Local Equilibrium Theory Research Articles

Comprehensive heat extraction performance and fractured reservoir cooling effect analysis of a novel mine enhanced geothermal system

Mining deep metal mines poses significant challenges due to the high-temperature conditions in such environments. However, the vast untapped geothermal energy within these mines holds great prospects for development and application. Herein, we proposed a novel technology for the deep mine cooling and enhanced geothermal system (DMC-EGS), which transforms the relationship between deep mining and geothermal resources from a source of heat harm to heat benefit, while also providing conditions for underground mining environment cooling. Understanding the fluid flow and heat transfer processes in the deep mine thermal reservoir is crucial for developing DMC-EGS. Based on the local thermal equilibrium theory, a three-dimensional thermal–hydraulic coupled model of the thermal reservoir in the Sanshan Island Mine containing multiple fractures was established. The impact of natural fractures and fracture number on the thermal recovery performance and cooling effect of the system was considered, and the optimization scheme of heat recovery wellbore was proposed for the deep thermal reservoir of Sanshan Island Mine. It can be found that fractures play a crucial role in fluid-rock heat exchange. Compared with scenarios without fractures, hydraulic fractures could significantly improve the heat transfer capacity and rock cooling effect, resulting in a 45.7% increase in the amplitude of rock matrix temperature decrease and more than a 1.76-fold increase in overall heat recovery efficiency. In addition, the number of fractures significantly impacted the temperature distribution within the rock formation, and an increased number of fractures was associated with more efficient heat recovery performance. When the number of fractures was 7, the cumulative thermal production could reach 6.767 × 109 J. Among the three thermal exploitation schemes compared, the DMC-EGS under the triple-well mode yielded the best heat recovery performance during the 40-year extraction period, superior to the conventional dual-well mode, while the one injection and two production mode demonstrated better heat recovery capacity and cooling effect.

A Study of a Two-Phase Heat Transfer Mechanism in a Vertical Sintering Cooling Furnace

In order to explore the law of gas–solid countercurrent cooling heat transfer in a vertical sinter cooling furnace at a high temperature, based on the Euler model and the local non-thermodynamic equilibrium theory, an exergy efficiency model was built to evaluate the heat transfer process in the vertical sinter cooling furnace with different parameter changes. It was found that the inlet temperature of cooling air and sinter inlet temperature are the main factors affecting the temperature field and gas–solid heat transfer characteristics in the furnace. Under the conditions of each parameter, the cooling air temperature presents a radial “M” shape distribution. The axial cooling section is the most intense area of gas–solid heat transfer, and this part has the best heat transfer effect. When the inlet temperature of cooling air and the inlet temperature of sinter increase, the outlet temperature of sinter and the outlet temperature of cooling air increase. When the sinter equivalent diameter increases, the cooling air outlet temperature decreases gradually, while the sinter outlet temperature increases gradually. When the diameter and height of the cooling section increase, respectively, the outlet temperature of the sinter decreases and the outlet temperature of the cooling air increases. Based on dimensional analysis, the heat transfer correlation formula suitable for certain test conditions is obtained.

Determination of hydrogen diffusibility and embrittlement susceptibility of high-strength steel evaluated at different temperatures based on the local equilibrium theory

