Migration and Evolution of Geothermal Fluids in Karst Reservoirs and Geothermal Energy Development Model: A Case Study

Abstract

Against the backdrop of the energy transition and to support the sustainable development of karst geothermal resources in the Laiyuan area, this study addresses the insufficient understanding of its formation mechanisms and thermal accumulation patterns. By innovatively integrating hydrogeochemical analysis, hydrogen–oxygen isotope tracing, and coupled water-heat numerical modeling, we systematically reveal the origin, evolution, and thermal controlling factors of geothermal fluids in this region. The results indicate that the geothermal water in Laiyuan is of the HCO₃–Ca–Mg type with low mineralization, which is controlled by carbonate rock weathering. The average temperature of the thermal reservoir estimated by the quartz geothermometer is 48.5 °C with a circulation depth of approximately 1363 m. Hydrogen and oxygen isotope data indicate that geothermal water originates from atmospheric precipitation, which undergoes deep circulation after vertical infiltration through karst fissures. Upon heating at depth, it ascends along compressional-torsional fault zones, thereby forming a regional thermal anomaly. Hydrothermal coupling modeling further confirms that groundwater flow in karst aquifers significantly controls the distribution of the geothermal field, while conductive faults serve as the main thermal pathways and demarcate the temperature field boundaries. The thermal reservoir volume method estimates the geothermal resources in the study area to be approximately 5.50 × 10¹⁵ kJ, indicating considerable exploitation potential. However, extraction schemes must be optimized based on geological conditions to delay thermal breakthrough. This study elucidates the genetic mechanism and heat accumulation model of the Laiyuan karst geothermal system, providing a scientific basis for the exploration and sustainable development of geothermal resources.

1. Introduction

Against the backdrop of global energy transformation, geothermal energyas a green, low-carbon, stable, reliable, and renewable mineral resourceholds significant strategic importance in mitigating the greenhouse effect, improving air quality, optimizing energy structures, and enhancing energy supply security. − Hydrothermal geothermal resources are widely utilized in district heating systems globally due to their high technical maturity. − China boasts abundant geothermal resources, with the low-to-medium-temperature hydrothermal resources in North China being particularly prominent. These resources account for 74.7% of the nation’s total geothermal reserves, underscoring their significant potential for development and utilization. − China’s geothermal heating network, with a coverage area exceeding 1 billion square meters, has substantially curtailed the reliance on coal-based heating and significantly lowered atmospheric pollutant emissions. − A comprehensive understanding of the characteristics and formation mechanisms of geothermal resources is essential for their precise exploration and efficient development. This knowledge holds significant importance for ensuring national energy security, supporting the achievement of the “dual carbon” goals, and enhancing public welfare. , The widely distributed karst thermal reservoirs in North China are regarded as highly promising hydrothermal geothermal resources. However, the lack of systematic understanding of the formation mechanisms, fluid migration pathways, and heat accumulation patterns of such karst thermal reservoir systems currently constrains the precise exploration and efficient, sustainable development of these resources.

Compared to leading geothermal resource countries, such as the United States, Iceland, and Turkey, the development and utilization of geothermal resources in China have progressed at a relatively slow pace. Analyzing cutting-edge theories and technological advancements in geothermal resource exploitation globally holds significant importance for accelerating China’s geothermal development efforts. Wang et al. (2023) have recently conducted a systematic investigation of geothermal resources in the North China coal-bearing region. Their work analyzes the formation mechanisms of the regional geothermal field, elucidates the distribution patterns of ground temperature and terrestrial heat flow, and identifies large-scale geothermal utilization in coalfields as a major focus for future research and development. Based on temperature logging of geothermal wells, terrestrial heat flow measurements, geothermal resource exploration, data from drilled geothermal wells, pumping tests, and long-term dynamic monitoring, Kang et al. (2024) conducted a comprehensive study that revealed the heat sources and accumulation mechanisms, water sources and enrichment processes, renewable capacity of hydrothermal systems, and the distribution patterns of geothermal reservoirs in Shandong Province. Their findings provide critical guidance for identifying targeted areas for geothermal well placement. Aliyu and Archer (2021) investigated the origin and hydrogeochemical characteristics of geothermal water in the thrust belt of northern Tunisia, elucidating the genesis and evolutionary patterns of the geothermal water. Innovatively applying geothermal water chemistry to mineral exploration, they systematically evaluated its potential health risks. Wang et al. (2025) utilized geological data from the Huaibei area to investigate the distribution characteristics of the regional geothermal field. By integrating typical geological profiles and applying constraints based on geothermal, geological, and hydrogeological conditions, they conducted coupled hydrothermal numerical simulations, with a specific focus on analyzing the influence of typical regional thrust nappe structures on geothermal distribution.

