport infrastructure not only reduces the wider economic impact by improving households’ welfare but also enhances economic growth. A 10 percent increase in road transport infrastructure investment funded by import tariff leads to a welfare improvement of 1.94% and 1.66% in both short and long terms compared to respective losses of 0.58% and 0.15% if the generated financial funds are allocated in non-productive infrastructure such as monuments, defense etc. The similar tendency is observed for the capital income tax funding. Thus, policymakers are recommended to accentuate the road construction, in order to shorten the complex interplay between public decisions and households’ living conditions.

Adsorptive removal of Pb2+ from aqueous solution by magnetic biodegradable and polymeric cellulose/Nylon 6 @Fe3O4 nanocomposite encapsulated with chitosan

A novel polymeric magnetic nanocomposite adsorbent (CNCs/N6 @ Fe3O4–CT) of low-cost, biodegradable, and ultra-permeable materials was prepared and characterized. The adsorbent was used to evaluate the effect of influencing factors and competitive ions on the adsorption of Pb2+ ions. The obtained data was fitted to equilibrium and thermodynamic models. The chemical and structural features of the adsorbent were investigated using a range of characterization techniques, including a vibrating sample magnetometer (VSM), Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). FTIR confirmed the presence of OH–, –NH2, and FeO sorption sites. SEM micrographs revealed presence of visible pores on the surface of the adsorbent, while VSM established a magnetic strength of 26.90 emu/g. The adsorption data fitted well with Langmuir isotherm, whereas the adsorption kinetics followed the pseudo-second-order kinetic model with a coefficient of determination (R2 >0.98). The thermodynamic parameters indicated that the adsorption of Pb2+ was exothermic and spontaneously adsorbed. The adsorption process was dominated by a chemical process with E > 10 kJ/mole, indicating an ion exchange process. The results established that the synthesized CNCs/N6 @ Fe3O4–CT nanocomposite adsorbent is viable for the removal of metal ions from aqueous solutions and has the potential for optimization and scale-up.

Drivers for Nominating First Women Executives: Empirical Evidence From Japanese Firms

Prior research on women in executive positions (WiE) has focused exclusively on the consequences of WiE by addressing how women executives influence firm strategy and performance, whereas little is known about the antecedents of WiE. However, to gain a comprehensive understanding of the overall impact of women executives on the firm, it is worthwhile to identify the triggers that prompt firms to appoint women executives for the first time. In this study, we have attempted to identify the antecedents of first appointments of women to executive teams (FAWE). On the basis of a theoretical frame incorporating the think crisis–think female perspective into the punctuated equilibrium model, we consider FAWE as the process of the transformational reform of an organization and examine the roles of three factors—firm performance (i.e., ROA and aspirational performance), environmental changes (i.e., industry dynamism, industry munificence, and industry complexity), and new CEO appointments—as antecedents of FAWE. We conducted a panel logistic regression analysis using 20 years of panel data (2000–2019) for Japanese listed firms. Our findings demonstrate that (1) poor firm performance (ROA and aspirational performance) was significantly related to the likelihood of FAWE in the subsequent year, and (2) a new CEO appointment was significantly related to the likelihood of FAWE in the subsequent year, whereas (3) hypotheses regarding environmental changes (industry dynamism, industry munificence, and industry complexity) were not confirmed. Implications for researchers and practitioners are discussed, along with the study’s limitations and suggestions for future research.

Analysis on temperature vacuum swing adsorption from wet flue gas carbon capture by using solid amine adsorbent with co-adsorption equilibrium models

Adsorption carbon capture has attracted extensive attention due to its low regeneration heat consumption, eco-friendly impacts and simplicity. However, there is a lack of comprehensive analysis of its energy consumption, economy and environment impact of adsorption carbon capture. This study aims to investigate the working performance using temperature vacuum swing adsorption (TVSA) from wet flue gas carbon capture utilizing co-adsorption equilibrium models for metal–organic framework (MOF) based amine materials. TVSA model is then carried out in terms of the continuous operational state, the dynamic changes in physical properties inside the bed, and the differences in properties at different positions within the bed layer. It is found that they often cannot simultaneously meet high CO2 recovery rates, productivity, and equivalent work. The analysis reveals that the optimal conditions, namely an adsorption temperature of 318 K and a CO2 component of 0.02 kmol during desorption, collectively result in reduced equivalent work and heightened productivity. The maximum productivity could reach 46.35 kg·m−3·h−1 for 5.6 v% water content and 308 K adsorption temperature. It is demonstrated that temperature vacuum swing adsorption for wet flue gas carbon capture using MOF based amine adsorbent is quite promising in terms of energy consumption and CO2 productivity in the future.

Assessing carbon capture and storage technology in industrial joint venture

Carbon Capture and Storage (CCS) technology can effectively reduce carbon dioxide emissions from industrial and energy production processes. Yet the commercialization of CCS technology is hampered by financial requirements. Existing research compares the costs and benefits of business models for individual CCS projects, no studies assess the industry and national levels. Here we use a dynamic computable general equilibrium model, constructure the vertical integration and joint venture business models for CCS. This study assesses the emission and economic impacts of joint ventures between China's high-emission industries and their upstream and downstream sectors. We find that adopting the joint venture model in the coal power sector, compared to the vertical integration model, initially exerts a negative economic impact but can mitigate 0.04 % of GDP by 2060. The chemical industry consistently benefits from the joint venture model both economically and in emission reductions. Downstream sectors of the steel and cement industries are unsuitable for participation in joint ventures. In addition, the joint venture model has significant industry linkage effects, affecting energy consumption, the scale and cost of CCS deployment. This work provides important information for the large-scale commercialization of CCS technology.

