Numerical Heat Transfer Model Research Articles

Simulation Study of Thermal Performance on the Inner and Outer Surfaces of Semi-Transparent Photovoltaic (STPV) Glass with Different Transparency

This paper used the experimentally verified one-dimensional steady-state heat transfer numerical model of the semi-transparent photovoltaic (STPV) glass to simulate the influence of wind speed, ambient temperature and air gap thickness on the surface temperature of PV modules, and analyzed the thermal performance of the inner and outer surfaces of STPV glazing with different transparency. Results shows that for every 1m/s increase in wind speed, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% decreased by 3 °C, 3.02 °C and 2.22 °C, respectively. For every 10 °C increase in ambient temperature, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% increase by 8.45 °C, 7.6 °C, and 7.79 °C, respectively. For the DL-STPV glass with transparency of 20% and 40%, for every 2 mm increase in the thickness of the air gap, the outer surface temperature increases by 0.13 °C and 0.12 °C, respectively. The heat transfer between the inner surface of the glass and the indoor environment increases the heat gain through the glass into the room in summer, which will lead to an increase in refrigeration energy consumption. However, in winter, the heat exchange between the inner surface and the in-door air to heat the indoor air reduces the heating energy consumption to a certain extent, and achieves the effect of building energy conservation to a certain extent.

Evaluation of Heat Transfer and Fluid Dynamics across a Backward Facing Step for Mobile Cooling Applications Utilizing CNT Nanofluid in Laminar Conditions

In a variety of engineering applications, the efficacy of heat dissipation in mobile cooling systems is greatly influenced by the Backward Facing Step. Its significance in optimizing cooling solutions for mobile devices is highlighted by the fact that its design and fluid dynamics are crucial in minimizing skin friction and improving passive heat transfer. In this paper, we present a verification of an advanced numerical model for heat transfer and fluid flow through a Backward Facing Step, used in mobile cooling. The objective of this study is to explore fluid separation, a method enhancing passive heat transfer and reducing skin friction. ANSYS/FLUENT software has been used to solve the backward facing step in a horizontal duct filled with pure water. Carbon nanotube (CNT) dispresed into the base fluid at different volume fractions of 0.2%, 0.65%, and 1%. This study focused on laminar flow conditions ranging from Reynolds numbers 200 to 900. In order to reduce the computation time and ensuring the accuracy and reliability of numerical simulations, a grid independence study has been conducted. The findings revealed a substantial rise in the average Nusselt number and heat transfer coefficient with increased Reynolds number and volume fraction of nanoparticles. Specifically, the nanofluid (CNT/water) exhibited the highest average Nusselt number and heat transfer coefficient with volume fractions 1%. Furthermore, the research showed a decrease in the skin friction factor as both Reynolds number increased and nanoparticles’ volume fraction decreased. The increments of nanoparticles' concentrations lead to increase viscosity, promotes agglomeration, alters flow behaviour by inducing turbulence, and enhances heat transfer. These factors collectively contribute to higher skin friction due to increased resistance to fluid flow and disrupted streamline patterns

Validating ANSYS Heat Transfer Models Using Experimental Data Analysis of Two Phase Change Materials with Differing Melting Temperatures

Phase change materials are becoming more and more popular as viable options for improving the thermal performance and energy efficiency of a variety of applications, especially in innovative building envelope designs. In this paper, experimental data from two different phase change materials with differing melting temperatures (21°C and 28°C) are used to validate numerical system heat transfer models. The experimental setup included a heat flux apparatus, which was utilized to ascertain average temperature and heat flow changes over time during both heating and cooling phases for both phase change materials. The data obtained from the experiments were utilized to generate ANSYS Fluent simulation models replicating the experimental setup. The parameters and boundary conditions for the models can be assigned in several ways within ANSYS Fluent software. Consequently, two simulation models were created: one integrated the thermal and physical properties of the experimental setup's system components, while the other utilized the measured heat-flux values over time from the experiments as an input source for calculating average temperatures within the phase change material. The average temperature data from both simulation and experimental results were compared to validate both ANSYS models. By aligning the simulated results with the experimental data, the accuracy and reliability of the numerical models have been established in predicting the thermal behaviour of the two phase change materials. The two numerical system heat transfer models developed in this study serve as valuable tools for conducting further analysis and optimization of systems based on phase change materials. This research highlights the significance of phase change materials in enhancing the thermal performance of building envelopes, particularly in solar energy applications.