The effects of diffusible or non-diffusible hydrogen on hydrogen trapping states and hydrogen embrittlement susceptibility of cold-drawn pearlitic steel have been quantitatively evaluated at temperatures of 30 °C and 240 °C based on Oriani's local equilibrium theory. Hydrogen absorbed in cold-drawn pearlitic steel had two trapping states; Peak 1 H desorbed below 200 °C and Peak 2 H desorbed above 200 °C as determined by thermal desorption analysis. Peak 1 H with a binding energy between hydrogen and a trapping site (Eb) of 56 kJ·mol−1 was diffusible and harmful to hydrogen embrittlement at 30 °C. That was because the Eb of Peak 1 H was lower than that of Oriani's local equilibrium condition of 69 kJ·mol−1 at 30 °C. In contrast, Peak 2 H with an Eb of 76 kJ·mol−1 was non-diffusible and innocuous. That was because the Eb of Peak 2 H was higher than 69 kJ·mol−1 at 30 °C. However, Peak 2 H was diffusible and harmful to hydrogen embrittlement at 240 °C. That was because the Eb of Peak 2 H was lower than that of the local equilibrium condition of 117 kJ·mol−1 at 240 °C. These findings indicate that hydrogen diffusibility and embrittlement at a certain temperature can be determined by the local equilibrium condition. Hydrogen embrittlement at 240 °C was presumably caused by solid-solution hydrogen because hydrogen was not trapped at dislocations and grain boundaries, and vacancy-type defects formed by plastic strain were annihilated at 240 °C.

Effect of initial hydrogen distribution on the parameter extraction of the thermal desorption spectra: A finite element study

The main objective of this study was to clarify whether the commonly encountered inhomogeneous hydrogen distribution in thermal desorption tests, resulting from unsaturated hydrogen charging and hydrogen release during specimen transfer, could affect the desorption curves and parameter determination. The transient hydrogen distributions in the specimen, both in normal lattice sites and trap sites, during absorption, air exposure, and thermal aging were simulated using finite element method based on the Oriani's local equilibrium theory. Results indicated the significant effect of initial inhomogeneous hydrogen distribution on the transient hydrogen distribution and the desorption spectra. This effect could result in both the shift of peak temperature and the artifact in desorption curves, depending on the trap binding energy. The effect of testing parameters and trap parameters on the validity of Kissinger's theory was also discussed.

Improving heat extraction performance of an enhanced geothermal system utilizing cryogenic fracturing

Engineered fractures play an important role in improving heat extraction performance of Enhanced Geothermal Systems (EGS). It is possible to create these engineered fractures with cryogenic fracturing technology. Cryogenic liquid nitrogen could be used as a stimulation fluid - causing severe thermal shock. This thermal shock would lead to a well-connected fracture network in a hot, low permeability reservoir. Based on local thermal equilibrium theory, a coupled thermal-hydraulic model has been developed to simulate the heat extraction process in an EGS as a function of different fracture configurations. The proposed model is validated against analytical solutions. Using this validated model, EGS heat extraction is simulated for different stimulation scenarios. The characteristics of the temperature distribution and heat extraction are analyzed and compared for the different stimulation scenarios. The production well temperature and flow rate, as well as the potential power output over a 30 year period are calculated and compared for four scenarios. The results indicate that fracture networks created by cryogenic fracturing could significantly improve the heat extraction performance of an EGS.

Numerical simulation for dendrite growth in directional solidification using LBM-CA (cellular automata) coupled method

To predict the dendrite morphology and microstructure evolution in the solidification of molten metal, numerically, lattice Boltzmann method (LBM) - cellular automata (CA) model has been developed by integrating the LBM to solve the mass transport by diffusion and convection during solidification and the CA to determine the phase transformation with respect to the solid fraction based on the local equilibrium theory. It is successfully validated with analytic solutions such as Lipton-Glicksman-Kurz (LGK) model in static melt, and Oseen-Ivantsov solution under the fluid flow conditions in terms of tip radius and velocity of the dendrite growth. The proposed LBM-CA model does not only describe different types of dendrite formations with respect to various solidification conditions such as temperature gradient and growth rate, but also predict the primary dendrite arm spacing (PDAS) and the secondary dendrite arm spacing (SDAS), quantitatively, in directional solidification (DS) experiment with Ni-based superalloy.

Effect of reservoir’s permeability and porosity on the performance of cellular development model for enhanced geothermal system

A fully coupled thermo-hydro-mechanical cellular development model is established to simulate the heat production in the artificial fractured geothermal reservoir. Influences of different coupling models on the evaluation result were investigated. The production performance of the cellular EGS model was studied, such as production temperature, heat extraction ratio, flow impedance and output thermal power. The reliability of the numerical model based on the local thermal equilibrium theory is verified by the Lauwerier’s solution and Bai’s solution from the view of thermal-hydraulic (TH) and thermo-hydro-mechanical (THM). Besides, the degree of grid refinement is deduced by the grid convergence index (GCI) method. The results show that the production capacity can be overestimated by 13.06% when without considering the variation of permeability and porosity of the rock matrix over a 40-years of operation. The anisotropic permeability of thermal reservoir is another important factor that affects the results of assessment. The production temperature of anisotropic model is less than that of isotropic model. Model 2 has a stronger advantage over the traditional doublet system (Model 1). And the high efficiency time of Model 2 account for 46% of the total operation time, which 1.59 times as long as Model 1 and 2 times as long as Model 3. Furthermore, Model 2 is affected greatly by the injection flow rate, elastic modulus and reservoir permeability. When the elastic modulus of thermal reservoir is more than 35 GPa, the performance of cellular development model will be greatly reduced. Model 2 can earn its commendation when H = 340 m, M = 30 kg/s, E = 30 GPa and N = 4. Those results can provide the significant guidance of development plan and coupling methods for enhanced geothermal system.

Design of bypass-simulated moving bed chromatography for reduced purity requirements

Bypass-Simulated moving bed (BP-SMB) chromatography, a process characterized by the possibility of over-purifying the raffinate and/or the extract product followed by blending with the feed, is studied. The BP-SMB provides additional degrees of freedom; the opportunity to increase productivity; increased robustness and operational flexibility compared to obtaining reduced purities directly from the SMB. Based on the local-equilibrium theory, explicit equations to calculate productivity are derived for systems following a linear isotherm based on the minimum switch time. It is shown that the BP-SMB offers productivity advantage compared to a reduced-purity SMB specifically at low purity requirements, high selectivity and high efficiency conditions. The effect of column efficiency and feed concentration for systems following non-linear isotherms are studied using numerical simulations. The production of high-fructose corn syrup, an industrial application of BP-SMB, is analysed. For the HFCS separation, it is shown that a BP-SMB operation while not providing any advantages in terms of productivity, provides operational flexibility and robustness.

Theory of dissolution and precipitation waves—redux

AbstractWe present a local equilibrium theory for the reactive transport of two salts that share an anion in an ideal solution. We revisit this classic problem using the theory of hyperbolic partial differential equations accounting for the volume of precipitates. We construct analytical solutions for the 2 × 2 system of conservation laws in the absence of hydrodynamic dispersion. The character of the system depends on the saturation of the salts, that is, whether the fluid is saturated with both, either of the two or none of the salts. We provide a comprehensive analysis of the system and its solution. Each primitive variable, the amount of precipitate and the concentration of ions, remains constant along one class of waves that propagate in the system. The analysis of the system allows identification of seven bifurcations with respect to the intermediate state.

Gradient elution behavior of proteins in hydrophobic interaction chromatography with U-shaped retention factor curves

Protein retention in hydrophobic interaction chromatography is described by the solvophobic theory as a function of the kosmostropic salt concentration. In general, an increase in salt concentration drives protein partitioning to the hydrophobic surface while a decrease reduces it. In some cases, however, protein retention also increases at low salt concentrations resulting in a U-shaped retention factor curve. During gradient elution the salt concentration is gradually decreased from a high value thereby reducing the retention factor and increasing the protein chromatographic velocity. For these conditions, a steep gradient can overtake the protein in the column, causing it to rebind. Two dynamic models, one based on the local equilibrium theory and the other based on the linear driving force approximation, are presented. We show that the normalized gradient slope determines whether the protein elutes in the gradient, partially elutes, or is trapped in the column. Experimental results are presented for two different monoclonal antibodies and for lysozyme on Capto Phenyl (High Sub) resin. One of the mAbs and lysozyme exhibit U-shaped retention factor curves and for each, we determine the critical gradient slope beyond which 100% recovery is no longer possible. Elution with a reverse gradient is also demonstrated at low salt concentrations for these proteins. Understanding this behavior has implications in the design of gradient elution since the gradient slope impacts protein recovery.