Efficient and sustainable utilization of geothermal resources relies on a comprehensive understanding of their origins. The chemical and isotopic signatures of geothermal fluids preserve extensive geochemical information from the formation and evolution of geothermal systems. These signatures serve as effective tracers for elucidating geological changes and for identifying the origins of geothermal fluids. They facilitate the quantification of the crust and mantle contribution to heat flow and the genetic mechanisms of heat sources, including aspects such as the source, temperature, chemical composition, water-rock reaction, and groundwater circulation pathways of geothermal water. , This also provides significant implications for assessing the quantity of deep geothermal resources and guiding their development and utilization. Specifically, major elements such as Na, K, Ca, and Mg can be utilized to identify the heat source types of geothermal water and assess the water-rock reaction. Furthermore, trace components in geothermal fluids offer additional insights into the geochemical processes that the system has undergone. , Hydrogen and oxygen isotopes serve as reliable indicators of groundwater mixing processes and water source origins. They are extensively applied to determine recharge sources, recharge elevation, age, and the mixing ratios of cold and hot water in geothermal fluid systems. Geothermometers based on SiO₂, cations, and anions are widely employed to estimate geothermal reservoir temperatures. , Li et al. employed the quartz geothermometer without steam loss to estimate the temperature of Cambrian geothermal water in the mining area and simultaneously determined its circulation depth.

Due to well-developed karst features such as caves and fractures, karst thermal reservoirs in North China exhibit high-yield potential and are conducive to wastewater reinjection after geothermal utilization, thus demonstrating significant development prospects. Regarding research on hydrothermal geothermal systems in complex karst environments, Wang et al. (2024) investigated the hydrochemical characteristics and formation mechanisms of karst geothermal water in northern Jinan. Their study revealed a chemical zoning evolution pattern from cold water in the south to hot water in the north. By innovatively integrating multivariate statistical analysis with hydrogeochemical modeling, they constructed a conceptual model of karst geothermal water flow systems, offering new insights into the genesis mechanisms of geothermal water under similar geological conditions. Wen et al. (2025) investigated the hydrochemical characteristics and circulation patterns of fault-controlled geothermal water in the karst area of western Yunnan. Their study elucidated the coupled control mechanism of faults and aquifers on geothermal water circulation. By innovatively applying hydrothermal coupled numerical simulation constrained by hydrochemical data, they identified multilevel groundwater flow systems and proposed a geothermal water circulation model suitable for the karst region of western Yunnan. This provides effective guidance for the sustainable development and utilization of regional geothermal energy. In terms of geothermal resource utilization, Jarma et al. (2022) employed pressure-driven membrane separation processes for desalinating geothermal reinjection fluids. Their study investigated the performance of nanofiltration and reverse osmosis membranes under varying brine-to-feed ratios. By innovatively proposing a strategy for the recycling of concentrated brine, they significantly enhanced water production flux and systematically assessed the feasibility of using the produced water for agricultural irrigation, along with its boron concentration limitations. Croucher et al. (2025) refined the numerical modeling approach for fluid production and reinjection in geothermal reservoirs by developing a novel technique that incorporates source term interactions into the nonlinear solver’s Jacobian matrix. This advancement effectively addressed the issues of poor convergence and the restricted time steps commonly encountered in conventional simulations. The method was subsequently integrated into the Waiwera open-source simulator, and its enhanced performance was validated through testing and real-world case studies. Despite the relative maturity of current methodologies, existing research predominantly focuses on the application of individual approaches or is limited to specific geological contexts. There is a notable lack of studies that systematically integrate hydrogeochemistry, isotopic data, and hydrothermal coupled numerical modeling, particularly in complex tectonic settings.

Laiyuan, located in Hebei Province, lies at the western margin of North China and serves as the source of the Juma River. It is endowed with abundant hydrothermal and geothermal resources. Therefore, this study focuses on the karst geothermal system in Laiyuan, Hebei, aiming to elucidate the genetic mechanisms of karst geothermal water. First, by analyzing the regional geothermal geological background, hydrochemical characteristics, and hydrogen–oxygen isotopic composition, the chemical evolution processes and recharge sources of the geothermal water will be clarified. Subsequently, the modes of heat transfer and heat accumulation will be explored to reveal the water-heat accumulation patterns of the hydrothermal geothermal system. In this regard, the reserves of the karst geothermal reservoir will be estimated, and a sustainable development and utilization model for geothermal resources will be proposed, so as to promote the efficient utilization of geothermal energy and the coordinated protection of groundwater resources.