Analysis of the Combined Effect of Major Influencing Parameters for Designing High-Performance Single (sBHE) and Double (dBHE) U-Tube Borehole Heat Exchangers

In this paper, a comprehensive analysis of the combined effect of major influencing parameters on heat transfer in a single U-tube BHE (sBHE) and a double U-tube BHE (dBHE) with two independent circuits was performed by using a validated numerical heat transfer model. Geometrical parameters, such as shank spacing (with maximum, average, and minimum values), borehole diameter (large, medium, and small borehole sizes), and borehole depth (shallow, average, and deep borehole depths) as well as the thermal conductivity of soil and grout, which ranges from minimum to high values, were considered. The combined impact of these parameters was included under the following four major cases: (1) the combined effect of borehole depth, borehole size, and shank spacing; (2) the combined effect of borehole depth and soil and grout thermal conductivity; (3) the combined effect of soil and grout thermal conductivity and borehole size; and (4) the combined effect of soil thermal conductivity, borehole size, and shank spacing. Each of these major cases has nine different design options for both sBHEs and dBHEs. A series of results of heat transfer per unit borehole depth were generated for all the considered various cases. With the given parameters, the BHE case that provides the highest heat transfer among the various cases of sBHEs and dBHEs were obtained.

Assessment of evaporative porous clay cooler for Building-Integrated photovoltaic systems via energy, exergy, economic and environmental approaches

A thorough study has been conducted for the energy, exergy, economic and environmental analysis to investigate the feasibility of utilizing an evaporative porous structure cooler for the building-integrated photovoltaic (BIPV) system at different building’s sides and directions. Photovoltaic panels within the BIPV systems dissipate their heat to the building’s sides which contribute to rise the interior building’s temperature. In the proposed system, a water-saturated evaporative porous clay cooler is being installed on the back surface of the PV panels to absorb and dissipate their heat by latent evaporation through an evaporation cooling process. A transient numerical heat and mass transfer model based on energy, exergy, economic and environmental approaches was proposed to assist the feasibility of cooling BIPV system via evaporative porous structure cooler. The model was also validated experimentally in the present study. The results exhibited that, comparing with conventional BIPV systems, the presented BIPV/Clay cooling system achieved a peak photovoltaic temperature reduction of 19.1 °C, with a maximum enhancement in the photovoltaic system’s electrical efficiency, electrical power, and exergy efficiency of 9.8 %, 12.6 % and 11.8 %, respectively. The ultimate reduction in the building’s annual thermal load was around 53.8 % when the clay evaporative cooling approach is applied, while the cost of electricity production reduced ultimately by 7.9 %, (from 0.151 $/kWh to 0.134 $/kWh). Further, the payback period decreased by 2.33 years and the annual amount of CO2 emissions decreased by 10.4 % for the utilized BIPV/Clay cooling system compared with the conventional BIPV system.

