Effect Of Heat Conduction Research Articles

Numerical simulation of heat transfer for Al-Si@Al2O3 composite phase change heat storage particles

Composite phase change heat storage particles (CPCHSPs) parpered using metals and alloys with excellent thermal properties can be used in different fields such as solar thermal energy management, industrial waste heat recovery. Acquiring their heat transfer behavior in the thermal cycle process is the necessary for their utilization. Previous studies have focused mainly on low-temperature phase change heat storage materials, and the effect of thermal radiation has not been considered in their mathematical models. In this study, the combined effect of heat conduction, convective heat transfer, and thermal radiation was considered to simulate the heat transfer behavior during the melting/solidification of a CPCHSP. To ensure accurate simulations, a suitable value of the mushy zone parameter was selected (Amush = 107), and the results were verified experimentally. The results showed that when the thermal conductivity of the PCM remained lower than 20 W·m−1·K−1, the effect of radiation on the thermal storage time was greater than 10%. In the thermal cycle process, the Al-Si alloy melts from the bottom and moves upwards along the inner wall till completely melts, and then solidifies to form a “V” shape. An unstable position of the instant maximum value was observed during the melting/solidification process, and the overall maximum static pressure (Pmax, t) reached a peak value of 23 MPa after the Al-Si alloy had melted completely. Based on the Pmax, t observed, an air volume fraction of 18% is recommended in the optimized structural design of the CPCHSPs to maintain a low overall maximum static pressure for high heat storage.

Investigation on Silver Modification of Different Shaped Filler on the Heat Conduction Performance Improvement for Silicone Elastomer

The continuous miniaturization and multi-function of electronic devices have put forward high requirements for the effective removal of the heat generated in the system. Developing thermally conductive polymer composite-based thermal interface materials is becoming the research hotspot. In addition to the usually concerned intrinsic thermal conductivity of the filler itself, surface modification is one of the important ways to form an effective heat conduction pathway and improve the overall thermal conductivity of materials. In this work, we used silicon rubber as the polymer matrix and achieved the thermal conductivity increment via various fillers with different shapes. The adopted fillers are spherical aluminum oxide (Al2O3), linear carbon fiber and boron nitride sheets, which can be considered as zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D) fillers respectively. We also prepared the silver-modified fillers and investigated the influence on the formation of heat conduction pathways and interfacial thermal resistance of different shaped fillers. An obvious increment in thermal conductivity of the composite with silver-modified fillers was observed compared to the composite with pristine fillers. Furthermore, through the practical thermal management performance investigation, we found the thermal conductivity increment did improve the actual heat transfer performance of composite elastomers functioning as thermal interface materials

Development and validation of a thermal simulation for the Czochralski crystal growth process using model experiments

The Czochralski (CZ) process is one of the most important techniques for the production of bulk single crystals. Various numerical models for CZ growth furnaces exist, however, a review of the recent literature demonstrates that their validation is often questionable due to missing in-situ measurement data. In this work, a new 2D open-source thermal CZ growth model is introduced, verified with analytical solutions, and validated using dedicated model experiments with tin and hence easy access for the required measurements. A three-step procedure is applied to identify critical modeling parameters, make adjustments of these parameters, and evaluate the resulting modeling accuracy. Gas and melt convection, modeled with heat transfer coefficients and an effective heat conductivity, are found to be crucial and are adjusted using experimental data. Comparison of measured temperatures in the crucible shows good agreement, with deviations of max. 0.3 / 1.3 K under natural / forced convection. The model is able to predict the influence of crystal pull velocity and melt temperature on crystal diameter qualitatively.

New preparation methods for coated heat exchangers in adsorption refrigeration and heat pumps applications

