Thermal Breakthrough Research Articles

Coupled heat-fluid-solid numerical study on heat extraction potential of hot dry rocks based on discrete fracture network model

Fracture networks within hot dry rock (HDR) geothermal reservoirs are complex, and heat extraction via water injection is thus a coupled process of heat-fluid-solid multifield. In this paper, utilizing the theory of normally distributed random functions, we develop a corresponding pre-processing subprogram to establish a discrete network model of complex fracture distribution in HDR reservoirs; then construct a heat-fluid-solid finite element model for heat extraction via water injection and compare the numerical solution with the analytical solution of the one-dimensional non-isothermal consolidation problem for verification. The numerical simulation results show that the main factors affecting the heat extraction efficiency of HDR reservoirs include fracture width, fracture density, fracture permeability, and matrix permeability. When a HDR reservoir is injected with water for heat extraction, there is a certain threshold value of these influential parameters, beyond which the outlet temperature drops significantly, resulting in an obvious thermal breakthrough. When injecting water for heat extraction, the values of these parameters should be controlled and kept at a reasonable level, otherwise, the HDR reservoir may enter a thermal breakthrough stage in advance, which is not conducive for long-period heat extraction. Influenced by the random distribution of complex fractures, the leading edge of the cold front may present an irregular distribution. During the process of heat extraction, the stress gradually changes from a compressional state to a tensile state, which induces further damage to the HDR reservoir.

Comparison of Supercritical CO2 With Water as Geofluid in Geothermal Reservoirs With Numerical Investigation Using Fully Coupled Thermo-Hydro-Geomechanical Model

Abstract In the present work, fully coupled dynamic thermo-hydro-mechanical (THM) model was employed to investigate the advantage and disadvantages of supercritical CO2 (SCCO2) over water as geofluids. Low-temperature zone was found in both SCCO2-enhanced geothermal system (EGS) and water-EGS systems, but spatial expansion is higher in water-EGS. Although, the spatial expansion of SCCO2 into the rock matrix will help in the geo-sequestration, the expansion of stress and strain invaded zones were identified significantly in the vicinity of fracture and injection well. SCCO2-EGS system is giving better thermal breakthrough and geothermal life conditions compared to the water-EGS system. Reservoir flow impedance (RFI) and heat power are examined, and heat power is high in the water-EGS system. Minimum RFI is found in the SCCO2-EGS system at 45 °C and 0.05 m/s. Maximum heat power for SCCO2-EGS was observed at 35 °C, 20 MPa, and 0.15 m/s. Therefore, the developed dynamic THM model is having greater ability to examine the behavior of SCCO2-EGS and water-EGS systems effectively. The variations occur in the rock matrix, and the performance indicators are dependent on the type of fluid, injection/production velocities, initial reservoir pressure, and injection temperature. The advantages of SCCO2-EGS system over the water-EGS system provide a promising result to the geothermal industry as a geofluid.

How groundwater flow field change affects heat transfer in groundwater heat pumps based on physical experiments

A groundwater heat pump (GWHP) is a form of ground-source heat pump that utilizes groundwater as its heat source and offers great efficiency, significant energy savings, and little pollution. As a GWHP system runs, thermal breakthrough is a crucial feature of system design that can result in a progressive shift in pumping water temperature and negatively impact GWHP performance. Variation in the groundwater flow field is crucial for heat transfer in terms of pumping and recharging well groups, especially when high porosity and permeability aquifers are taken into account, as this has a direct impact on the development of the groundwater temperature field. The primary goal of this study was to evaluate the impact of groundwater flow field variation due to groundwater velocity and recharge rate allocation changes on heat-transfer characteristics using laboratory physical experiments, to study the evolution trends of the groundwater flow field and groundwater temperature field, and to compare and determine various pumping and recharge well-group layout schemes to improve GWHP operation efficiency. The test results showed that the rise rate of pumping water temperature and the thermal breakthrough occurrence time increase with the increase of groundwater velocity, and when the groundwater velocity is the same, the thermal breakthrough occurrence time and the rise rate of pumping water temperature in the vertical well layout scheme are 0.48–0.76 times and 1.36–4.0 times that of the parallel well layout scheme, respectively. In addition, the recharge rate allocation has a greater impact on the parallel well layout scheme but a smaller impact on the vertical well layout scheme. The physical test results can provide a scientific basis for future research.

