Fractal analysis for heat extraction in geothermal system

Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection

Analytical solution for thermal-diffusion induced stress model and numerical simulation of battery structure during charging-discharging process

During the course of thousands of charging and discharging cycles, batteries commonly undergo capacity fade and resistance growth, known as electrode aging. This phenomenon is attributed to local inhomogeneous deformation, as well as the possibility of fracture within electrode particles due to complex multi-physical couplings. To mitigate electrode aging and slow down the rate of fading, it is crucial to develop protective designs and tailored battery management strategies. However, accurately predicting potential fracturing and conducting precise battery simulations remain open challenges. This study presents a battery aging simulation model that incorporates multiphysical couplings of heat, concentration, stress, electric, and phase fields to assess battery performance at both the structural and electrode particle levels. Initially, an analytical solution is derived to determine stress distribution at the particle level within the thermal-concentration-mechanical deformation coupling, enabling quick calculation of stress distribution. Subsequently, a comprehensive battery structure is constructed to simulate discharge performance. Furthermore, the model computes the stress levels and fracture potential of the electrodes, thereby identifying locations prone to aging. Analytical and numerical findings indicate that tensile stress on the surface of an individual electrode acts as the driving force for fracture during lithium intercalation. Moreover, electrodes in close proximity to the electrolyte generate higher heat, while those near the electrode current collector are more susceptible to fracturing

Iterative Analytical Solutions for Nonlinear Two-Phase Flow with Gas Solubility in Shale Gas Reservoirs

The governing equations of a two-phase flow have a strong nonlinear term due to the interactions between gas and water such as capillary pressure, water saturation, and gas solubility. This nonlinearity is usually ignored or approximated in order to obtain analytical solutions. The impact of such ignorance on the accuracy of solutions has not been clear so far. This study seeks analytical solutions without ignoring this nonlinear term. Firstly, a nonlinear mathematical model is developed for the two-phase flow of gas and water during shale gas production. This model also considers the effects of gas solubility in water. Then, iterative analytical solutions for pore pressures and production rates of gas and water are derived by the combination of travelling wave and variational iteration methods. Thirdly, the convergence and accuracy of the solutions are checked through history matching of two sets of gas production data: a China shale gas reservoir and a horizontal Barnett shale well. Finally, the effects of the nonlinear term, shale gas solubility, and entry capillary pressure on the shale gas production rate are investigated. It is found that these iterative analytical solutions can be convergent within 2-3 iterations. The solutions can well describe the production rates of both gas and water. The nonlinear term can significantly affect the forecast of shale gas production in both the short term and the long term. Entry capillary pressure and shale gas solubility in water can also affect shale gas production rates of shale gas and water. These analytical solutions can be used for the fast calculation of the production rates of both shale gas and water in the two-phase flow stage

A Thermal-Hydrological-Mechanical-Chemical Coupled Mathematical Model for Underground Coal Gasification with Random Fractures

In this paper, in order to understand the development process and influencing factors of coal underground gasification, taking the two-dimensional underground gasification area of the plane as the simulation object, the characteristics of the multi-physical field coupling process of exudate mass heat transfer and combustion gasification reaction in the process of horizontal coal seam underground gasification are analyzed, and a two-dimensional mathematical model of thermal-hydrological-mechanical-chemical coupling of a porous medium is established. The temperature distribution of coal rock from the gasification point, the distribution of gas water vapor pressure and stress-strain, the temperature contour distribution of fractured coal rocks of different densities of heterogeneity, and the influence of different water-oxygen ratios and different fractured coal rocks on the gas components generated by the gasification reaction were studied. The results show that the tensile damage caused by the tensile strain volume expansion of the coal underground gasification center, the shear damage caused by the compression of the edge compressive strain volume, and the temperature conduction rate decrease with the increase in the coal rock fracture, but in the heterogeneous coal rock, the greater the fracture density, the faster the temperature conduction rate, which has a certain impact on the gasification combustion reaction. The ratio of CO2, H2 and CO in the case of simulating that the water-to-oxygen ratio is 1:2, 1:1, and 2:1 is 1:0.85:0.73, 1:1.1:0.97, and 1:1.76:1.33, respectively. At a water-oxygen ratio of 2:1, the concentration ratio is the most ideal, and the main gases, CO, CO2, and H2, are 32%, 21%, and 37%. Furthermore, the reaction rate increases with the increase of fracture density. The gas component concentration simulated in this paper has good consistency with the results of the previous experimental data, which has important guiding significance for the underground coal gasification project

A Thermal-Hydraulic-Gas-Mechanical Coupling Model on Permeability Enhancement in Heterogeneous Shale Volume Fracturing

Heat treatment on shale reservoirs can promote the development of secondary fractures in a matrix on the basis of hydraulic fracturing, forming multi-scale gas–water seepage channels and strengthening the gas desorption. Experimental evidence shows that heat treatment can enhance gas recovery in the same mining life. Heat treatment on a shale gas reservoir is a multi-physical and multi-phase coupling process. However, how the thermal stimulation interacts with nonlinear two-phase flow in heterogeneous shale volume fracturing has not been clear. In this paper, a fully coupled THGM model for heating-enhanced shale-gas recovery in heterogeneous shale reservoirs is proposed. First, the governing equations are formulated for the shale-reservoir deformation involving both gas adsorption and thermal expansion, the permeability evolution model for the cracking process of fractured shale, the gas–water two-phase continuity equation considering the effects of gas solubility and the heat transfer equation for heat conduction and convection. The interactions among stress, temperature and seepage in a heterogeneous shale reservoir were studied. Secondly, a test on shale permeability after 50 °C temperature treatment was conducted. The evolution of temperature, capillary pressure, water and gas saturation and the permeability of shale during the heat treatment of the reservoir were numerically analyzed. Finally, the gas production from a shale gas reservoir was numerically simulated with this THGM model. The numerical results indicated that the thermal-induced fracturing, gas desorption and separation from water make predominant contributions to the evolution of permeability. The heat treatment can enhance cumulative gas production by 58.7% after 27.4 years of heat injection through promoting gas desorption and matrix diffusion