Adsorption refrigeration systems and heat pumps still possess a relatively reduced market share as compared to the traditional compression systems. Despite having the great advantage of being powered by cheap heat (instead of expensive electric work), the implementation of systems based on adsorption principles remains limited to few specific applications. The main drawback that needs to be solved is their reduced specific power due to the low thermal conductivity and low stability of the adsorbents. The current state of the art of commercial adsorption cooling systems rely on adsorbers based on coated finned heat exchangers to optimize the cooling power. It is a well known result, that the reduction of the thickness of the coating derives in a reduction of the mass transport impedance, and that the increment of the ratio surface to volume of conductive structures increases the power without reducing the efficiency. The metallic fibres used in this work can offer a ratio of specific surface in the range of 2500–50,000 m2/m3.Three methods of preparing very thin but stable salt-hydrate coatings on metallic surfaces, including metallic fibres, for the production of coated heat exchangers with high specific power, are presented for the first time. A surface treatment based on aluminium anodizing was chosen to create a stronger bond between coat and substrate. The microscopic structure of the resulting surface was analysed by Scan Electron Microscopy. To verify the presence of the desired species Attenuated Total Reflectance-Fourier Transformed Infrared and Energy dispersive X-ray spectroscopy were employed in the analysis. Their capacity to form hydrates was verified via simultaneous Thermogravimetric Analysis (TGA)/Differential Thermogravimetry (DTG). Over a mass difference of 0.07 g(water)/g(composite) was detected in the coating of MgSO4, which showed signs of dehydration at temperatures around 60 °C, and repeatability after rehydration. Also positive results were obtained with SrCl2 and ZnSO4 with mass differences around 0.02 g/g below 100 °C. Hydroxyethyl Cellulose was chosen as additive to increase the stability and adherence of the coatings. The adsorption properties of the product were evaluated with simultaneous TGA-DTG, while their adherence was characterized by means of a procedure based on the test described in ISO2409. Coatings of CaCl2 displayed a much improved consistency and adherence, while retaining its adsorption capacity, showing mass differences of around 0.1 g/g at temperatures below 100 °C. Also MgSO4 retains the capacity of forming hydrates, showing a mass difference of more than 0.04 g/g below 100 °C. Finally, coated metallic fibres were investigated. Results show that the effective heat conductivity of a fibre structure coated with Al2(SO4)3 can be up to 4.7 times higher as compared to a block of pure Al2(SO4)3 . The coverage of the pursued coatings was visually investigated and the internal structure was evaluated by microscopic imaging of cross-sections. Coatings of around 50 µm of Al2(SO4)3 were generated, but in general the process requires optimization to achieve a more uniform distribution.

Impact of viscous dissipation on the conjugate heat transfer between the walls of a porous microchannel

In this work, the finite element method was used to study numerically the viscous dissipation that occurs when a Newtonian fluid circulates through a porous microchannel that operates as a heat sink, in which a constant heat flux is applied from the outer walls of the porous microchannel into the fluid. Taking into account that this is a conjugate problem, where the temperature fields of both the porous medium and the wall are unknown, there are two well-known asymptotic limits in the literature that allow us to obtain the solution for this problem: the first one is the thermally thick wall limit , which has been widely studied previously by other authors; the second one is the thermally thin wall limit , where the longitudinal effects of heat conduction in the microchannel wall are considerably more important than the ones occurring in the transverse direction. Therefore, in this study, we analyze the competition between these effects and viscous dissipation, as well as the influence that both have on the temperature profiles of the fluid and the wall. The results show that for Br ≥ 0.1, a notable temperature increase occurs in the system, which offers interesting results that have not been reported in the literature yet, because from χ = 0.6 (Br = 0.1), there is a higher temperature in the center of the microchannel than in the vicinity of the wall; that is, the fluid temperature is higher at η = 0 with respect to the temperature value at η = 1. This situation becomes more evident as the Brinkman number increases; for example, for Br = 1, the temperature in the center of the microchannel increases up to 23% with respect to the fluid temperature at the wall. Finally, the decrease of the Darcy number does not have a considerable effect on the temperature profiles.

Investigation of concurrent multiscale topology optimization for designing lightweight macrostructure with high thermal conductivity

Lightweight and high heat conductive solid structures are playing important role in various fields of engineering. To maximize the design performance for such structures, we investigated multiscale topology optimization for excessive lightweight heat-conductive porous structures and introduced a mathematical optimization model formulation for concurrently optimizing the structures (macrostructure) and the constitutive pores (microstructure). The microscale is considered a representative volume element and designed using the asymptotic homogenization method. For each iteration, the effective heat conductivity tensor of the microstructure is evaluated during the optimization process and used as the heat conductivity of the macrostructure. Sensitivity analysis on this concurrent optimization scheme was derived to address the macro and microstructure coupling. To broaden the scope of the research applicability, three topology optimization methods, i.e., SIMP, level set and ESO are investigated, and the results are compared and discussed. The suggested formulations showed a successful application of the concurrent multiscale optimization formulations and good coupling on the macro and microscale. Also, the formulations demonstrated a strong influence between the macro and the microscale of the design problem for the topology optimization methods. Increasing the design freedom by introducing various microstructures for the macro design domain showed superior performance associated with attaining high weight reduction. In addition, the concurrent optimization scheme has enabled the microstructures to attain a good spatial layout of materials while taking into account the weight reduction constraint. The spatial arrangements of the designed microstructures have achieved conducting heat in a shorter path toward the heatsink zone of macrostructure design. This allows attaining good performance with high weight reduction. Furthermore, numerical examples of different mesh numbers were used to study mesh dependency of multiscale topology optimization. The scope of the study was broadened by the inclusion of 3D case studies. Implementing Isosurface technique to achieve high detail model was also used to attain high detailed concurrently optimized design with minimal mesh number to minimize the computational cost. The 3D optimized case was investigated experimentally.