Integrated geological assessment and numerical simulation for Olkaria's East and Southeast geothermal fields

Olkaria East and Southeast geothermal fields are located in the East African Rift System and are approximately 120 km from Nairobi, Kenya. It was the first geothermal field in the country to start power production in 1981 Unit I (15 MWe). It has steadily increased its capacity from Olkaria I-VI units to 278.3 MWe (2022). Despite the steady increase in power generation, there has been a notable pressure decline of 10–15 bars. To ensure optimum resource utilization, a frequent appraisal is necessary to track productivity and management practices that will guide future investments. Reservoir simulation using TOUGH 2 computational code was employed to assess natural geo-controlling structures for optimal productivity and prediction of future developments in the geothermal field. A summarized review of geological and geochemical features was used to determine input parameters for the numerical model and assigned fault and reservoir rock properties were computed using temperature-dependent fluid movement equations which reduce the ambiguity involved in the trial-and-error approach used to construct a conceptual model. The initial state model was calibrated using measured temperature and pressure profiles from 16 wells. Subsequently, the production and reinjection model was set up to investigate reservoir performances before and after reinjection. Different water reinjection scenarios were tested with changing well location (infield and outfield), well depth and recharge rate. It was discovered that declining pressure trends up to 19 bars after a period of 29 years when 1656 t/hr mass is extracted while 42% water reinjection occurs. The extraction of 717 t/hr from new wells caused a further decline in production life to 13 years. The optimum reinjection program depended on recharge rate, well location and depth interval to mitigate reservoir pressure decline and thermal breakthrough. This study suggested hot and condensate water reinjection of 1530 t/hr (74% of extracted fluid) south of Olkaria East field.

NUMERICAL SIMULATION ON THE HEAT EXTRACTION OF ENHANCED GEOTHERMAL SYSTEM WITH DIFFERENT FRACTURE NETWORKS BY THERMAL-HYDRAULIC-MECHANICAL MODEL

Hot dry rock (HDR), as a kind of geothermal energy resource, has attracted much attention due to its wide distribution and huge reserves. This paper presents a numerical study on energy mining in the HDR by the enhanced geothermal system (EGS). The thermal-hydraulic-mechanical coupling model is employed in these simulations. The multi-field evolution process and the influence of the fracture parameters on the heat recovery performance of an EGS are analyzed comprehensively. The results show that the fractures parallel to the connecting line of the injection-production well can lead to an early thermal breakthrough, resulting in a thermal recovery performance decrease, while fractures perpendicular to the connecting line between the production and injection wells can enhance the production temperature of an EGS, when compared with the reservoir without fractures. The production temperature drop rate of the EGS with percolated fracture network is much quicker than that of the EGS with an isolated fracture network. Additionally, short fractures can lessen the potential for working fluid preferred flow channels to emerge; therefore, an EGS with short fractures may operate better than an EGS with lengthy fractures.

Economic optimization of enhanced geothermal systems using a fully analytical temperature profile

ABSTRACT In enhanced geothermal systems (EGS), the efficiency of the energy recovery process is highly dependent on the produced fluid’s temperature. In this work, a new analytical scheme is proposed for predicting the spatiotemporal evolution of temperature profile based on the three-dimensional energy conservation equation solved on the vertical plane passing through the wells. The solution is given in an error-function form which suits well for feasibility studies. An economic study is then conducted on the cost of operation based on the analytically described temperature and pressure distribution. The cumulative gain of operation, including the cost of pumping and reduced gain due to thermal breakthrough, is optimized with respect to the well spacing and the water injection rate. Optimum well spacing – injection rate combinations have been obtained for varied project life times. The maximum cumulative gain calculated by this method can be used for capex analyses and project lifetime predictions.