2. Regional Geological Setting

2.1. Regional Geological Conditions

The Laiyuan area is located in the eastern North China Craton, and its tectonic evolution since the Neoarchean has been primarily controlled by regional tectonic movements. Influenced by the Taihang Mountains fold-fault tectonic belt, the region is characterized by a series of fold structures and fault systems. The fold structures exhibit multiphase composite superposition and can be classified into basement folds and cover folds. The basement folds, composed of an Archean gneissic series, are intensely and complexly deformed with prominent polycyclic superposition features. The cover folds developed within the Middle-Upper Proterozoic to Mesozoic strata, forming broad, gentle synclinal sedimentary basins. Fault structures are extensively developed and predominantly controlled by NE-SW- and NW-SE-trending faults formed under intense crustal compression and shear, mainly thrust-type and strike-slip-type (Figure ). The principal faults include the Taihang Mountain Front Fault and the Laiyuan-Fuping Fault. The Taihang Mountain Front Fault marks the boundary between the Taihang Mountains and the North China Plain, acting as a major thrust fault controlling mountain uplift and plain subsidence. The Laiyuan-Fuping Fault is a significant NE-SW-trending structure influencing the regional geological framework and geomorphological evolution. ,

1.

Simplified map of stratigraphy and fault distribution in the Laiyuan area.

Laiyuan County is located in the contact zone between the eastern foothills of the Taihang Mountains and the Yanshan Mountains, featuring rolling mountains and faulted valleys. The Laiyuan Basin is a typical synclinal karst catchment basin that evolved from the Tuanyuan compound syncline as a Cenozoic fault-depression basin. Together with the Zoumayi Basin to the south and the Dongtuanbao Basin to the north, it exhibits an en-echelon distribution from south to north in an east-northeast direction.

2.2. Regional Hydrological Conditions

The Laiyuan Basin groundwater system, centered on the Laiyuan Basin, constitutes a closed catchment basin where the natural surface water divide and groundwater divide essentially coincide. Controlled by the Paifang-Fengcunnan compressive-torsional fault within the region, the basin is divided into southern and northern sections. In the spring region, exposed strata from the south to north successively include the Archean Fuping Group and Wutai Group metamorphic rock series. The basin is mostly covered by Quaternary strata; Cenozoic Paleogene strata occur sporadically in the southern part; the Proterozoic, Paleozoic Cambrian, and Ordovician are widely distributed in mountainous areas; while the Archean, Proterozoic Changcheng System, and Mesozoic Jurassic occur as minor outcrops in the southern spring region. Groundwater in the Laiyuan Basin can be classified into two hydrogeological zones: a bedrock fissure water zone and a pore water zone. The bedrock fissure water zone is distributed in the mid-high mountainous areas surrounding the basin and consists of limestone and dolomite from the Proterozoic to Ordovician. Cambrian mudstone serves as the sole aquitard. Aquifer water abundance is heterogeneous and strongly controlled by geological structures. In most areas, fracture development is limited, resulting in a limited capacity for rainfall recharge. The pore water zone is mainly distributed in the central part of the basin. In the northern part, the phreatic aquifer is primarily composed of Quaternary alluvial-proluvial sandy gravel and pebble deposits with relatively good water abundance; Paleogene confined water is locally distributed. In the southern part, the phreatic aquifer consists mainly of Paleogene conglomerate and sandy shale, exhibiting a poor water abundance.

3. Hydrogeochemical Characteristics and Implications

3.1. Geothermal Water Chemical Composition

The chemical composition of geothermal water is governed by multiple geological factors, including geological structures, lithological properties, groundwater flow pathways, stratigraphic architecture, tectonic activities, and climatic conditions. Identifying and interpreting the genetic processes of geothermal water through hydrogeochemical characteristics is a vital approach in geothermal research, providing a scientific basis for the utilization of geothermal resources. , In this study, hydrogeochemical data from geothermal fluids in the Laiyuan area of North China (Table ) were collected and subjected to visual analysis. The data indicate that the chemical compositions of geothermal water samples from various locations in the Laiyuan area exhibit a smaller gap. Total Dissolved Solids (TDS) concentrations range from 240 to 604 mg/L, and pH values fall between 7.3 and 8.12, collectively reflecting a weakly alkaline character. Under normal conditions, the TDS value of groundwater gradually increases along the direction of groundwater flow. In the Laiyuan area, bedrock groundwater converges from both flanks toward the core of the Tuanyuan syncline, resulting in a gradual increase in TDS values. The Piper trilinear diagram is a widely utilized technique in hydrochemical analysis, effectively illustrating the characteristics of major ion compositions in groundwater and enabling the differentiation of mixing extents among waters from various sources or evolutionary processes. A Piper trilinear diagram was constructed based on the hydrochemical data of geothermal water (Figure ). Ca²⁺ is the principal cation, accounting for 40% to over 80% of the total cationic composition. Mg²⁺ accounts for 20% to 60%, while Na⁺ and K⁺ are present in lower proportions, each comprising less than 20%. Carbonate ions (CO₃ ^2– and HCO₃ ^–) are the dominant anions, accounting for over 70% of the anionic composition. Cl^– and SO₄ ^2– account for less than 30% of the total anions. Ion concentrations indicate that the geothermal water in the study area is predominantly bicarbonate-type, specifically classified as HCO₃–Ca–Mg, and characterized as slightly mineralized hot water. This composition is consistent with the hydrochemical type of fracture-controlled geothermal water.