On the Lie symmetries of characteristic function hierarchy in compressible turbulence

We compute the Lie symmetries of characteristic function (CF) hierarchy of compressible turbulence, ignoring the effects of viscosity and heat conductivity. In the probability density function (PDF) hierarchy, a typical non-local nature is observed, which is naturally eliminated in the CF hierarchy. We observe that the CF hierarchy retains all the symmetries satisfied by compressible Euler equations. Broadly speaking, four types of symmetries can be discerned in the CF hierarchy: (i) symmetries corresponding to coordinate system invariance, (ii) scaling/dilation groups, (iii) projective groups and (iv) statistical symmetries, where the latter define measures of intermittency and non-gaussianity. As the multi-point CFs need to satisfy additional constraints such as the reduction condition, the projective symmetries are only valid for monatomic gases, that is, the specific heat ratio, $\gamma = 5/3$ . The linearity of the CF hierarchy results in the statistical symmetries due to the superposition principle. For all of the symmetries, the global transformations of the CF and various key compressible statistics are also presented.

Temperature Transient Analysis of Naturally Fractured Geothermal Reservoirs

Summary A potential approach to develop geothermal energy is by producing low-to-medium temperature fluids from naturally fractured geothermal reservoirs (NFGRs). Pressure transient analysis (PTA) is the most common approach to characterize such reservoirs for improving development efficiency. However, pressure inversion leads to nonuniqueness and cannot be used to estimate thermal properties. Moreover, reliable methods to evaluate the development potential of fractured geothermal reservoirs are lacking. To address the gap, this work aims to study the temperature behavior and explore a suitable analysis method for characterizing geothermal reservoirs and evaluating development potential. We developed numerical and analytical models to analyze the temperature behavior in NFGRs. The developed models account for the Joule-Thomson [J-T effect (μJT)], adiabatic heat expansion/compression effect (ζ), reservoir formation damage, heat conduction, and convection effects. The developed numerical solution is verified and found to agree with the proposed analytical solutions. The results show that temperature transient analysis (TTA) with constant or temperature-dependent μJT and ζ assumption leads to a minor difference when reservoir temperature changes significantly. Moreover, three heat radial flow regimes (HRFR) and a thermal interporosity regime with a V-shape characteristic have been identified. The results also show that temperature data provide information not accessible by PTA. The results reveal that temperature derivative curves signify a “hump” when formation around a wellbore is damaged, and the temperature data can be used to characterize the skin-zone radius and permeability. It is demonstrated that the properties such as J-T coefficient, effective adiabatic heat expansion coefficient, and fracture intrinsic porosity can be estimated using TTA. The results indicate that fracture thermal storativity (ωT) and matrix thermal interporosity coefficient (αT) can be estimated from the thermal interporosity regime exhibited on the temperature derivative curve. The results also suggest that commercial geothermal energy harness is more difficult when the ωT is high or the αT is very small. Finally, we introduced an integrated workflow of combining PTA and TTA to characterize NFGRs. Simulated test examples are interpreted to demonstrate the applicability of the developed workflow. This work aids in better understanding the potentials of temperature data on geothermal reservoir characterization.

Simultaneously developing flow and heat transfer in circular and parallel-plates microchannels with velocity slip and temperature jump