Peak Force Visible Microscopy for Determination of Exciton Diffusion Length in Organic Photovoltaic Blends

In this article, we developed a new nano spectroscopic technique, peak force visible (PF-vis) microscopy, which is based on the peak force tapping mode in an atomic force microscope to both visualize nanoscale morphology and estimate exciton diffusion lengths of donor domains in organic photovoltaic blends. Nano phase-separations in P3HT:PCBM and TFB:PCBM blend films were clearly revealed by PF-vis microscopy with a high spatial resolution less than 10 nm. A model that correlates PF-vis signal and the exciton diffusion length was also developed to estimate the diffusion lengths of P3HT and TFB to be 2.9±0.3 and 9.0±1.5 nm, respectively. PF-vis microscopy is expected to assist the evaluation of OPV materials, therefore accelerating the pace of innovation of OPVs

Analytical Solutions for Gas-Water Two-Phase Flow in Multiseam Coalbed Methane Production

Multiseam coalbed methane (CBM) exploitation can not only reduce single-well investment but also increase the length of service of the well and significantly enhance the CBM economic recovery of the entire basin. To compare with and further to guide the actual project of CBM production, this study proposed a conceptual gas-water two-phase separate flow model for single coal seam considering the solubility of gas. This mathematical model was solved analytically by separation of variables and verified through history matching of the production data from the No. 3 seam of 1# test well of Jincheng and then applied to investigate the effect of gas solubility on the gas pressure. Furthermore, based on the coupled two-phase separate flow model of single seam, another two-phase separate flow model for the development of multicoal seam development was established. Similarly, the analytical solution of this model for multicoal seam layers was matched with the in situ data of TS-1 well of Liupanshui coal mine. It is found that the height difference and pressure difference between the two seams play key roles in the multiseam CBM development comprehensively

Characteristics of Stress, Crack Evolution, and Energy Conversion of Gas-Containing Coal under Different Gas Pressures

In order to study the meso-mechanism of deformation, crack evolution, and energy conversion of gas-containing coal under loads, considering the gas pressure and adsorption expansion, the gas-solid coupling calculation program of MatDEM software was developed, and the triaxial compression process of gas-containing coal under different gas pressures was numerically simulated. The results show that the strength and stiffness of gas-containing coal decrease with the increase of gas pressure. During the loading process, the permeability of the coal sample decreases first and then increases, while the initial permeability, minimum permeability, and maximum permeability all decrease with the increase of gas pressure. There are far more shear cracks in coal samples than tension cracks, and the number of cracks increases simultaneously with the peak stress drop. With the increase of gas pressure, the macroscopic cracks in coal samples gradually change from large-angle shear cracks to multiple intersecting small-angle ones, and the coal sample gradually changes from brittle failure to ductile. There is an initial accumulation of elastic energy inside the gas-bearing coal, and the dissipated damping heat presents a stage change. As the loading stress level increases, the gas pressure gradually produces a degrading effect. The rockburst tendency of gas-bearing coal changes from weak to none with the increase of gas pressure, which is related to the evolution of the accumulated elastic energy and dissipated damping energy in the coal

Mineral Composition, Pore Structure, and Mechanical Characteristics of Pyroxene Granite Exposed to Heat Treatments

In deep geoengineering, including geothermal development, deep mining, and nuclear waste geological disposal, high temperature significantly affects the mineral properties of rocks, thereby changing their porous and mechanical characteristics. This paper experimentally studied the changes in mineral composition, pore structure, and mechanical characteristics of pyroxene granite heated to high temperature (from 25 °C to 1200 °C). The results concluded that (1) the high-temperature effect can be roughly identified as three stages: 25–500 °C, 500–800 °C, 800–1200 °C. (2) Below 500 °C, the maximum diffracted intensities of the essential minerals are comparatively stable and the porous and mechanical characteristics of granite samples change slightly, mainly due to mineral dehydration and uncoordinated thermal expansion; additionally, the failure mechanism of granite is brittle. (3) In 500–800 °C, the diffraction angles of the minerals become wider, pyroxene and quartz undergo phase transitions, and the difference in thermal expansion among minerals reaches a peak; the rock porosity increases rapidly by 1.95 times, and the newly created pores caused by high heat treatment are mainly medium ones with radii between 1 μm and 10 μm; the P-wave velocity and the elastic modulus decrease by 62.5% and 34.6%, respectively, and the peak strain increases greatly by 105.7%, indicating the failure mode changes from brittle to quasi-brittle. (4) In 800–1200 °C, illite and quartz react chemically to produce mullite and the crystal state of the minerals deteriorate dramatically; the porous and mechanical parameters of granite samples all change significantly and the P-wave, the uniaxial compressive strength (UCS), and the elastic modulus decrease by 81.30%, 81.20%, and 92.52%, while the rock porosity and the shear-slip strain increase by 4.10 times and 11.37 times, respectively; the failure mechanism of granite samples transforms from quasi-brittle to plastic, which also was confirmed with scanning electron microscopy (SEM)