1. Hydrogeochemical Composition of Geothermal Water in the Laiyuan Area.

Sample	pH	K+	Na+	Ca2+	Mg2+	Cl–	SO4 2–	HCO3 – + CO 3 2–	SiO2	TDS (mg/L)	Data source
S-1	8.12	2.07	13.6	42.4	22.3	6.7	9.27	198	-	240	This work
S-2	7.88	2.04	13.64	45.55	32.52	5.92	30.71	282.7	15.53	425.7
S-3	7.64	2.57	13.99	46.17	31.95	5.25	30.5	296.6	18.76	442.9
Q-1	7.4	0.27	21.3	46.4	31.1	4.2	38.2	254	-	458	Qiu et al.
Q-2	7.3	4.66	4.28	79.3	36.5	14.5	53.3	300	-	512
Q-3	7.4	1.86	9.61	64.5	16.7	7	61.1	152	-	388
Q-4	7.5	0.67	8.11	61.9	43.6	2.5	90.2	258	-	567
Q-5	7.4	2.05	10.4	46.6	39.9	21.5	29	295	-	544
Q-6	7.5	0.14	2.59	58.3	31.7	16	52.9	211	-	433
Q-7	7.4	0.62	1.25	49	28.3	4.5	10.8	266	-	269
Q-8	7.3	0.63	2.18	36.8	40.7	7.1	5.32	250	-	415
Q-9	7.4	0.36	1.58	78.4	24	20.5	10.8	272	-	477
Q-10	7.4	2.5	25.1	96.2	26.3	17.2	85.5	307	-	604
Q-11	7.4	1.85	16.1	78.9	25.5	14.5	59.5	243	-	407

2.

Piper diagram of geothermal water in the Laiyuan area.

The Gibbs model has been widely acknowledged for its effectiveness in analyzing the influences of atmospheric precipitation, rock weathering, and evaporation-crystallization on natural water bodies. − This method utilizes the ionic ratios of Na⁺/(Na⁺ + Ca²⁺) for cations and Cl^–/(Cl^– + HCO₃ ^–) for anions along with the TDS value to macroscopically assess the controlling factors of major ions in water. The results demonstrate that the geothermal water samples from the Laiyuan area are characterized by a high Na⁺/(Na⁺ + Ca²⁺⁾ ratio, a low Cl^–/(Cl^– + HCO₃ ^–) ratio, and moderate TDS. The geothermal water in the Laiyuan area is predominantly controlled by rock weathering, where the dissolution of various minerals introduces Ca²⁺ and Mg²⁺ into the water body, leading to a relative decrease in the concentrations of Na⁺ and K⁺. These characteristics are indicative of typical karst geothermal water (Figure ).

3.

Gibbs diagram of geothermal water from the Laiyuan area.

3.2. Geochemical Geothermometers

After chemical equilibrium is established between minerals and fluids in the deep geothermal reservoir, the geothermal water maintains its chemical composition largely unchanged during migration and ascent to the surface despite a decrease in temperature. Therefore, the equilibrium temperature of chemical reactions, as reflected in the chemical composition of geothermal fluids, can be utilized to estimate the temperature of deep geothermal reservoirs. − The temperature of geothermal water is a crucial parameter for analyzing the genesis of geothermal systems and assessing the potential of geothermal resources. Currently, utilizing geochemical geothermometers to calculate reservoir temperatures represents the most effective approach. , The geothermal water in the Laiyuan area is in the early stage of water-rock interaction, where the ions in the water have not yet reached equilibrium, making it unsuitable for various ion geothermometers (Figure ). Different crystalline forms of SiO₂ exhibit distinct solubilities, and at temperatures below 300 °C, the solubilities of quartz and amorphous SiO₂ are largely unaffected by pressure and salinity. Therefore, SiO₂ can be employed as a geothermometer to estimate geothermal reservoir temperatures. The SiO₂ geothermometer is employed to calculate the geothermal reservoir temperature and to estimate the circulation depth of groundwater. The calculation follows eq :

$$T=\frac{1039}{5.19-\lg S}-273.15$$ 1

4.

Na–K–Mg diagram of geothermal water in the Laiyuan area.

Where T is the geothermal reservoir temperature, °C; S is the mass concentration of SiO₂, mg/L. Based on the comprehensive water quality analysis data presented in Table , the calculated average limestone reservoir temperature is 48.5 °C.