Fiscal policy in the face of the health crisis: A simulation using a hybrid DSGE‐SIR model

AbstractThis study employs a dynamic stochastic general equilibrium (DSGE) model, integrated with a Susceptible‐Infected‐Recovered (SIR) epidemiological framework, to assess the macroeconomic impacts of fiscal policy during the COVID‐19 pandemic in Morocco. Calibrated with Moroccan COVID‐19 data, the model links epidemiological dynamics to macroeconomic variables, offering a detailed analysis of fiscal interventions. The primary objective is to evaluate the effectiveness of various fiscal measures, including government spending shocks, consumption tax cuts, and labor tax reductions, in stimulating economic activity and supporting households and businesses impacted by the pandemic. The results indicate that government spending shocks significantly stimulated economic activity and employment, but also led to increased public debt and inflationary pressures, thereby illustrating the inherent trade‐offs. Consumption tax cuts, intended to boost demand, had mixed effects on inflation; while prices for some goods declined, higher demand caused price increases in others. Labor tax reductions, aimed at enhancing employment, generated varied effects on labor supply and contributed to rising public debt due to lower tax revenues. The study underscores the necessity of balanced fiscal strategies to achieve both immediate economic recovery and long‐term fiscal sustainability, highlighting the critical role of well‐calibrated fiscal policies in mitigating the economic consequences of pandemics.

Transmission of flood damage to the real economy and financial intermediation: Simulation analysis using a DSGE model

We assess physical risk associated with floods in Japan, using a dynamic stochastic general equilibrium (DSGE) model. We construct a model that incorporates transmission mechanism of floods and estimate the model using the data of flood-induced damage to capital stock and public infrastructure collected by the government in the last 40 years. The result of the analysis is threefold. First, a flood that reduces the private capital stock by about 0.1% as a direct effect causes GDP to fall by about 0.1% in the first period, with a gradual recovery to pre-flood level. Second, floods dampen GDP through multiple channels. From the supply side, a decline in capital stock inputs and total factor productivity (TFP) reduce GDP. From the demand side, the balance sheets of firms and financial intermediaries are impaired, resulting in disruptions to financial intermediation and depressing GDP. Based on our estimates, all these channels are quantitatively comparable in magnitude. Third, the quantitative impacts of flood shocks on GDP up to now have been minor compared to the standard structural shocks that are considered important in existing macroeconomic studies. However, according to the estimates that use the relationship between the key variables in our model together with climate change scenarios published by the Network for Greening the Financial System (NGFS), the impacts of these shocks could become somewhat larger in the future.

Economic effects of shocks in the coal industry: An analysis based on DSGE model

This paper examines the impact of the coal sector on the economy from the perspective of industry shocks. Existing research primarily focuses on the relationship between coal consumption and the economy. An 8-sector dynamic stochastic general equilibrium (DSGE) model is constructed, based on China's input-output tables from 2005 to 2020, to depict the economic effects of coal sector shocks. The research findings are: (1) The DSGE model reveals a close connection between the coal industry and the macroeconomy. (2) The coal sector shocks have the largest impact on the electricity sector. (3) Coal sector shocks primarily affect the macroeconomy through non-energy manufacturing sectors. (4) As the economic development level increases, the influence of coal sector shocks on the macroeconomy gradually diminishes. The econometric analysis indicates that the role of coal is no longer significant in the high stage of economic development. The results of the panel quantile regression model also show the same result. Based on these conclusions, this paper suggests that as China gradually enters a new stage of development, it can gradually reduce coal consumption.

Combination of two-fluid model and delayed equilibrium model for the critical flow in a slit

Accurately predicting the mass flux, pressure profile, and velocity profile of the critical flow in a slit is essential for analyzing the breaking process of the liquid phase and calculating the aerosol source term for leak-before-break (LBB) monitoring and Loss of Coolant Accident (LOCA) risk analysis. A new critical flow model combining Two-fluid Model (TFM) and Delayed Equilibrium Model (DEM) is built to get accurate profiles while avoiding the same phase velocity in DEM and the arbitrary critical flow criterion in TFM. The new model is verified using past experiments of the critical flow in a slit. It proves to be accurate in mass flux but not in critical pressure, with maximum relative errors of around 25% in mass flux and around 80% in critical pressure. The new model is optimized for higher accuracy in critical pressure. The empirical equation of saturated phase mass flow rate fraction gradient is optimized by conducting approximate pressure profile calculation and regression analysis. The maximum relative error decreases little while the ratio of critical pressure relative errors lying in the range of ±40% increases after optimization. In contrast, the difference in the average abstract relative error of pressure between original TFM-DEM and DEM is much larger, for the maximum relative error of mass flux and critical pressure are around 25% and 110%. The comparison between the original and optimized TFM-DEM proves that the new critical flow model is accurate in mass flux and can be optimized to raise pressure calculation accuracy. The comparison between the original TFM-DEM and DEM proves that the phase velocity difference is the major source of accuracy improvement in the pressure profile.