Numerical analysis of electrothermoconvection of a dielectric nanofluid in a heated cavity

A numerical analysis of electrohydrodynamic (EHD) flow and heat transfer of nanofluid in a heated rectangular cavity is presented. A two-dimensional (2D) rectangular cavity heated from the bottom is considered. An electric potential difference is applied vertically, with the bottom wall acting as a high-voltage electrode, and the top wall is grounded. TiO2-25 # transformer oil nanofluid with nanoparticle volume fraction ranging from 0–5% is considered. The numerical model for EHD flow and heat transfer of nanofluid is implemented in the finite-volume method (FVM) based numerical framework of OpenFOAM. A single-phase approach based on the effective properties is adopted to model the nanofluids. A two-way coupled EHD flow model is employed to consider mutual interactions of flow and electric field variables. The flow and heat transfer behavior of nanofluids in the presence of an electric field is quantified with reference to the key parameters, electric Rayleigh number (T), and the nanoparticle volume fraction ϕ. The addition of nanoparticles increased the viscosity and marginally reduced the natural convective flow and heat transfer. However, EHD flow induced by the electric field aided in overcoming the weak natural convection flow in nanofluids. Results confirm that nanofluids’ net effective heat transfer rates are notably increased in the presence of the electric field. For the parameters under consideration, combining electric fields with nanofluids led to a significant heat transfer enhancement of up to 32.3%. The present study showcases the feasibility of combining passive heat transfer enhancement using nanoparticles and active heat transfer enhancement using EHD flow.

A GPU based accelerated solver for simulation of heat transfer during metal casting process

The metal casting process, which is one of the key drivers of the manufacturing industry, involves several physical phenomena occurring simultaneously like fluid flow, phase change, and heat transfer which affect the casting yield and quality. Casting process modeling involves numerical modeling of these phenomena on a computer. In recent decades, this has become an inevitable tool for foundry engineers to make defect-free castings. To expedite computational time graphics processing units (GPUs) are being increasingly used in the numerical modeling of heat transfer and fluid flow. Initially, in this work a CPU based implicit solver code is developed for solving the 3D unsteady energy equation including phase change numerically using finite volume method which predicts the thermal profile during solidification in the metal casting process in a completely filled mold. To address the computational bottleneck, which is identified as the linear algebraic solver based on the bi-conjugate gradient stabilized method, a GPU-based code is developed using Compute Unified Device Architecture toolkit and was implemented on the GPU. The CPU and GPU based codes are then validated against a commercial casting simulation code FLOW-3D CAST® for a simple casting part and against in-house experimental results for gravity die casting of a simple geometry. Parallel performance is analyzed for grid sizes ranging from 10 × 10 × 10 to 210 × 210 × 210 and for three time-step sizes. The performance of the GPU code based on occupancy and throughput is also investigated. The GPU code exhibits a maximum speedup of 308× compared to the CPU code for a grid size of 210 × 210 × 210 and a time-step size of 2 s.

Enhanced numerical modeling of natural heat convective phase change for generalized non-Newtonian fluids at high Rayleigh number

Numerical modeling of convective heat transfer employing non-Newtonian fluids is a key issue and represent an interesting challenge in many engineering applications. For this reason, this work develops an enhanced numerical model to predict fast and accurately the convective phase change for generalized non-Newtonian fluids. The strongly thermally coupled model is solved by an improved pressure-correction algorithm (SIMPLERnP) and the Finite Volume Method with accuracy of the third order for the transient terms and second order for the convective boundary conditions and the velocity gradients that allows to calculate the apparent viscosity. The study examines the natural heat convective solidification of the ternary Al-27 %Cu-5.25 %Si alloy with the Herschel-Bulkley rheology at a high Rayleigh number (>107). In addressing the main problem, four crucial aspects are discussed: the validation of the numerical scheme with numerical and experimental results; the modeling of the non-linear temperature variation of the liquid phase change fraction; the non-Newtonian effects of the power index (0.1 ≤ n ≤ 1.9) and yield stress (0≤τ0≤5 Pa) on the heat transfer mechanisms; and finally, the time of computation with the high-order numerical scheme and the enhanced pressure-correction algorithm. The main finding is that FVM/SIMPLERnP provides a significant reduction in the time of computation compared to reliable pressure-correction schemes (SIMPLER and IDEAL), being a robust, accurate and efficient scheme to solve complex natural heat convective phase change problems involve generalized non-Newtonian fluids at high-Rayleigh numbers.