Additionally, the circulation depth of geothermal water was calculated by using eq :

$${Z=G(t-t}_0{)+Z}_0$$ 2

Where Z is the depth of the circulating geothermal reservoir of karst groundwater, m; t ₀ is the temperature of the isothermal zone, 8.5 °C; G is the geothermal warming gradient, m/°C. This Geothermal warming gradient was determined as 33.3 m/°C through analysis of validated downhole temperature logging data. Z ₀ is the depth of the isothermal zone: 30 m. Based on these parameters, the average geothermal water circulation depth in the region is calculated to be 1,363 m.

3.3. Isotope Signature

The hydrogen and oxygen isotopic compositions (δD and δ¹⁸O) remain stable and unaffected by external environmental changes. The meteoric water line, established based on the relationship between δ¹⁸O and δD in atmospheric precipitation, serves as a crucial reference in isotope hydrology. It is widely applied in hydrogeology and geothermal geology to determine the origin, recharge mechanisms, exchange rates, and age data of groundwater. − Based on the hydrogen and oxygen isotope results of geothermal water in the Laiyuan area (Table ), the δD and δ¹⁸O values in geothermal water are relatively depleted and exhibit minimal variation among the samples. The average δD value is −72.69‰, and the average δ¹⁸O value is −10.22‰. In 1961, Craig established the Global Meteoric Water Line (GMWL) equation, which serves as a fundamental reference for analyzing hydrogen and oxygen isotopic patterns in atmospheric precipitation. This study adopts the regional meteoric water line for Laiyuan to investigate the source, recharge mechanisms, and hydraulic connectivity of local geothermal waters. The geothermal water samples are distributed near the regional meteoric water line, indicating that atmospheric precipitation is the primary source of the geothermal water (Figure ).

2. Hydrogen and Oxygen Isotope Compositions of Geothermal Water in the Laiyuan Area.

Sample	δD/‰	δ18O/‰	Data source
S-1	–77	–11	This work
S-2	–78	–11
W-1	–76	–10.8	Wang et al.
W-2	–76	–10.9
W-3	–73	–10.1
W-4	–76	–10.9
W-5	–66	–9.3
W-6	–68	–9.7
W-7	–71	–10.1
W-8	–69	–9.6
W-9	–73	–10.3
W-10	–72	–10.1
W-11	–73	–9.8
J-1	–70.3	–9.83	Jiao
J-2	–72	–9.8

5.

Relationship between δ¹⁸O and δD in geothermal water samples.

Based on the integration of tectonic geological conditions, hydrogeochemical analyses, and hydrogen and oxygen isotope distribution characteristics, the model of groundwater recharge, flow, and discharge in the Laiyuan area can be preliminarily established (Figure ). The karst mountainous area in the northern periphery of the Laiyuan Basin receives atmospheric precipitation as the infiltration recharge. The precipitate percolates vertically through karst fissures and pores and subsequently flows downward, forming karst groundwater. Owing to the impermeable barrier provided by regional aquiclude formations, such as mudstone and shale, karst water is segregated into aquifer systems composed of limestone and dolomite. The limestone aquifer group is governed by the syncline structure, resulting in groundwater convergence from the limbs toward the axis and subsequent flow along the axis from northeast to southwest. Owing to the barrier effect of the anticline in the southwest, karst water accumulates in the valley zone and flows along the karst development zone toward the northern basin. The dolomite aquifer group, situated on both sides of the syncline, is governed by northeast-trending structural controls and the barrier effect of intrusive rocks in the eastern basin. As a result, karst water flows predominantly along the valley development zones at the basin periphery toward the basin interior. Governed by the concealed fault zone at the basin margin, the majority of karst water flows along the fault zone to deeper levels, mixes within the limestone and dolomite aquifer groups, and subsequently converges toward the basin center. Controlled by the barrier effect of compressional-shear faults, deep karst water ascends along the fracture zone, ultimately giving rise to ascending spring groups such as the Beihai Spring.

6.

Schematic diagram of groundwater recharge, flow, and discharge in the Laiyuan area.