Local equilibrium theory analysis of chromatographic peak shapes in the presence of adsorbing modifiers

The nature and shapes of solute and modifier peaks for a situation when the modifier and solute adsorb competitively through the Langmuir isotherm is studied using the local-equilibrium theory. The analysis yields 10 different cases depending on the relative adsorption strengths and the concentrations of the modifier and the solute. The origin of positive and negative Langmuirian/anti-Langmuirian-type peaks, even when the adsorption isotherms are strictly Langmuirian, and explicit conditions under which each combination is observed are derived. A fundamental explanation to the origin and propagation of rounded peaks reported in liquid and supercritical fluid chromatography [1–3] is offered. A rigorous theoretical basis for the rule of thumb proposed by Fornstedt and Guiochon [1,2] about the nature of peak shapes when an adsorbing modifier is present, is established.

Adsorption equilibrium of benzaldehyde and benzyl alcohol onto polymeric resin from supercritical CO2

A frontal chromatographic technique was used to measure the adsorption isotherms of benzaldehyde and benzyl alcohol onto a polymeric resin in supercritical CO2 (scCO2). The effect of temperature and pressure (density) on adsorption behavior was investigated. It was observed that benzyl alcohol has stronger adsorption than benzaldehyde. The desorption of benzaldehyde using scCO2 from the polymeric resin adsorbent was studied under the same temperature and pressure ranges. The local equilibrium theory was found to reasonably predict the desorption profiles. A phenomenological statistical thermodynamic model combined with classic Peng–Robinson equations of state was used to correlate the adsorption equilibrium isotherms of the solutes from scCO2. This theoretical model with three parameters is able to describe the adsorption behavior over wide temperature and pressure ranges.

Thermocline characteristics of molten-salt thermal energy storage in porous packed-bed tank

Based on the local thermal equilibrium theory in porous media, a two-dimensional numerical model is developed to investigate the heat storage and heat release processes of a molten-salt thermocline in a porous packed-bed tank. The numerical model is validated by comparing the simulation results with the experimental data. The performance of the heat storage system is analyzed using the thermocline thickness and the heat storage efficiency with a focus on energy balance. The results show that stable thermocline layers can form during heat storage or heat release processes. Because of the existence of the thermocline and replaced porous fillers, the heat storage efficiency in a porous packed-bed tank is slightly lower than that of pure molten-salt thermocline heat storage. The volumetric heat capacity of porous media is a key factor in heat storage performance. Improving the performance of the porous filler and setting the condition of a reasonably low flow rate, it can enable optimization control of the thermocline evolution in heat storage/release processes and improve the thermal efficiency of the heat storage system, which reveals directions for further research.

The effect of three-dimensional fields on bounce averaged particle drifts in a tokamak

The impact of applied 3D magnetic fields on the bounce-averaged precessional drifts in a tokamak plasma are calculated. Local 3D MHD equilibrium theory is used to construct solutions to the equilibrium equations in the vicinity of a magnetic surface for a large aspect ratio circular tokamak perturbed by applied 3D fields. Due to modulations of the local shear caused by near-resonant Pfirsch-Schlüter currents, relatively weak applied 3D fields can have a large effect on trapped particle precessional drifts.