Numerical modelling of heat and mass transfer during cake baking

This article deals with the development of a numerical multiphysics model to study heat and mass transfer phenomena as well as the swelling during the baking of a cake contained in mold. The aim of this study is to provide an effective numerical tool, experimentally validated, for a better understanding of mechanisms leading to the desired end product. Based on the governing equations for heat and mass transport and under few assumptions (homogenous medium, local thermodynamic equilibrium, ideal gas mixture…), the problem consists in solving a system of five coupled partial derivative equations. Temperature, moisture content, total gas pressure, porosity and displacement are used as state variables in this study. The swelling of dough caused by the increase of total gas pressure is predicted by a viscoelastic model. This thermo-hydro-mechanical model is implemented in finite elements code. Moreover, an experimental laboratory set-up was developed in order to continually acquire temperatures, water losses, deformation and to correctly apprehend the boundaries conditions. The numerical results are then compared with experimental data. They are overall in good agreement. Various operating conditions are tested to check the robustness of predictions.

Conjugate heat transfer analysis of the transient thermal discharge of a metallic latent heat storage system

Thermal energy storage systems utilizing metallic phase change materials exhibit great potential as a technology for mobile applications, offering high storage densities and high thermal discharge rates. First experimental investigations show the functionality and performance characteristics of this system. For a deeper understanding of the thermal discharge, this paper presents a numerical model and analysis of the transient conjugate heat transfer. For validation of the numerical model, the results of the simulations are compared to the available experimental data. The investigated storage is based on an aluminum silicon alloy and a box-shaped graphite container design. In this system, heat extraction is achieved by forced convection of ambient air. The transient thermal discharge was simulated from 650 °C to 100 °C, and the solidification of the storage material at around 577 °C was simulated using an enthalpy-porosity approach. The discharge time and total heat flow show good agreement with the experimental data, indicating the model’s successful validation. An empirical study was carried out to determine the thermal contact resistance at the interface between the storage material and the graphite container. The present study contributes new physical insights regarding the thermal discharge of a novel metallic latent heat thermal energy storage system.

Experimental and numerical study on photovoltaic thermoelectric heat storage system based on phase change temperature control

To improve the thermal and electrical performance of photovoltaic (PV) systems, a novel system was proposed, in which the PV panel, phase change material (PCM), thermoelectric (TE), and thermal collection devices (PV-PCM-TEG-T) were combined. The experimental device of the PV-PCM-TEG-T system was put up, and its electrical and thermal characteristic was experimentally studied by comparing it with the standard PV panel on the condition of 3-hour radiation and 3-hour non-radiation. A heat transfer numerical model of the PV-PCM-TEG-T system is established and verified by experiments. The comparison of the PV-PCM-TEG-T system and standard PV panel and the effects of PCM thicknesses, and melting temperatures on the temperature of photovoltaic devices were numerically analyzed in 24-hour operating conditions. The results show that under an experimental condition of 3-hour solar radiance of 800 W/m2 and 3-hour non-radiance, the novel system has better temperature control performance, which could increase the PV panel’s output power and power generation efficiency by 10.4 % and 1.9 % respectively. Under 24-hour simulation conditions, the temperature of the novel system is significantly lower than that of the standard PV panel, with a maximum temperature difference of 10.1 °C. The PV-PCM-TEG-T system with thicker PCM has the same temperature as the system with thinner PCM, but higher TE power generation. And the temperature control is better with the lower PCM melting point. This study has a good promoting effect on the efficient utilization of solar energy.