4. Thermal Accumulation and Hydrothermal Coupling of the Geothermal System

4.1. Thermal Accumulation Model in Geothermal Systems

Based on the analysis of controlling factors, including intrusive rocks of various ages and phases, structural distribution, comprehensive water quality, and hydrothermal convection and conduction in the Laiyuan area, a thermal accumulation model suitable for the thermal manifestation areas is proposed (Figure ). The northwestern region of Laiyuan is characterized by karst mountain terrain, where atmospheric precipitation infiltrates and recharges the groundwater. This water percolates vertically through dissolution fissures and pores, subsequently flowing downward to form karst water. Karst water primarily flows along the peripheral gully development zones into the basin, controlled by concealed fault zones at the margins of the fault-depression basin. Except for a portion that laterally recharges the loose pore water within the basin, the majority descends along these fault zones into deeper regions. The magmatic intrusion during the Yanshanian period of the Mesozoic era in the Laiyuan area provided the heat source for the geothermal system. Meanwhile, deep-seated faults developed in the region, cutting through the deep crust, offering pathways for the upwelling of deep thermal fluids. The karst water, after flowing into deeper zones, is heated and transformed into geothermal water. In the Laiyuan area, tectonic fractures resulting from structural activity provide storage space and migration pathways for subsurface fluids, thereby establishing the essential hydrogeological conditions required for the development of geothermal activity zones. The study area is influenced by faults such as the Donggou-Daning and Paifang-Fengcun faults, which provide favorable pathways for thermal reservoirs. Deep geothermal water, constrained by compressional-shear faults that impede its flow, ascends along fracture zones, generating a regional thermal anomaly and forming the geothermal field in the Beihai Spring area.

7.

Conceptual diagram of the local heat accumulation model for the Beihai Spring geothermal field in the Laiyuan area.

4.2. Hydrothermal Coupling Simulation of Geothermal Systems

In the Laiyuan area, geothermal water is primarily controlled by fault structures, where the intersections and compounding zones of multiple fault groups exhibit well-developed fractures and fragmented rocks, forming an abundant limestone thermal reservoir. Therefore, numerical simulations were conducted on both local and regional hydrogeological profiles of the Beihai Spring area in Laiyuan to elucidate the influence of fracture structures on water conduction and heat transfer and to further analyze the regional geothermal water occurrence environment. The influence of water-conducting fractures on geothermal distribution is complex and diverse, and it is governed by the physical properties of the fault fracture zone. Variations in fault thickness, burial depth, and occurrence result in distinct effects on the geothermal distribution. Therefore, this simulation primarily investigates the impact of water-conducting faults on the geothermal field distribution. The simulation was performed by using COMSOL Multiphysics software. In this study, the model was applied to depths up to 1500 m with the rock formation treated as a porous medium. Internal fluid flow was governed by Darcy’s law, and heat transfer was modeled as conduction through the porous medium. , After the model was established and the parameters and boundary conditions were defined, a hydrothermal coupling simulation was conducted for the Beihai Spring area in the Laiyuan area. The simulation results are presented in the figure (Figure ). The results indicate that groundwater is heated at a depth and ascends along fractures. At the F₁ fault, the upward flow of geothermal water is obstructed by the overlying Quaternary loose sedimentary layers and the mudstone on both sides of the fault. In contrast, at the F₂ fault, the absence of a caprock allows geothermal water to rise, forming the Beihai Spring area.

8.

Local-scale hydrothermal coupling simulation of the Beihai Spring geothermal field in the Laiyuan area.

To further investigate the influence of groundwater flow on the distribution of the temperature field within the strata of the study area, a hydrothermal coupling simulation was conducted for the hydrogeological profile (Figure ), with the results illustrated in the figure (Figure ). The results indicate that groundwater flow within karst aquifers can profoundly alter the distribution of the temperature field in the regional strata. Based on the calculated results, temperature data at a depth of 1.0 km from the model were extracted over time and plotted in Figure . As shown in the figure, F₃, F₄, and F₅ serve as groundwater recharge pathways. With the continuous infiltration of cold water through karst aquifers exposed at the surface, the temperature along these fault zones becomes significantly lower than that of the adjacent strata on both sides. After it penetrates the deep subsurface, the cold water migrates further downward and converges with the deep thermal flow at F₁, heating the surrounding rock strata. However, obstructed by the overlying cap layer, it is unable to ascend and instead seeps toward the center of the basin. At F₂ and F₆, where no cap layer is obstructed, geothermal water ascends under the influence of compressional-shear fractures and emerges to form hot springs, consistent with the aforementioned inferences regarding the overall geothermal system. Moreover, the figure illustrates that the temperature of the strata at the fault zone exhibits pronounced fluctuations, demarcating the boundary between temperature decreases and increases. This demonstrates that water-conducting fractures can profoundly alter the distribution of the temperature field in the strata, as the distinct permeability of the fault zone compared to the surrounding rock modifies groundwater flow, thereby influencing the temperature field distribution. ,

9.

Results of hydrothermal coupling simulation for the Laiyuan hydrogeological cross-section.

5. Geothermal Resource Utilization

5.1. Calculation of Geothermal Resource Reserves

The thermal reservoir volume method was selected to calculate the geothermal resource reserves of the thermal reservoir in the Laiyuan area. This method is commonly used in geothermal resource potential assessment and is primarily employed to estimate the total amount of thermal energy stored in the reservoir. The fundamental principle involves calculating the thermal energy contained within the reservoir by integrating parameters, such as the volume, porosity, temperature, and thermophysical properties of the rock and fluid in the thermal reservoir.