A model for microinstability destabilization and enhanced transport in the presence of shielded 3D magnetic perturbations

A mechanism is presented that suggests shielded 3D magnetic perturbations can destabilize microinstabilities and enhance the associated anomalous transport. Using local 3D equilibrium theory, shaped tokamak equilibria with small 3D deformations are constructed. In the vicinity of rational magnetic surfaces, the infinite-n ideal MHD ballooning stability boundary is strongly perturbed by the 3D modulations of the local magnetic shear associated with the presence of near-resonant Pfirsch–Schlüter currents. These currents are driven by 3D components of the magnetic field spectrum even when there is no resonant radial component. The infinite-n ideal ballooning stability boundary is often used as a proxy for the onset of virulent kinetic ballooning modes and associated stiff transport. These results suggest that the achievable pressure gradient may be lowered in the vicinity of low order rational surfaces when 3D magnetic perturbations are applied. This mechanism may provide an explanation for the observed reduction in the peak pressure gradient at the top of the edge pedestal during experiments where edge localized modes have been completely suppressed by applied 3D magnetic fields.

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

Mesoscopic transport equations and contemporary thermodynamics: an introduction

The local equilibrium hypothesis is a very successful basis for non-equilibrium thermodynamics over a wide range of phenomena and physical situations. However, the increasing interest in small systems in nanotechnology, in rarefied gases in high-altitude aeronautics, in high-frequency behaviour in information processing, or the search for new materials with sophisticated internal microstructures and tailored thermal properties have led one to ask about the limits of validity of this hypothesis, and to go beyond it. Here we do so in a constructive way, i.e. not only pointing out at these limits, but also embedding the local-equilibrium theory in a more general framework which explicitly exhibits these limits and suggests how to go beyond them, in search for a wider range of applications and a deeper understanding of the foundations.

Dispersive transport in porous media with biofilms: local mass equilibrium in simple unit cells

In this work, we continue our study of upscaling biofilm processes in porous media from the pore scale to the Darcy scale. We adopt a continuum-level description of biofilms at the pore scale on the basis of work reported in Wood et al. (2002b). We upscale from the pore scale to the Darcy scale using the method of volume averaging and we predict the effective dispersion tensor with two- and three-dimensional closure problems. Our results indicate that, for a one-equation local mass equilibrium theory, the primary influence of the biofilm is that the effective diffusion coefficient is smaller than it would be without the presence of biofilm. This effect is important primarily at low Peclet numbers.

Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm. 2. Wave Interactions and Chromatographic Cycle

The generalized Langmuir isotherm model was recently developed to describe the competitive adsorption equilibria of a binary mixture [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This formalism captures the competitive effect of solutes that show either Langmuirian or anti-Langmuirian behavior. This results in four isotherm types that show markedly different chromatographic behavior. The equilibrium theory of chromatography was developed in a previous work to study Riemann problems (saturation, elution, and the chromatographic cycle) that are of practical relevance [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This work focuses on the development of the equilibrium theory to account for wave interactions and is divided into two parts. In the first part, the theory of wave interactions is developed on the basis of the method of characteristics. It is shown that the rules developed for competitive Langmuir isotherms can be extended to describe possible wave interactions in the case of ...

Influence of austenite deformation on ferrite growth in a Fe–C–Mn alloy

The kinetics of ferrite transformation in a Fe–0.2C–2Mn (mass%) alloy after deformation in undercooled austenite region were studied with regard to alloying element-partitioned and partitionless growth. According to the local equilibrium theory of diffusion-controlled growth, partitioned growth controlled by slow Mn diffusion occurs at a low undercooling, whereas partitionless growth at a larger undercooling is the much faster process, which is controlled by carbon diffusion. The alloy with or without deformation was isothermally reacted at temperatures that encompass the two growth modes. The ferrite growth rate at each temperature increases by austenite deformation. The acceleration at higher temperatures is more significant, probably due to the larger contribution of stored deformation energy in the total driving force for ferrite transformation. The transition temperature from partitionless to partitioned growth of ferrite as well as Ae 3 temperature increases after austenite deformation, resulting in acceleration of ferrite growth rates between the previous and new transition temperatures by 1–2 orders of magnitude.