The entrance effect has an important influence on the heat transfer characteristics in microchannels. It is necessary to determine the influence to design microchannel heat sinks properly. In this work, the simultaneously developing flow and convective heat transfer were investigated numerically inside circular and parallel-plates microchannels. The effects of the Knudsen number (0–0.1) and Peclet number (25–1000) on the local Nusselt number were taken into consideration in the slip flow regime. The numerical results were calculated via an incompressible and steady computational fluid dynamics algorithm under the boundary conditions of the velocity slip and temperature jump. The user-defined functions were used to achieve the velocity slip boundary condition, and a thermal resistance model was first proposed to easily impose the temperature jump boundary condition. The numerical approach was verified using both the analytic solutions of the thermally developing flow and the exact solutions of the fully developed flow, which was then employed to obtain the influences of the axial heat conduction and the rarefaction on the local Nusselt number of the simultaneously developing flow. The results of the apparent friction factor and the heat transfer coefficient were graphically presented as functions of the Knudsen number, Reynolds number or Peclet number, and non-dimensional axial length. It was found that the effect of the axial heat conduction on the entrance effect can be ignored when Pe > 500. The heat transfer performance of the simultaneously developing flow can be predicted by the results of the thermally developing flow when the Knudsen number is large enough. General correlations were also proposed for the apparent friction coefficients, local Nusselt number in circular and parallel-plates microchannels.

Wearable Thermoelectric Cooler Based on a Two-Layer Hydrogel/Nickel Foam Heatsink with Two-Axis Flexibility.

A wearable thermoelectric cooler (w-TEC) shows promising prospects in personal thermal management due to its zero emission, high efficiency, lightweight, and long-term stability. The flexible heatsinks are able to promote the cooling effect of coolers, but the cooling capacity of current coolers still has much room for improvement because of the relatively large thermal resistance between the cooler and heatsink. In this work, the two-layer heatsink units composed of hydrogel and nickel foam are fabricated and attached to a thermoelectric cooler via the thermal silica gel. Thanks to the high thermal conductivity of nickel foam and a tight bond between the hydrogel and nickel foam, effective heat conduction from the cooler to the body of the heatsink was achieved. In addition, the discrete heatsink units endow the w-TEC with excellent flexibility. The bending radius of this w-TEC is as small as 7.5 mm, and a long-term temperature reduction of ∼10 °C can be realized at an input current of 0.3 A for a flat or bent w-TEC. In the on-body testing, a stable temperature reduction of 7 °C can be obtained using an AA battery with an input voltage of 1.5 V.

Approximate structures of thermoelastic fields induced by a penny-shaped thermal-medium crack in a transversely isotropic layer

It is of practical significance to investigate thermoelastic fields at the front of a penny-shaped crack embedded in a material with finite thickness. The existing works always focus on numerical solutions of the derived integral equations and approximate solutions are seldom studied. In the present study, the problem of a penny-shaped crack in a transversely isotropic layer is addressed under uniform heat flow and mechanical loadings. The extended thermal-medium crack model with a nonlinear relation between heat flow of crack interior and crack opening displacement is used to capture the effect of heat conduction inside crack. The Hankel transform technique is applied to solve governing partial differential equations, then Fredholm integral equations of the second kind are derived. Applying integral kernel series expansion method, approximate solutions to the derived Fredholm integral equations are analyzed and determined. Approximate structures of thermoelastic fields around penny-shaped crack are further obtained. Theoretical analysis and numerical results are carried out to show the applicability of approximate solutions. The observations reveal that the determined approximate solutions have some significance to a practical engineering application. The advantages of the developed methods are to make approximate solutions visible, and some penny-shaped crack problems of thermo-piezoelectric and thermo-magnetoelectroelastic layers could be solved similarly.

Assessment of the impact of the kinetic effect of ion parallel heat conduction on DEMO-relevant SOL plasma using integrated SOL-divertor code SONIC

In plasmas of lower collisionality, such as the scrape-off layer (SOL) of a fusion tokamak device, the parallel heat conductivity of ions becomes smaller than the classical Spitzer–Harm model due to a nonlocal kinetic effect. We have assessed, by simulation, the impact and role of the kinetic effect of ion heat conductivity (abbreviated as ion KE in this paper) on DEMO-relevant tokamak SOL plasma, using the Japanese demonstration tokamak reactor concept JA DEMO. A series of test simulations, where the ion KE is modeled by a widely used free-streaming energy (FSE)-limited model, has demonstrated: (a) the ion KE decreases the ion parallel heat flux density in JA DEMO SOL (at the baseline operation scenario) around the X-point and further upstream of the low-field side (LFS) area along the separatrix, where the parallel collisionality is smaller. Up to 40%–60% decrease is observed, compared to the case without (w/o) ion KE, among the test cases where the ion KE level is scanned over the possible range (i.e. parameter α i of the FSE-limited model is varied over ); (b) the ion KE leads to significant increase in the ion temperature T i (up to 600% increase) and significant decrease in the ion density n i (up to −80%) over wide area of the SOL upstream. Energy balance analysis has suggested that the ion KE affects the upstream n i and T i by the power of 0.4 and −0.4, respectively, of the flux limiting factor, as long as spatial changes in plasma parameters are moderate. The results of this study serve as a fundamental assessment of the ion KE for DEMO- relevant SOL plasma, clarifying the need for further sophistication of the model toward more quantitative prediction.