The thermal reservoir volume method is expressed as eq :

$$Q_{\mathrm{total}}=[(1-\phi )·{\rho }_{\mathrm{r}}·C_{\mathrm{r}}+\phi ·{\rho }_{\mathrm{w}}·C_{\mathrm{w}}]·V·(T_{\mathrm{r}}{-T}_0)$$ 3

Where Q _total is the total geothermal resource reserves, J; φ is the porosity of the reservoir rock; ρ _r is the density of the reservoir rock, kg/m³; C _r is the specific heat capacity of the reservoir rock, kJ/(kg·°C); ρ _w is the density of geothermal water, kg/m³; C _w is the specific heat capacity of geothermal water, kJ/(kg·°C); V is the volume of the reservoir; T _r is the temperature of the reservoir, °C; T ₀ is the annual average temperature, °C.

As an example, consider a heat reservoir area of 100 km² in the study area with a limestone thickness of 500 m. Using the specified parameters: the density of limestone (ρ _r) is set to 2700 kg/m³; the specific heat capacity of limestone (C _r) is set to 0.921 kJ/(kg·°C); geothermal water density (ρ _w) of 1000 kg/m³; specific heat capacity of water (C _w) of 4.2 kJ/(kg·°C); limestone porosity of 15.25%; reservoir temperature (T _r) of 48.5 °C; and annual average temperature (T ₀) of 8.5 °C. The calculation reveals that the reserves of the 100 km² limestone thermal reservoir in the Laiyuan area amount to approximately 5.50 × 10¹⁵ kJ, equivalent to about 1.88 × 10⁸ tons of standard coal. This considerable reservoir capacity highlights its substantial potential for exploitation.

5.2. Injection-Production Simulation

Numerical simulation enables an assessment of the long-term exploitation potential and system lifespan of geothermal water. Existing studies have demonstrated that geothermal water reinjection can effectively extend reservoir lifespan and mitigate groundwater level decline; however, the advancing cold front from injected water may eventually reach production wells, leading to a thermal breakthrough. Thermal breakthrough time, defined as the moment when extracted geothermal fluid exhibits a measurable temperature decline (typically 1 °C), serves as a critical parameter for evaluating the operational lifespan of geothermal systems. This study employs the finite element method through COMSOL numerical simulation software, with the model constructed by extending a local stratigraphic profile (Figure ) into a three-dimensional representation measuring 1500 × 1000 × 980 m (Figure ). A production well and an injection well were configured with a well spacing of 500 m and a depth of 700 m, both completed in the reservoir. The geological formations are treated as porous media, where groundwater flow follows Darcy’s law, and heat conduction in the rock adheres to Fourier’s law. Several assumptions were also made: the groundwater remains in a liquid state with no loss during flow; the properties of the rock remain constant throughout the simulation; and there are no chemical reactions between the porous medium and the injected fluid.

10.

Model domain dimensions for numerical simulation.

Both lateral boundaries of the model are set as open boundaries connected to permeable layers, and the effect of the rock heat generation rate is not considered during the calculations. The model surface is set at a standard atmospheric pressure of 1 × 10⁵ Pa, with a vertical formation pressure gradient of 0.01 MPa/m. The temperature of the injected geothermal water was set at 8.5 °C. The temperature of the injected geothermal water was set at 8.5 °C, corresponding to the temperature of the neutral zone. The mesh was discretized by using triangular elements, and a mesh independence test was conducted. Both lateral boundaries of the model were defined as being insulated. The simulation was conducted under transient conditions, with time measured in years and an output time step defined as a range (0, 0.1, 50). The simulation results remained essentially consistent as the mesh density increased, demonstrating that the mesh configuration had a minimal impact on the simulation. To reduce the computational costs, Mesh3 was selected for the configuration. The complete mesh consists of 237,310 domain elements, 32,536 boundary elements, and 4,353 edge elements (Figure ). The fault thickness was set to 0.005 m. The model parameters are configured as shown in Table . Model parameters were configured based on existing data from this study, simulating temperature variations in the production well under different extraction rates (150 m³/h, 200 m³/h, and 250 m³/h), with injection rates maintained equal to the extraction rates.

11.

Mesh generation for the numerical model.

