Fracture distribution plays a significant role in the behavior of subsurface environments, affecting such activities as geothermal production, exploitation and management of groundwater resources, and long-term storage of nuclear waste and carbon dioxide. A key challenge in these and other applications is to estimate the fracture network properties from sparse and noisy observations. We evaluate the utility of cross-borehole thermal experiments for this task, using both physics-based particle-tracking (PBPT) heat-transfer approach and its deep neural network (DNN) surrogates. Synthetic data are provided by the PBPT simulations and used to train and test the DNN surrogates over a full range of the fracture network properties. We propose regionalized and step-by-step training techniques to reduce the computational cost of expensive PBPT forward solves over large ranges of the (to-be-estimated) parameters. Our numerical experiments suggest the feasibility of training a regionalized DNN surrogate over parameter ranges for which the PBPT solves are fast and extrapolating its predictions to parameter ranges with few additional data. We analyze the balance between computational cost and model accuracy, and provide both PBPT and DNN models for applications to others kinds of data.

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The multi-physics coupling process during the heat extraction from enhanced geothermal system, encompassing thermo(T)-hydro(H)-mechanical(M)-chemical(C) interactions, plays a pivotal role in changing geothermal reservoir characteristics. However, a comprehensive quantitative assessment of these multi-physics behaviors has been lacking. In this study, a novel approach was proposed to calculate the magnitude of mechanical, chemical, strong mechanical-chemical coupling, and weak mechanical-chemical coupling effects on the variations of reservoir characteristics. In particular, mechanical-chemical coupling effects are quantified for the first time. They are obtained by the fracture aperture difference results across five distinct coupling models (thermo-hydro, thermo-hydro-chemical, thermo-hydro-mechanical, partially-coupled four-field, and fully-coupled four-field models). The findings indicate that mechanical effects lead to an increase in fracture aperture, while chemical effects contribute to its reduction under underbalanced injection conditions. Strong mechanical-chemical coupling effects, exhibiting a negative correlation with chemical effects, conversely result in a diminished fracture aperture. The influences of these effects are investigated from the temporal and spatial perspectives. Temporally, mechanical effects dominate early production while chemical effects become prominent in later stages. Spatially, there mainly exists two zones when stable production: a mechanical-controlled region surrounding injection wells, and a chemical-controlled area distant from the injection wells. Furthermore, sensitivity analysis of injection concentration indicates its alternation changes the reservoir traits and production performance by modifying the magnitudes of chemical and mechanical-chemical coupling effects. This quantification of multi-physics effects offers insights into optimizing injection strategies for better geothermal development. The approach could hold promising potential in other geo-energy scenarios like carbon and hydrogen storage in reservoirs.

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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.

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There are chemical dissolution and precipitation in geothermal formations with the long-term exploitation of hot dry rocks, which would induce the remarkable alteration of fracture transmissibility and evolution of thermal performance. The objective of this study is to identify the influence of various parameters incorporating chemical reactions to provide suggestions for the operation of the enhanced geothermal system (EGS). A 3D thermal-hydraulic-chemical coupling model is established for a fractured EGS considering silica-water reaction kinetics at fracture surface. Parametric study and sensitivity analysis are innovatively conducted to investigate the effects of key operation and formation parameters, including injection concentration (c_in), injection temperature (T_in), injection rate (Q_in) and initial formation silica reactant content (C_i), on thermal extraction performance. Results indicate that undersaturated injection causes chemical dissolution while oversaturated injection leads to silica precipitation. Higher c_in relieves the thermal breakout (10 °C) but enhances the injection-production pressure difference (13.5 MPa). The selection of c_in is an efficient way to adjust geothermal production, especially for oversaturated injection. The influence degrees of c_in on production temperature (T_out) and pressure difference (Δp) under oversaturated injection are 8 times and 2 times larger than those under undersaturated injection. T_in (<80 °C) exerts little influence on the chemical reaction. The remarkable water storage phenomenon will be induced with the increase of Q_in when precipitation occurs. Higher C_i results in lower T_out and Δp. The sensitivity analysis provides the rank of major parameters to thermal performance: Q_in, T_in, c_in and C_i. The standard sensitivities of Q_in to T_out, Δp and net thermal power N are 0.78, 0.63, and 0.88 respectively. As for the contribution ratio, c_in contributes the most (89%) to the variation of fracture aperture while T_in (<80 °C) contributes the least (nearly 0%). The research will provide a significant reference for the selection of parameters during the development of geothermal energy.