Extreme Enhancements of Electron Temperature in Low Latitude Topside Ionosphere During the October 2016 Storm

AbstractWe use the in‐situ observations of DMSP and SWARM satellites to report the changes of the topside ionospheric electron temperature during the October 2016 storm. Electron temperature in the afternoon sector dramatically increases in low latitudes in the recovery phase of the storm. Furthermore, the temperature enhancements have an obvious dependence on longitude and are mainly centralized around 100°–150°E in different satellite observations. The temperature enhancements attain more than 2,000 K at 840 km and 1,500 K at 450 km around the magnetic equator. The decrease in the electron‐ion collision cooling rate, resulting from the lessened topside electron density, could not fully explain the temperature enhancement. At the same time, the electron densities in crests of the equatorial ionization anomaly are suppressed drastically at 100°–150°E, which cause a less heat conduction effect from the equatorial topside ionosphere to low altitudes via magnetic field lines and heat the topside ionospheric electron temperature. Further analysis indicates that dayside westward disturbance dynamo electric field presents a significant longitude structure and is a primary driver for the topside ionospheric temperature enhancement during the storm.

Enhancing hydrovoltaic power generation through heat conduction effects

Restricted ambient temperature and slow heat replenishment in the phase transition of water molecules severely limit the performance of the evaporation-induced hydrovoltaic generators. Here we demonstrate a heat conduction effect enhanced hydrovoltaic power generator by integrating a flexible ionic thermoelectric gelatin material with a porous dual-size Al2O3 hydrovoltaic generator. In the hybrid heat conduction effect enhanced hydrovoltaic power generator, the ionic thermoelectric gelatin material can effectively improve the heat conduction between hydrovoltaic generator and near environment, thus increasing the water evaporation rate to improve the output voltage. Synergistically, hydrovoltaic generator part with continuous water evaporation can induce a constant temperature difference for the thermoelectric generator. Moreover, the system can efficiently achieve solar-to-thermal conversion to raise the temperature difference, accompanied by a stable open circuit voltage of 6.4 V for the hydrovoltaic generator module, the highest value yet.

A novel design of discrete heat and cold sources for improving the thermal performance of latent heat thermal energy storage unit

The low thermal conductivity of phase change materials (PCMs) severely limits the operating efficiency and flexibility of the latent heat thermal energy storage (LHTES) unit. In this study, a novel LHTES unit with discrete heat and cold sources was proposed and investigated numerically, including symmetrical and staggered arrangements with side-heat and bottom-heated LHTES units. The consecutive and simultaneous heat storage and release processes of the seven developed models were comprehensively considered and compared for the first time. The results show that with the discrete arrangement of source, the additional heat conduction effect and natural convection in the side-heated LHTES unit would be significantly improved. More importantly, the heat storage and release cycle of the side-heated and symmetrical arrangement was shortened by 49.9%, the steady-state time was advanced by 46.6%, the steady-state liquid fraction was increased by 4.2%, and the heat transfer rate was increased by 22.3%. The discrete source arrangement had no obvious improvement on the performance of the bottom-heated LHTES unit. In addition, energy analysis showed that the side-heated LHTES unit stored more sensible heat. The discrete heat and cold sources effectively improved the thermal performance and flexibility of the LHTES unit.

Influence of gas axial conduction enhancement factor on the oscillating flow behavior of an inertance pulse tube cryocooler

Most one-dimensional simulation models developed so far to estimate the theoretical performance of pulse tube cryocoolers ignore the effect of heat loss arising out of thermal dispersion in porous media and turbulent conduction in pipes. In this paper one-dimensional numerical simulation of an inertance type pulse tube cryocooler has been carried out to illustrate the effect of thermal dispersion and turbulent conduction on the oscillating gas flow and heat transfer behavior. The study has been conducted under three conditions: simulation of cryocooler without considering gas axial heat conduction effects, simulation of cryocooler with gas axial heat conduction but neglecting the influence of thermal dispersion and turbulent conduction, and simulation of the cryocooler with gas axial heat conduction including the influence of thermal dispersion and turbulent conduction. The effect of thermal dispersion and turbulent conduction in the gas phase has been expressed in terms of an axial-conduction-enhancement-factor in the gas energy equation. It is revealed that the inclusion of axial-conduction enhancement factor in the porous media and tubes of the pulse tube cryocooler creates a positive phase shift in all oscillating physical quantities. This phase change causes an adverse effect on the cooling mechanism of the pulse tube cryocooler. It is found that, the coefficient of performance decreases by 8.6% and the minimum cooling temperature increases by 6.67% when the axial-conduction enhancement factor is included in the one-dimensional simulation model.