3. Parameters for Hydrothermal Coupling Simulations.

Rock Strata	Specific Heat Value(J/(kg·K))	Porosity	Thermal Conductivity Value(W/(m·K))	Permeability Value(m2 )	Density Value(kg/m3)
Quaternary	1.5	1e–17	5	800	2600
Paleogene	1.8	1e–16	10	850	2700
Cambrian	2.78	2e–16	15	850	2750
Ordovician	5.0	4e–14	18	900	2700
Fault	2.50	1e–11	20	750	2600

The numerical simulation results demonstrate that the thermal breakthrough time decreases significantly with increasing extraction rates (Figure ). At an extraction time of 24.5 years, which marks the occurrence of thermal breakthrough under an extraction rate of 200 m³/h, the figure also shows that the cold front induced by reinjection precisely reaches the production well (Figures and ). This indicates that while increasing the extraction rate can enhance heat recovery, it shortens the operational lifetime of the geothermal system. Therefore, geothermal resource extraction should be optimized based on local conditions and demand to determine an appropriate extraction rate.

12.

Temperature variation curves for different extraction rates.

13.

Profile of reservoir temperature variation with extraction time at 700 m depth under an extraction rate of 200 m³/h.

14.

Vertical profile of thermal reservoir temperature variation with extraction time at an extraction rate of 200 m³/h.

5.3. Limitations and Future Work

Compared with traditional single-method studies, this research innovatively integrates hydrogeochemistry, isotope tracing, and hydrothermal coupling numerical modeling to systematically elucidate the genetic mechanisms and thermal controlling factors of the Laiyuan karst geothermal system, providing a scientific basis for the sustainable development of geothermal resources in the area. However, this study still has certain limitations:

• (1)The numerical simulations are based on a series of simplified assumptions and fail to fully account for the heterogeneity and dynamic evolution of actual geological conditions, which may lead to deviations between the simulation results and the behavior of the real system. Future work should involve conducting fine-scale multiphase and multicomponent simulations that incorporate chemical reactions, anisotropy, and heterogeneity to enhance prediction reliability.
• (2)The limited number of geochemical and isotopic samples, coupled with their uneven spatial distribution, constrains our ability to comprehensively characterize the spatial variability and temporal evolution of regional geothermal fluids. Currently, only the Gibbs model has been employed for a single reaction analysis, which is insufficient to delineate the complex water-rock interactions and mineral phase transitions involved. Future work should increase the density and frequency of sampling, coupled with long-term dynamic monitoring data, to establish a high-resolution model of the geochemical evolution of fluids. Additionally, thermodynamic models and atmospheric precipitation chemistry data should be employed, utilizing relevant geochemical tools to analyze the extent of water-rock reactions and the processes of mineral phase transitions.
• (3)The estimation of geothermal resources was simply conducted using the thermal reservoir volumetric method, without accounting for the impacts of uncertainties in critical parameters such as porosity, temperature, and thermal properties on accuracy, nor was an economic feasibility assessment performed. Future work should further establish multidimensional resource assessment models to provide robust support for practical development decision-making.
• (4)Mine geothermal resources follow a seasonal utilization pattern, being used for irrigation in summer and for mine heating and wellbore insulation during winter. However, during nonheating seasons, the utilization pathways for thermal resources remain constrained, often resulting in wastage of geothermal energy. Therefore, future research should focus on developing rational utilization methods for geothermal resources in nonheating periods.

6. Conclusion

Based on the geological structure and hydrogeochemical characteristics of the study area, this research analyzes the heat accumulation mechanisms in the mining region, establishes a coupled hydrothermal numerical simulation model for karst geothermal water, and explores the development and utilization of regional geothermal resources. From the research findings presented above, the following key conclusions are drawn:

• (1)The geothermal water in the Laiyuan area is chemically characterized as HCO₃–Ca–Mg type with low mineralization, indicating typical karst water origins controlled by water-rock interaction. Geothermometer calculations yield an average reservoir temperature of 48.5 °C and a circulation depth of 1363 m.
• (2)Isotopic compositions of hydrogen and oxygen reveal that atmospheric precipitation is the primary recharge source. The water infiltrates vertically through karst fractures and conduits, undergoes deep circulation and heating, and ascends along compressional-shear faults that act as both pathways and hydrological barriers, thereby creating regional thermal anomalies.
• (3)Hydrothermal coupling simulations demonstrate that groundwater flow in the karst aquifer significantly controls the geothermal field distribution. Water-conducting faults not only act as major conduits shaping the subsurface temperature pattern but also constitute thermal boundaries that demarcate temperature gradients.
• (4)Based on volumetric estimation, the limestone aquifer in the 100 km² study area contains approximately 5.50 × 10¹⁵ kJ of geothermal energy, indicating substantial resource potential. Simulation results for different exploitation scenarios demonstrate that higher extraction rates enhance short-term heat recovery but accelerate system decline. Therefore, sustainable extraction rates should be carefully determined based on long-term demand.

Data used is available throughout the manuscript text.

The authors declare no competing financial interest.