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As a kind of clean renewable energy, the production and utilization of geothermal resources can make a great contribution to optimizing the energy structure and energy conservation and emission reduction. The circulating heat extraction process of working fluid will disturb the equilibrium state of physical and chemical fields inside the reservoir, and involve the mutual coupling of heat transfer, flow, stress, and chemical reaction. Revealing the coupling mechanism of flow and heat transfer inside the reservoir during geothermal exploitation can provide important theoretical support for the efficient exploitation of geothermal resources. This paper reviews the research advances of the multi-field coupling model in the reservoir during geothermal production over the past 40 years. The thrust of this paper is on objective analysis and evaluation of the importance of each coupling process and its influence on reservoir heat extraction performance. Finally, we discuss the existing challenges and perspectives to promote the future development of the geothermal reservoir multi-field coupling model. An accurate understanding of the multi-field coupling mechanism, an efficient cross-scale modeling method, as well as the accurate characterization of reservoir fracture morphology, are crucial for the multi-field coupling model of geothermal production.@en

Global warming induced by excessive carbon dioxide emission generated from fossil fuels consumption is becoming increasingly severe. Development and utilization of clean and renewable energy is a significant measure to contribute for the carbon neutrality. Geothermal resource is an important clean and renewable energy, because of its advantages of abundant reserves, exploitation without restrictions from the climate and season. Extracting heat from the high temperature geothermal reservoir requires well drilling, completion and fracturing. However, due to some particular conditions in geothermal development, such as high temperature, erosion, leakage, and hard rocks, traditional petroleum well drilling and completion technologies are not well applicable in the geothermal industry. In this paper, the state-of-the-art geothermal drilling, and completion technologies as well as several fracturing methods, such as foam drilling, air hammer drilling, hydrothermal jet drilling, expansion casing technology, high temperature resistant drilling fluid and cement, chemical stimulation and thermal stimulation are comprehensively reviewed. Besides, heat extraction performances of water and CO₂ as working fluids in the geothermal system are discussed. A few novel heat extraction methods including closed loop, open loop, enhanced geothermal systems are compared and analyzed. This review is expected to provide suggestions for research fields worthy of study for geothermal drilling and exploitation.

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Geothermal energy is gaining attention as an environmentally friendly and sustainable alternative to fossil fuels. There exist complicated coupling processes among fluid flow, heat transfer, mechanical deformation, and chemical reaction in fractured geothermal reservoirs. Understanding of thermo-hydro-mechanical-chemical (THMC) coupled process is of significance for the efficient development of enhanced geothermal systems. This research aims to quantify the contributions of mechanical and chemical behaviors to reservoir feature variation during geothermal production. Herein, a fully coupled THMC model is developed for the production of an enhanced geothermal system based on fracture aperture alternation. The key improvement lies in the inclusion of mechanical-chemical (MC) coupling where chemical behaviors cause stress to be redistributed. On a geographical and temporal scale, the unique proportion technique is employed to study ratios of mechanical to chemical effects and poroelasticity to thermoelasticity. The findings emphasize the necessity of incorporating the MC coupling when analyzing reservoir characteristic variations. The mechanical effect plays a major role near the injection well and in a short term. The chemical effect is dominated far from the injection well and its time scale of action is long-term. The intensity of thermoelasticity is stronger than that of poroelasticity. Moreover, the proportion analysis reveals that when stable production is achieved, there are primarily thermo-driven and chemical-driven regions. To improve production performance and adjust geothermal reservoir features, injection temperature and solute concentration should be optimized. This paper serves as a valuable reference for both the theoretical multi-physical coupling model and practical geothermal production.