Numerical Modeling of Non-Isothermal Laminar Flow and Heat Transfer of Paraffinic Oil with Yield Stress in a Pipe

This paper presents the results of a study on the non-isothermal laminar flow and heat transfer of oil with Newtonian and viscoplastic rheologies. Heat exchange with the surrounding environment leads to the formation of a near-wall zone of viscoplastic fluid. As the flow proceeds, the transformation of a Newtonian fluid to a viscoplastic state occurs. The rheology of the Shvedoff–Bingham fluid as a function of temperature is represented by the effective molecular viscosity apparatus. A numerical solution to the system of equations of motion and heat transfer was obtained using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The calculated data are obtained at Reynolds number Re from 523 to 1046, Bingham number Bn from 8.51 to 411.16, and Prandl number Pr = 45. The calculations’ novelty lies in the appearance of a “stagnation zone” in the near-wall zone and the pipe cross-section narrowing. The near-wall “stagnation zone” is along the pipe’s radius from r/R = 0.475 to r/R = 1 at Re = 523, Bn = 411.16, Pr = 45, u1 = 0.10 m/s, t1 = 25 °C, and tw = 0 °C. The influence of the heat of phase transition of paraffinic oil on the development of flow and heat transfer characteristics along the pipe length is demonstrated.

Comprehensive numerical modeling of intermittent flow cooling with enhanced photovoltaic efficiency in PVT/NPCM systems

The photoelectric conversion efficiency of photovoltaic thermal (PVT) systems is a key concern in solar energy research. The widespread use of continuous nanofluid cooling in PVT/NPCM (Nano-Enhanced Phase Change Material) systems leads to heightened energy consumption. In order to improve efficiency of the PVT/NPCM systems, a two-dimensional transient heat transfer numerical model is established to analyze the PVT/NPCM system with intermittent flow cooling. Corresponding govern equations with boundary conditions are proposed, and numerically solved by using the finite element method. Simulation results are compared with experimental data, showing a deviation of less than 7 %. The findings indicate that the intermittent cooling reduces the flow energy consumption required to drive 2220 L of nanofluid compared to continuous cooling over a 7-h period. Furthermore, under intermittent cooling conditions, the average electrical efficiency stands at approximately 19.7 %. Notably, the electrical efficiency of PVT/NPCM systems employing intermittent flow cooling closely aligns with those employing continuous flow cooling, exhibiting a maximum deviation of merely 0.0348 %. Additionally, intermittent flow cooling emerges as a favorable choice under solar radiation intensities surpasses 1000W/m2, enabling a significant reduction in overall energy consumption while maintaining commendable cooling performance.

Numerical modeling and experimental validation of heat and mass transfer within decomposing carbon fibers/epoxy resin composite laminates

CFRP composite laminates decompose by pyrolysis/oxidation when exposed to high heat fluxes. While gaseous and solid residues created within the composite material are ignored in most models, a multi-species approach is proposed to describe transient decompositions from the virgin to the final charred state of the material. The model is based on a porous medium description that includes gas creation and transport within the laminate, respectively driven by Arrhenius and Darcy’s laws. Orthotropic heat transfer and decomposition gas transport within the laminate up to the surface remain often uninvestigated while it can drastically act upon the dynamics of a fire event. An experiment is carried out to analyze multi-dimensional heat and mass transfer during the charring processes of a composite laminate exposed to a high power laser beam. Transient temperature measurements on the unexposed surface of the material are confronted to 3D unsteady numerical results to validate the model formulation.

Hydrothermal performance of a wavy minichannel heatsink with longitudinal vortex generators

Wavy channels and vortex generators (VGs) are potential heat transfer enhancement methods, and their combination can provide a remarkable hydrothermal performance. In this study, a water-cooled top and bottom walls sinusoidal wavy minichannel equipped with 14 VGs on each of its side walls is experimentally and numerically investigated. The pressure drops and average base temperatures are recorded for the Reynolds numbers (Re) between 500 and 1300 and the obtained experimental data are employed to validate the numerical conjugate heat transfer model. 3 configurations of the wavy channel with inline VGs and 3 with staggered VGs which differ by the attack angle of VGs are numerically investigated. The hydrothermal performances of the cases are studied and compared with a wavy channel without VGs. The Nusselt number (Nu), friction factor (f), and thermal performance factor (TPF) are utilized to evaluate the hydrothermal performances. The most significant TPF is found to belong to the wavy channel with staggered VGs, periodically titled for 45° in the direction of the first part of the local curve of the wavy walls. Its TPF is found to be in the range of 1.4–1.46, while the TPF of the wavy channel without VGs is in the range of 1.17–1.36 for the studied Re range.

Assessment of the effect of heat storage on the production of clean geothermal energy using the medium and deep U-type borehole heat exchanger system

Heat storage is a critical measure to realize the utilization of waste heat and to enhance the heating capacity of the medium-deep U-type borehole heat exchanger (MDUBHE) system. However, the effects of heat storage on the operation of the MDUBHE system remain unclear. The effects of heat storage measures on the building and the environment have not been assessed. In this paper, the effects of heat storage measures on system performance are revealed and assessed using the numerical heat transfer model. The results show that heat storage measures are particularly necessary in severe cold regions of China. The minimum value of the storage inlet temperature in this study should be more than 42.25 °C, and the flow rate is recommended at no more than 15 kg/s. Although increasing the inlet temperature of heat storage enhances the MDUBHE system's heating performance, the storage system's energy and exergy efficiencies are attenuated. Heat is mainly stored in the underground region within 6 m from the MDUBHE and at a depth of up to 2000 m, and the shape of the thermal plume is an inverted funnel. After adopting heat storage measures, the heating area supplied to buildings by the MDUBHE system increases, and reduces environmental pollution. Compared with the no heat storage measure, the heating area of the MDUBHE system is increased by 6770 m2 when the storage inlet temperature is 80 °C, and the corresponding solar collector area needs to be 756.1 m2. When Tins increases from 45 °C to 80 °C, the reduction of CO2 emissions increases by 12.43 tons, 21.05 tons, 38.26 tons, 55.41 tons, and 72.50 tons, respectively. This study could promote the application of the MDUBHE system and the heat storage system in severe cold regions.

Heat Transfer through Double-Chamber Glass Unit with Low-Emission Coating

The numerical modeling of radiation and convective heat transfer through a double-chamber glass unit was carried out to substantiate the increase in the heat transfer resistance of this unit via the application of low-emission coatings to glass surfaces. In the space between the panes of a window without low-emission coatings, the amount of heat transferred via radiation exceeds the amount of heat transferred via thermal conductivity and convection. The question of the effect of low-emissivity coatings on reducing heat loss through a window has not yet been sufficiently studied. This problem is also not sufficiently reflected in the literature. In this regard, this paper presents the results of numerical simulation aimed at studying the effect of low-emissivity coatings on heat transfer through a double-chamber glass unit. Simulation is carried out by numerically solving a system of equations of fluid dynamics and energy for the air gap and glass. Boundary conditions of the fourth kind are set on the internal surfaces of the chambers, taking into account the radiation and conduction components of the total heat flux emanating from the glass. The results of modeling heat transfer through a glass unit with ordinary glass show that about 60% of the heat is transferred by radiation. Therefore, an effective measure to reduce heat loss through windows is to reduce the radiation component of the total heat flux by applying a low-emissivity coating to the internal surfaces of the glass unit. This allows for the reduction of the overall heat flux (and, accordingly, heat loss to the environment) by 20–34%, depending on the number of glass surfaces with such a coating.

Numerical Modeling and Analysis of Transient and Three-Dimensional Heat Transfer in 3D Printing via Fused-Deposition Modeling (FDM)

Fused-Deposition Modeling (FDM) is a commonly used 3D printing method for rapid prototyping and the fabrication of plastic components. The history of temperature variation during the FDM process plays a crucial role in the degree of bonding between layers. This study presents research on the thermal analysis of the 3D printing process using a developed simulation code. The code employs numerical discretization methods with an implicit scheme and an effective heat transfer coefficient for cooling. The computational model is validated by comparing the results with analytical solutions, demonstrating an agreement of more than 99%. The code is then utilized to perform thermal analyses for the 3D printing process. Interlayer and intralayer reheating effects, sensitivity to printing parameters, and realistic printing patterns are investigated. It is shown that concentric and zigzag paths yield similar peaks at different time intervals. Nodal temperatures can fall below the glass transition temperature (Tg) during the printing process, especially at the outer nodes of the domain and under conditions where the cooling period is longer and the printed volume per unit time is smaller. The article suggests future work to calculate welding time at different conditions and locations for the estimation of the degree of bonding.

Numerical modeling of natural convection heat transfer from radial branching heat sinks for LED cooling applications

Light Emitting Diodes (LEDs) have revolutionized the lighting industry due to their high energy efficiency. However, LEDs require effective thermal management to preserve their lifespan and luminous efficiency. In the current study, the design of a branching radial heat sink is numerically investigated and optimized for cooling LED panels of downlights under natural convection. Branching fins arranged radially on a horizontal circular plate were considered in the current study. The buoyant fluid flow over the heat sinks is observed and characterized using parameters such as fin length, height, inclination angle, and number. The dependency of Nusselt number, heat transfer coefficient and thermal resistance on the design parameters are explained by studying the buoyant fluid flow characteristics over the heat sink. Both heat transfer coefficient and thermal resistance decrease with geometric parameters such as fin length, height, and number. Due to branching, the Nusselt number decreases by 17% at lower fin lengths and by 20% at higher fin lengths, respectively. However, the thermal resistance of the heat sink arrays decreases by around 13% at lower fin lengths and remains constant at higher fin lengths due to branching. A comparative study is performed by plotting a contour map between the cooling performance of a radial branching heat sink and a radial flat plate heat sink using a heat transfer enhancement factor. Branching fins with angles above 25°and fin heights over 19 mm outperform plate-fin heat sinks of the same height and length for fin number n = 20. Finally, a correlation is proposed to predict the average Nusselt number of the fin arrays as a function of the design parameters.

ERT data assimilation to characterize aquifer hydraulic conductivity heterogeneity through a heat‐tracing experiment

AbstractGeothermal energy systems, such as heat pumps relying on aquifers, use renewable sources of energy that are accessible in urban areas. It is necessary to characterize the subsurface hydraulic properties prior to the installation of such systems. In this context, a heat‐tracing experiment is a typical field test that can help with the characterization of the subsurface. During a heat‐tracing experiment, monitoring with downhole temperature sensors, water‐level pressure transducers and electrical resistivity tomography (ERT) can be used to help characterize the hydrogeological properties. Previous monitoring tools have shortcomings, such as low‐resolution data and over‐smoothing; thus, they fail to reproduce the heterogeneity of hydrogeological properties. Ensemble Kalman filter (EnKF) is a promising tool that can overcome the over‐smoothing problem to replicate the hydrogeological property heterogeneity. In this work, we proposed a new procedure to assimilate time‐lapse cross‐borehole ERT data into a numerical model of groundwater flow and heat transfer, where the groundwater is extracted and heated water is reinjected into an unconfined sandy‐gravel aquifer. The finite element model (FEFLOW 7.3) of groundwater flow and heat transfer is integrated with petrophysical relationship and electrical forward modelling (ResIPy) to estimate cross‐borehole ERT measurements. Then, the estimated apparent resistivity is assimilated to update the hydraulic conductivity model using EnKF. The results of the application of the proposed approach to an experimental site located in Quebec City (Canada) demonstrate that the heterogeneity of K is correctly reproduced as the updated K model is reasonably consistent with the lithological log. In addition, the proposed approach was able to replicate the cross‐borehole ERT field and temperature measurements. The comparison between prior and posterior distribution of K with slug test results shows that the EnKF made the final (assimilated) distribution of K move towards K values inferred with slug tests.