Simulation-based evaluation of the effectiveness of fiber-optic sensing in monitoring and optimizing water circulation in next-generation enhanced geothermal systems

The success of multi-stage hydraulic fracturing technology in unconventional oil and gas reservoir development has attracted much attention from the geothermal community. Some pilot field experiments have been conducted to investigate the multi-stage hydraulic stimulation along horizontal or high-deviated wellbores in geothermal reservoirs (denoted as next-generation enhanced geothermal systems). One common output of such stimulation is that the created hydraulic fractures show various conductive capabilities, which could potentially lead to undesirable flow localization, early thermal breakthrough, and low cold water sweep efficiency. Monitoring the water circulation between horizontal wellbores connected through hydraulic fractures becomes important in avoiding early severe producing temperature reduction in practical operations. In this study, we investigate the effectiveness of distributed temperature sensing (DTS) and distributed strain sensing (DSS) in identifying dominant flow paths in geothermal reservoirs with multi-stage hydraulic stimulation and horizontal well completion designs. A coupled thermo-poro-elastic model for general-purpose geothermal reservoir simulation is developed and solved using a combined finite volume/finite element method, together with a fully implicit sequential coupling scheme. The temperature and strain responses along horizontal production wells are simulated and analyzed during water circulation. Reservoir temperature reduces in the area that is close to the water flow paths, which induces thermal contraction. These thermoelastic characteristics can be monitored by fiber-optic sensing, forming distinct signatures for flow-localization identification. DTS data may be dominantly influenced by the fractures with higher conductivity, ‘masking’ the signals related to fractures in the downstream, but DSS data can provide additional information for accurate identification of high conductive fractures. Successful mitigation strategies, for example plugging the dominant fractures illustrated in this study, could substantially increase the producing fluid temperature. The analyses in this study show that fiber-optic sensing is an effective technology to monitor and optimize water circulation in next-generation enhanced geothermal systems.

Comparative study on heat extraction from Soultz-sous-Forêts geothermal field using supercritical carbon dioxide and water as the working fluid

Energy extraction from the deep subsurface requires engineering using a working fluid circulation in well doublet. This study developed a field-scale hydro-thermal model to examine the heat extraction potential from Soultz-sous-Forêts with CO2 and water as the working fluid. A better understanding of the heat extraction mechanism is established by considering the reservoir response and the wellbore heat exchange. Sensitivity analyses are performed for different injection temperatures and flow rates for 50 years. Results show that the wellbore effect is multiple times higher than the reservoir response to the production temperature. Furthermore, lowering the injection temperature eventuates to a smaller temperature reduction at the subsurface, enhancing the overall heat extraction potential with a minor impact on thermal breakthrough. The cold region developed around the injection wellbore may affect the production fluid temperature due to its proximity to the production wellbore near the top of the reservoir. To reach higher heat extraction efficiency, it is essential to use sufficient wellbore spacing. CO2 can be used as working fluid for over 50 years as it does not show significant thermal breakthrough and temperature plume evolution in the reservoir under studied conditions. CO2 shows lower temperature reduction for all injection rates and temperatures for 50 years of operation.

Multi-objective balanced method of optimizing the heat extraction performance for hot dry rock

Geothermal energy, a kind of clean and environmentally friendly energy source, is an important object of future natural resource development and utilization, among which, hot dry rock is one of the important deep geothermal resources. In the current multi-objective optimization of heat extraction performance, reservoir production models are less considered and the effects of different optimization ideas are not compared comprehensively. To improve the heat extraction efficiency and prolong the exploitation life of geothermal reservoirs, this paper determines the appropriate operating parameters of geothermal system (injection temperature, injection rate, production pressure and injection-production well spacing) based on the coupled thermal-hydraulic-mechanical model of hot dry rock exploitation in the Gonghe area of Qinghai and three heat extraction optimization methods. In addition, the heat extraction performances of different schemes are comparatively evaluated. And the following research results are obtained. First, the sensitivity analysis of injection and production parameters shows that power generation and recovery factor are in a reverse relation with injection-production pressure difference, which is the direct reason for the adoption of multi-objective optimization. Second, the optimization scheme prepared on the basis of parametric study indicates that the shortest life of a geothermal reservoir is 10 years, the injection-production pressure difference is up to 67 MPa, there is a significant thermal breakthrough phenomenon and the reservoir safety faces challenges. Third, by virtue of multi-objective optimization and decision making integration, the optimal operation parameter combination of hot dry rock system is determined, the life of geothermal reservoirs can exceed 20 years and balanced optimization is achieved. In conclusion, the idea of multi-objective optimization is feasible and applicable to geothermal energy exploitation and this method provides a reference for the efficient geothermal energy development and utilization and is helpful to the realization of “double carbon” goal in China.

Numerical investigation on delaying thermal breakthrough by regulating reinjection fluid path in multi-aquifer geothermal system

Thermal breakthrough time of geothermal system directly affects its service life. When a geothermal system consists of multiple aquifers with different permeability, a highly permeable reservoir may lead to an earlier thermal breakthrough. It is a key issue that how to increase the service life of geothermal system by regulating the hydrothermal cycle to inhibit the preferential passage of the geothermal system. In this paper, an innovative method to delay thermal breakthrough by adjusting fluid viscosity is presented. A THC coupling model with variable viscosity is established, and a PID controller is used to realize the constant flowrate reinjection. The flowrate, temperature and tracer concentration during reinjection are analyzed by numerical simulation. The response mechanism of hydrothermal cycle of geothermal system to changing viscosity condition is discussed, and the regulation of hydrothermal cycle by adding viscosity regulator to reinjection fluid is simulated. The results show that in the multi-aquifer geothermal model in this paper, adding 1.5 % Methyl Cellulose into the reinjection fluid can delay the thermal breakthrough time from 1190 days to 1800 days, increasing the service life of the geothermal system by about 50 %. The research results prove that the method of regulating reinjection fluid pathway by adjusting viscosity can effectively delay the thermal breakthrough of geothermal system, substantially prolong the lifespan of certain geothermal fields.

Practical workflow for assessment of seismic hazard in low enthalpy geothermal systems

It is of vital importance to be able to determine the seismic hazard in advance of any geothermal operation in the subsurface, especially in a densely populated area such as The Netherlands. The author aims to arrive at a practical assessment of the seismic hazard in low-enthalpy geothermal doublet systems specifically designed for heat exchange in porous and permeable aquifers operated on a volume balance, at a depth range of 1800 to 3300 m having temperatures in the range of 60 °C to 100 °C. The article presents a practical workflow aiming to determine the probability distribution for mechanical re-activation along pre-existing weak faults. After presenting the tectonic structural setting the criticality criterion based on shear mobilisation is introduced. Existing stress models are reviewed and a practical manner to estimate and limit all geomechanical input parameters is presented, including fault mechanical properties. The workflow is demonstrated both for early period operation times and at final thermal breakthrough. The uncertainty is addressed through probabilistic logic tree analysis quantifying the variation of the four most uncertain input parameters: fault cohesion and friction coefficient, the thermal stress parameter and the initial minimum Earth stress. The probabilistic hazard assessment is characterised by four output parameters: the expected value, the probability that unity is exceeded and two more probabilities. In case unity is exceeded the range of fault dips prone to mechanical re-activation is shown. Exceedance of this first necessary condition requires the assessment of the other two necessary conditions: seismogeneity and moment magnitude.Article highlightsThe article presents a practical workflow to assess the seismic hazard associated with geothermal operations.To be able to perform the necessary uncertainty analysis, four main input parameters are treated probabilistic.The first necessary condition for seismicity to occur is characterised by four probabilities: the expected probability, the probability that seismicity can occur and two higher probabilities.

A robust assessment method of recoverable geothermal energy considering optimal development parameters

It is known that development parameters such as injection and production rate, injection temperature, and well location and spacing play an important role in determining the recoverable geothermal energy in a licensed region during the exploitation stage, but they are seldomly considered in geothermal resource assessment. In this study, a robust assessment method of recoverable geothermal energy considering the optimal development parameters is developed. To maximize the recoverable geothermal energy whilst avoid environmental disasters including reservoir pressure declining, thermal breakthrough and surface subsidence, an efficient approach of optimizing development parameters is proposed using the fully coupled thermo-hydro-mechanical reservoir model, experimental design and proxy model, and multiple response optimization method. Based on the case study of two doublets in the Tongzhou district, China, the robustness and reasonability of the developed assessment method are demonstrated. The results show that the optimal development parameters can significantly increase the recoverable geothermal energy, but the optimal development parameters for different doublets are different due to the complexity in geological structures and the heterogeneity in reservoir parameters. Therefore, it is highly recommended to maximize the recoverable geothermal energy by selecting the optimal development parameters.

Study on heat extraction characteristics in a rock fracture for the application of enhanced geothermal systems

Enhanced geothermal systems (EGS) technologies aim to extract geothermal energy from hot dry rock (HDR). Heat extraction performance is of great importance for thermal efficiency and life cycle of EGS. It is intuitively considered that EGS reservoir modeling should be established based on accurate measured data of thermal and hydraulic properties of rock matrix and fluid, such as thermal conductivity, heat capacity and fracture permeability, however, which are time-consuming to obtain in some projects. This paper aims to clarify the influence of these parameters on heat extraction performance, which can provide basis for reservoir model simplification during preparation process of engineering scheme. Numerical simulations were carried out based on a rough fracture of granite rock at core scale, which has been validated by amount of experiments. First, the differences between simulation results and the previous experiment results were presented and analyzed, for variations of heat extraction rate per flow rate. Compared with the method with constant flow rate, the compensating method with various flow rate greatly increased the heat extraction rate and postpone thermal breakthrough time. Therefore, a simplified method was proposed in this paper to optimize the flow rate or predict the heat extraction rate when EGS operation with various flow rates. The method are applicable for geothermal reservoir management for efficient and stable heat extraction. Finally, the effects of properties of rock mass and fracture were studied. The production temperature and heat extraction rate were larger with larger thermal conductivity and heat capacity. It was found that the maximum influence on heat extraction rate were less than 20% and 10% within the common value ranges of thermal conductivity and heat capacity, respectively. There were almost no differences in the heat transfer process in fractures with different fracture permeabilities. It can be concluded that the prediction error of heat extraction performance is tolerable for engineering reservoir simulations, even without precise experimental test for thermal and hydraulic properties variations with temperature or pressure.

Modeling flow and heat transfer of fractured reservoir: Implications for a multi-fracture enhanced geothermal system

The EGS (enhanced geothermal system), particularly the multi-fracture EGS, is expected to be a key method to effectively develop the deep geothermal resource. The accurate modeling of flow and heat transfer in an EGS reservoir, particularly the fracture, is challenging. Therefore, an improved model considering the LTNE (local thermal non-equilibrium) and non-Darcy flow in a rough fracture is proposed. Then, the flow and temperature fields in the matrix are comprehensively investigated. The relationship between matrix and fracture is analyzed. The LTNE and LTE (local thermal equilibrium) are compared to determine the specific thermal process in the fracture. The difference between non-Darcy and Darcy flow in the fracture is studied to evaluate the actual flow behavior. The influences of the rough and smooth fractures are discussed. The results show that the direct contribution of the fracture to production is close to 100%, while the matrix mainly plays an indirect role as a heat source. There is a noticeable local low-pressure region induced by fluid density change in the matrix, while the heat conduction, especially rock conduction, dominates the heat transfer of the matrix. The intense heat convection in the fracture leads to a heat transfer rate difference of up to 5000 times compared with the heat conduction of the matrix, causing a marked thermal breakthrough. The non-Darcy flow represents the actual flow in the fracture, and the velocity is significantly lower than the Darcy flow velocity when a high injection flow rate is employed in the EGS production. The total extracted heat difference between rough and smooth fractures reaches 7.51%. • A model considering LTNE and non-Darcy flow in a rough fracture is established. • The heat conduction of the rock dominates the heat transfer process in the matrix. • The direct contribution of the EGS fracture to production is close to 100%. • The heat transfer rate in EGS fracture can be thousands of times that in the matrix. • The non-Darcy flow may well represent the actual flow behavior in EGS fracture.

Tracer test and design optimization of doublet system of carbonate geothermal reservoirs

The imbalance between large-scale exploitation and reinjection year by year has led to the decline of the water level of the geothermal reservoirs in the North of China. The reinjection tracer test was carry out based on the doublet system in the Xianxian geothermal field in China with sodium naphthalene sulfonate as the tracer in this paper. The 1D and 3D models were modeled on the software COMSOL in this study to simulate the predictive analysis of multiple exploitation-reinjection schemes and optimize the design. The monitoring data of the tracer concentration in the water samples collected at the wellhead of the exploitation well showed that the tracer was firstly detected on 30th days after the tracer test started. Afterwards, the tracer concentration reached a peak on the 100th day and then gradually decreased until ∼ 140th day, with a tracer recovery rate of 0.0225%. And one dominant fissure channel between the exploitation well and reinjection well with a length of ∼ 513.7 m was shown in the test. The thermal breakthrough time of the exploitation well was defined as the time when the temperature decreases by 2 °C after 100 years of geothermal exploitation. Based on this, the optimal exploitation solution of the geothermal resources was proposed as the spacing between the exploitation well and reinjection well should be set as ∼ 375 m and the exploitation and reinjection volume is 75 m3/h.

Causes of a premature thermal breakthrough of a hydrothermal project in Germany

Sustainable heat extraction is of utmost importance for the economic life of geothermal production systems. Especially in hydrothermal sedimentary basins, a temperature decrease at the production well prompts a financial loss. A premature thermal breakthrough occurred in one of the geothermal projects in the Greater Munich Area, a well-known region for deep, low enthalpy geothermal development in the Upper Jurassic carbonate reservoir (syn. Malm) beneath the North Alpine Foreland Basin. Accordingly, questions are raised regarding the geologic controls on the reservoir´s permeability, the occurring type of heat and mass transport mechanism, and the fitting reservoir model type. 3D seismic data interpretation delineates seismic scale structures potentially influencing the reservoir permeability. Geophysical borehole data characterize sub-seismic scale elements (fractures, karst, and lithofacies), where we correlate them with the inflow zones and the interpreted seismic scale structures. The integration of both scales delineates the reservoir heterogeneity controlled by a lateral change in the carbonate lithofacies overprinted by faults and fractures. A NNW-SSE oriented seismic scale structure matches the orientation of hydraulically active sub-seismic scale fractures, where they are aligned with the maximum horizontal stress orientation. This structure induces additional anisotropic permeability, providing a preferential hydraulic pathway between the wells of the project. This study recommends considering fractured reservoir models to simulate the mass and heat flow in the highly heterogeneous Malm carbonates instead of composite reservoir models of equivalent hydraulic properties. Finally, we present a hydrogeological model describing the reservoir's structural and matrix permeability distribution to act as a basic concept for future thermal-hydraulic numerical modeling. The applied methods in this study are applicable in similar geothermal systems with adequate seismic and geophysical borehole data for future geothermal reservoir characterization, modeling, and management.

Simulation of the flow and thermal breakthrough of a forced external circulation standing column well

The flow and thermal breakthrough phenomenon in a forced external circulation standing column well (FECSCW) directly affects heat transfer efficiency and load-carrying capacity. A numerical model for FECSCW is developed to analyze the migration of the temperature and velocity front under the flow and thermal breakthrough. The results indicated that thermal breakthrough began after simulation running 2.5 min and was completely formed after 12 min. The inlet water, which directly entered the production well without heat exchange with the aquifer, accounted for 12.8%. When the porosity of the backfill material decreased from 0.35 to 0, the coefficient of performance (COP) of the heat pump unit increased by 1.6% on average, and the thermal breakthrough strength decreased by an average of 45.3% within 25 min. Where seepage velocity near the well wall was greater than 1 × 10−3 m•s−1, faster velocity front migration was observed, while the migration advantage of the temperature front was more prominent outside of this region. Through quantitative analysis of flow and thermal breakthrough, temperature and velocity front migration, and COP change of heat pump unit, theoretical suggestions were provided for the thermal transfer mechanism near the thermal well wall. The extended research in this study can be applied to the design and optimization of forced external circulation standing column well system.

Estimation of flow-channel structures with uncertainty quantification: Validation by 3D-printed fractures and field application

Reinjection is an integral part of operating enhanced geothermal systems. Since cooling of reservoirs may occur due to cold-water injection, the possible effects of injection should be assessed. Subsurface structures, especially surface areas of flow channels connecting injection and production wells, determine the onset and rate of thermal breakthrough at a production well caused by reinjection. Previously, a method to estimate the surface area using temperature data was proposed (temperature-based surface area estimation method), which has only been applied to synthetic data from numerical simulation models and field data from geothermal fields with limited structural information available. In this study, we validated the temperature-based surface area estimation method through thermal flow experiments using a 3D-printed fracture network with known structural and physical properties. Based on measured temperature data, the flow-channel surface area was estimated with an approximate Bayesian uncertainty quantification method. The estimated uncertainty bounds were in good agreement with the design of the 3D-printed sample. We also applied the estimation method to field data from a well-studied experimental field. The estimates were consistent with other geophysical observations and previous numerical modeling studies, which had been used previously to probe fluid pathways in the field. It is expected that the thermal response estimation approach validated in this study can be useful for designing reinjection strategies. Furthermore, 3D-printed flow-channel networks may be useful for validating other estimation methods.

Axisymmetrical analytical solution to the transient heat transfer problem in geological media

Laplace transforms were used in this paper to obtain analytical solutions for the axisymmetric problem under a constant well temperature using the convective heat transfer boundary condition, which included the conduction and convection in the aquifer as well as heat exchange at the boundary. This solution curve intuitively illustrates the temperature distribution within the aquifer. The effects of various parameters on this analytical solution were analyzed. According to this parametric analysis there exists a quasi-steady-state of temperature distribution in the axisymmetrical situation, which is different from the planar symmetry problem. In addition, the thermal breakthrough increases with the injected rate and decreases with the increasing convective heat transfer coefficient. Our analytical solution matched the results yielded by the numerical simulation quite well.

Seepage and heat transfer characteristics of sandstone thermal reservoir under aquitard damage

Flow and thermal breakthroughs are the main reasons for the reduction in the operational efficiency of a single-well groundwater heat pump (SWGWHP) system. Furthermore, a large initial pumping flow rate, attributed to the large initial heating/cooling load of the building, can consolidate and damage the aquifer. In this study, an aquitard damage test bench was constructed to investigate the formation and development of flow and thermal breakthroughs during the operation of the SWGWHP system by varying the initial recharge rate (Q), aquifer thickness (H), and the time difference between pumping and recharge (Δt); and to investigate the aquifer damage, seepage, and heat transfer patterns. The results indicated that pressure was the main factor that damaged the aquitard. Aquitard damage can cause or aggravate the flow breakthrough phenomenon. The flow breakthrough strength is the main factor affecting the thermal breakthrough strength. The results of the orthogonal test analysis indicate that the order of the primary and secondary influencing factors of the flow breakthrough strength and operating time efficiency is aquitard thickness (H) > initial recharge rate (Q) > pumping and recharging time difference (Δt). The existence of the aquitard reduced the flow breakthrough strength by 15.2–33.2% and prolonged the efficient operation time of the system by 2.5–5 times. Based on quantitative analyses of the flow and thermal breakthrough strengths, and the variation in the system coefficient of performance, this study reveals the reasons for the formation of thermal breakthrough and provides theoretical suggestions to ensure a safe and stable operation of the SWGWHP system. The results of the study can guide practical installations as well as future research on SWGWHP systems.