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Geothermal reservoir scaling controlled by reactive flow is a common phenomenon during geothermal development, which might lead to the decline of geothermal productivity and abandonment of geothermal projects. It is significant to reveal chemical influence on the geothermal reservoir characteristics and production performance to provide the reference for geothermal sustainable development. In this work, a thermal-hydraulic-chemical coupling model is developed for a triple-well fractured enhanced geothermal system considering the silica dissolution and precipitation at the fracture surface. It is focused on the evolution of fracture aperture and geothermal productivity. The results indicate that undersaturated injection will cause mineral dissolution which leads to the rise of fracture transmissibility and a thermal break. The fracture width is enhanced by 0.093 mm, and the permeability is 8 times the initial value after 20-year production. The oversaturated injection will cause mineral precipitation which leads to the reduction of fracture aperture and the increase of pressure difference. The opening is reduced by 0.041 mm and the permeability goes down by 2 orders of magnitude. The maximum increases of average production temperature and differential pressure are 10 °C and 13.5 MPa respectively in the 20th year from undersaturation to supersaturation. Besides, it is figured out that reaction rate denotes the evolution of fracture aperture. Both of them are distributed as a band at a fracture plane, which is determined by saturation index and temperature together. The former controls the reaction pattern (dissolution/precipitation) while the latter controls the reaction speed. Furthermore, the evolution of opening is uneven around the production well at different exploitation stages. Fracture width is higher on the strong side in the first 8.7 years but is higher on the weak side in later development when undersaturated water (0 mol/kg) is injected. The phenomenon can be employed to judge the production status, guide the descaling, etc. Production analysis indicates that oversaturation delays the heat breakthrough and undersaturation reduces the surface pump input. This study will provide a significant reference for the geothermal sustainable production influenced by chemical reactions in an enhanced geothermal system.

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Operational parameters optimization is of great significance to improve overall heat extraction performance from the hydrothermal or enhanced geothermal system. Injection flowrate, injection temperature, and production pressure are several of the easily human-controlled parameters to make the best of limited geothermal resources during the planned life. The net heat power and flow impedance are two contradictory production indexes to be optimized for efficient exploitation of long-term geothermal production. In this study, an integrated approach of finite element, multiple regression, non-dominated sorting genetic algorithm, and the technique for order preference by similarity to ideal solution is proposed and applied to the multilateral-well system to realize the optimization of geothermal development. Firstly, parametric cases coupling with thermal and hydraulic models are analyzed. Then, multiple regression is employed to obtain the net heat power and flow impedance functions considering human-controlled operational parameters and reservoir physical properties. Afterward, the multi-objective optimization algorithm is used to gain the Pareto solution set of injection and production parameters. Finally, the technique for order preference by similarity to ideal solution is employed to select the optimal combination of operational parameters for geothermal extraction. It is concluded that water loss and thermal drawdown are necessarily considered in the optimization process. The proposed approach represents global optimization. Operational parameters for the optimal case are (Q_in, T_in, p_out) which equal (49.98 °C, 62.21 kg/s, 27.44 MPa) under the conditions of this study. From the comparison between the base case and optimal case, it is observed that horizontal spread length, 2D swept area and 3D swept volume of the low-temperature scope is reduced by 77.9 m, 10 × 10⁴ m², and 16 × 10⁶ m³. Besides, the thermal breakthrough has been delayed by 1.1 years. The water loss decreases by 36.23%. The optimal case demonstrates a great improvement in production performance. Sustainable exploitation is achieved through multi-objective optimization for operational parameters. The proposed method reflects superiority, efficiency, and intelligence in geothermal development.

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Operational parameter optimization is of great significance to improve overall heat extraction performance from hydrothermal or enhanced geothermal systems. Injection flowrate/temperature and production pressure are relatively easy to control to optimize the exploitation of geothermal resources during the planned reservoir lifetime. The net heat power and flow impedance are two contradictory production indexes for describing the exploitation effect. One indicates energy efficiency from reservoirs, the other represents the mining difficulty or artificial energy input. In this study, a multi-objective optimization procedure is proposed and applied to a synthetic multilateral-well system for 30 years. Firstly, a multilateral-well geothermal model coupled with thermal and hydraulic parameters is established. Then, a multiple regression method is employed to obtain the net heat power and flow impedance functions with injection/production parameters and physical properties of the reservoir. Finally, a multi-objective genetic algorithm is used to gain a Pareto solution set of injection and production parameters. A comparison with the base case indicates the superiority, high efficiency, and intelligence of multi-objective optimization.

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A model for real gas flow in shale gas matrices is proposed and consists of two main steps: (a) developing a microscopic (single pore) model for a real gas flow by generalizing our previously reported Extended Navier-Stokes Equations (ENSE) method and (b) by using fractal theory concepts, up-scaling the single pore model to the macroscopic scale. A prominent feature of the up-scaled model is a predictor for the apparent permeability (AP). Both models are successfully validated with experimental data. The impact of the deviation of the gas behavior from ideality (real gas effect) on the gas transport mechanisms is investigated. The effect of the structural parameters (porosity Ф, the maximum pore diameter D_max, and the minimum pore diameter D_min) of the shale matrix on the apparent permeability is studied and a sensitivity analysis is performed to evaluate the significance of the parameters for gas transport. We find that (1) the real gas transport models for a single pore and porous shale matrix are both reliable and reasonable; (2) the real gas effect affects the thermodynamic parameters of the free gas and the adsorption and transport capacity of the adsorbed gas; (3) the real gas effect decreases the effective permeability for convective flow and surface diffusion; i.e., the derivation degree of the effective permeability for bulk diffusion and Knudsen diffusion increases with increasing pressure but presents a bathtub shape when the pore diameter is smaller than 10 nm; and (4) the apparent permeability increases with Ф, D_max, and D_min. It is more sensitive to D_max, followed by the porosity. D_min has a minor impact.

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Natural gas flow in shale matrices consisting of both organic and inorganic components was modeled using fractal concepts. The expression of the apparent permeability (AP) of such shale systems was derived following three main steps: (a) modeling real gas flow in a single pore by generalizing our previously reported Extended Navier-Stokes Equations method, then (b) using fractal theory concepts to obtain the apparent permeability for both the organic and inorganic-matter cells, and finally (c) upscaling the AP model to the sample scale, accounting for the heterogeneous distribution of the organic matter. The up-scaled AP model is more realistic, because it considers not only the varying cross-section shapes and tortuosity of the pores, but also the characteristic flow mechanisms and multi-scale pore size distribution in heterogeneous shale matrix systems. The model was successfully validated with experimental data from real samples. The effects of the organic matter and shape of the pores on the AP are investigated. The sensitivity of the AP to the total organic carbon (TOC), porosity, pore shape, and structural parameters of both organic and inorganic systems is studied. The results indicated that the AP would be overestimated by up to 24.1% if the characteristics of the organic matrix are ignored, and the AP proves more sensitive to the effect of the pore shape in the inorganic matrix. In addition, the top three key parameters affecting the AP are pore shape, maximum pore diameter in the inorganic matrix, and porosity. The AP is more sensitive to the pore size within the inorganic matrix than within the organic matter. The proposed model provides some theoretical and technical support for shale gas simulations.

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A model for gas flow in nano-pores was developed based on the extended Navier–Stokes equations with the assumption of neglecting adsorption and desorption. The model describes multiple flow regimes, including continuum regime, slip flow regime, transition regime, as well as molecular regime. The total mass flux includes a convective motion term and a diffusion mass transport term. The latter was obtained as a weighted superposition of bulk and Knudsen diffusion. The mass flux, contributed by different transport mechanisms, was analyzed by varying the Knudsen number (ratio between mean free path of the molecules and the pore diameter). The effect of the ratio coefficient (the power-law exponent in the relation between bulk and Knudsen diffusion), the pore size and the pressure on the gas transport was investigated using the proposed model. The predictions of the newly developed model are in good agreement with the Direct Simulation Monte Carlo (DSMC) method and with the results of the experiments. Our results show that: (1) As the Knudsen number increases, the contribution of viscous flow to gas transport decreases monotonically, bulk diffusion increases to a peak, and then decreases, whereas the Knudsen diffusion increases monotonically. (2) For a larger ratio coefficient, the bulk diffusion changes more rapidly and the peak is higher. The changing trend of the bulk diffusion is opposite to the Knudsen diffusion. (3) The pressure range in which the viscous flow dominates becomes larger and the peak of bulk diffusion is smaller in larger pores. When the pore pressure is higher, the viscous flow and the bulk diffusion tend to dominate.

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