A Three-Dimensional Homogenization Approach for Effective Heat Transport in Thin Porous Media

Heat transport through a porous medium depends on the local pore geometry and on the heat conductivities of the solid and the saturating fluid. Through upscaling using formal homogenization, the local pore geometry can be accounted for to derive effective heat conductivities to be used at the Darcy scale. We here consider thin porous media, where not only the local pore geometry plays a role for determining the effective heat conductivity, but also the boundary conditions applied at the top and the bottom of the porous medium. Assuming scale separation and using two-scale asymptotic expansions, we derive cell problems determining the effective heat conductivity, which incorporates also the effect of the boundary conditions. Through solving the cell problems, we show how the local grain shape, and in particular its surface area at the top and bottom boundary, affects the effective heat conductivity through the thin porous medium.

Nonlocal dual-phase-lag thermoelastic dissipation of size-dependent micro/nano-ring resonators

The modeling of thermoelastic damping or dissipation (TED) is significant but challenging for the quality-factor estimation of the size-dependent micro/nano-resonator operating in some extreme situations, such as the ultra-instantaneous thermal heating and ultra-high frequency excitation. Considering these special situations, this study intends to explore the more generalized TED mechanism for the micro/nano-ring resonator with the size-dependent effect and non-Fourier heat conduction effect. In this work, one/two-dimensional (1D/2D) TED models of rings are firstly developed by adopting the nonlocal dual-phase-lag (DPL) model and the modified-couple-stress (MCS) model. In detail, the size-dependent effects both in the elastic and thermal fields are respectively characterized by the length-scale parameters lQ and lM, while the effect of non-Fourier heat conduction is characterized by DPL times τQ and τT. In simulations, two typical materials involving silicon and gold popularly manufactured in micro/nano-devices are selected, and the results obtained by previous models are shown for comparison. Firstly, the fluctuation temperature and TED spectra under the MCS size-dependent and nonlocal-DPL effects are investigated. Secondly, the peak phenomenon of TED spectra is analyzed, then the equivalent relaxation times for the 1D case are discussed according to the peak-frequency calculation. Results demonstrate that the MCS size-dependent effect can slightly improve the quality factor of the ring by weakening TED, but its existence should be recognized. Meanwhile, thermal behaviors of solid resonators at micro/nano-scales are jointly affected by the amount relationship of τ1, τQ, τT, and τl. When the characteristic dimension of the resonator is in the level of lQ referring to the mean-free path of energy carries, the nonlocal size-dependent effect is necessary to be considered.

COUPLING A GEOMECHANICAL RESERVOIR AND FRACTURING SIMULATOR WITH A WELLBORE MODEL FOR HORIZONTAL INJECTION WELLS

Reservoir cooling during waterflooding or waste-water injection results in thermo-poro-elastic stresses that can significantly alter the reservoir stress tensor field. In addition, colloidal particles in the injected water can filter on the borehole and fracture surfaces resulting in matrix permeability reduction. Fractures are likely to initiate and propagate from injectors because of these thermal and filtration effects. These fractures are of great concern for both environmental reasons and their strong influence on reservoir sweep and oil recovery. In this paper, a fully coupled reservoir-fracture-wellbore model was developed. Fluid flow, solid mechanics, energy balance, fracture initiation and propagation, and particle filtration are modeled in the reservoir, fracture, and wellbore domains. The coupled non-linear systems of equations are solved implicitly using the Newton-Raphson method. Simulation results show that water quality and thermal effects control fluid leak-off and fracture growth. While it is difficult to predict the exact location of fracture initiation due to reservoir heterogeneity, we propose a reasonable method to handle fracture initiation and growth without a predefined fracture location. In open-hole completions, "thief" fractures may propagate deep into the reservoir. Thermal stress changes in the injection zone are shown to be significant because of the combined effects of forced convection, heat conduction, and poro-elasticity. Accurate predictions of thermal stress in different reservoir layers allow us to conduct numerical studies on fracture height growth and containment. We show that controlling the injection water temperature and the water quality are an effective way to ensure fracture containment.

Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids

A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l. This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-Herbst-Prüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic.