Hydraulic Relationships Research Articles

A start-up optimization strategy of a hydroelectric generating system: From a symmetrical structure to asymmetric structure on diversion pipes

This study focuses on the start-up optimization strategies for a Hydroelectric Generating System (HGS). A mathematical model of HGS to describe the complex hydraulic coupling relationship, between the water diversion pipes, the hydro-turbine, the governor and the generator, is proposed. This allows to accurately describe the start-up process and identifying the effect of successive start-up time interval (ΔT) and the pipe structure on the water head and the rotational speed of HGS. The result shows that the successive start-up strategy with ΔT = 9s maximally reduces the water head fluctuation of units #1 and #2 by 30.94% and 25.77% compared with the simultaneous start-up strategy when the branch pipe is symmetric. For the asymmetric branch pipe, the unit behind branch B# starts up first is beneficial to reduce the water head fluctuation of the unit behind branch #A when the flow inertia time constant of branch #A is larger. Finally, the parameters of the start opening as well the PID governor parameters are optimized by a multi-objective particle swarm optimization for the asymmetric pipe in order to minimize the unit speed overshoot and the speed rise time. These results in this work provide a theoretical guidance for the selection of optimal start-up strategy in the case of symmetric and asymmetric HGS branch pipe structures.

Research on clearance model for electricity market with cascade hydropower stations

Together with power structural reform, the intended contribution target of carbon neutral and carbon peaking aims to promote the market-based consumption of renewable energy, which has become an essential task for the construction of China’s power market. Cascade hydropower is a special form of hydro-generation, the upstream and downstream power stations have a close hydraulic coupling relationship with each other. In order to ensure the fair participation of all generation entities in the market and improve the feasibility of the transaction results, the operational characteristics of the cascade hydropower should be integrated into the market clearance model. In this paper, a day-ahead market case including six generation entities is designed, and the rationality and practicality of the clearance model are verified by analyzing the results of market transaction in different operation scenarios.

From cells to stems: the effects of primary vascular construction on drought-induced embolism in fern rhizomes.

While a considerable amount of data exists on the link between xylem construction and hydraulic function, few studies have focused on resistance to drought-induced embolism of primary vasculature in herbaceous plants. Ferns rely entirely on primary xylem and display a remarkable diversity of vascular construction in their rhizomes, making them an ideal group in which to examine hydraulic structure-function relationships. New optical methods allowed us to measure vulnerability to embolism in rhizomes, which are notoriously difficult to work with. We investigated five fern species based on their diverse xylem traits at the cellular, histological, and architectural levels. To link below- and above-ground hydraulics, we then measured leaf-stem vulnerability segmentation. Overall, rhizome vulnerability to embolism was correlated most strongly with cellular but not histological or architectural traits. Interestingly, at P6-12 , species with increased architectural dissection were actually more vulnerable to embolism, suggesting different hydraulic dynamics at low compared to high percent embolism. Importantly, leaves fully embolize before stems reach P88 , suggesting strong vulnerability segmentation. This is the first study to explore the functional implications of primary vascular construction in fern rhizomes and leaf-stem vulnerability segmentation. Strong segmentation suggests that leaves protect perennial rhizomes against severe drought stress and hydraulically induced mortality.

Rationalizing the Differences Among Hydraulic Relationships Using a Process‐Based Model

AbstractThe use of power law forms to describe hydraulic geometry is a classic subject with a history of over 70 years. Two distinct forms of power laws have been proposed: at‐a‐station hydraulic geometry (AHG) and downstream hydraulic geometry (DHG). Although the utility of these semiempirical expressions is widely recognized, they remain poorly understood in terms of the mechanisms underlying the differences between AHG and DHG, as well as the variability among different systems. In this study, we attempt to address these basic issues. Two hypotheses are proposed: (a) the different geomorphic relationships represented by AHG and DHG result from the control of lateral adjustment of the bank and flow turbulence over short and long timescales, respectively; and (b) the systematic variability of the AHG and DHG exponents is related to the description of the frictional resistance. These two hypotheses are embedded in our theoretical models and lead to explicit functional forms for AHG and DHG. The verification of our hypotheses is based on a large data set consisting of over 550 b‐f‐m exponents and 120 power law hydraulic relations. The analysis highlights the role of uncertainties in data acquisition and theoretical/statistical explanations. In addition, the theoretical expressions of AHG also provide an explanation of at‐many‐stations hydraulic geometry (AMHG) in a physical sense. Overall, our work provides new insights into the fundamental theory of power laws and hydraulic geometry.

Hydraulic properties of unsaturated calcarenites by means of a new integrated approach

Most infiltration and water retention models for unsaturated porous media proposed in the literature often are based on simplified representations of the pore system and use the matric head as the main state variable.An integrated study on the hydraulic properties of homogeneous calcarenites with a complex pore network is presented, aimed at assessing water infiltration and retention mechanisms, starting from dry to wet conditions under high water inflow.Medium-grained grainstones and fine-grained packstones were used as material for laboratory testing and model set up. Petrophysical characterization and bimodal distribution of pore volume was obtained by standard and unconventional procedures. Permeability test under saturated conditions was performed with constant and falling head tests. Falling head infiltration tests at bench scale were carried out to estimate the hydraulic properties of the materials under unsaturated conditions.Unsaturated hydraulic relationships such as the soil water retention curve (SWRC) and hydraulic conductivity function were examined. The advection–diffusion form of Richard’s equation, together with the pore bundle model and dual porosity concept under equilibrium conditions represent the theoretical framework used to investigate the unsaturated hydraulic behavior of the calcarenites in the falling head infiltration test. The SWRC, relative hydraulic conductivity and celerity were determined through the capillary theory and pore bundle concept considering the bi-modal nature of the pore-size distribution. Theoretical solutions and model predictions were compared with experimental data, which demonstrated the dominant control of macro-porosity on water flow and infiltration rate. In particular, our experimental results indicate that the wetting front propagates mainly through the macropores with a gravity driven flow velocity higher than the diffusive flow through the micropores. The effect of texture, degree of saturation and boundary conditions on infiltration dynamics is discussed.

Identification of Hydraulic Connection Points between Different Confined Aquifers in the Liyazhuang Coal Mine

Water inrush from coal seam floors is one major geological obstacle hindering safe and efficient production activities in mines. Determining the source of water inrush can facilitate its prediction and guide decisions regarding measures for prevention and control. The process of identifying the location of hidden hydraulic contact points in different confined aquifers forms the basis of hydrogeological explorations. It is also the basis for categorizing mine areas prone to water inrush and making qualitative decisions regarding the prevention and control of water inrush. In this study, the positions of hidden hydraulic contact points between the Ordovician Fengfeng and Shangmajiagou formations in the basement of the Liyazhuang coal mine were determined using numerical simulations of the flow fields. First, each node of the finite element grid was considered as a water inrush point to determine the water level at other nodes. Subsequently, the error between measured and simulated water levels, determined based on the flow fields, was determined using the least squares method. The node with the minimum error was then considered as the hidden hydraulic contact point. The simulation results for the flow field indicate a distance of 5000 m between the hydraulic connection and the water inrush points located between the peak formation and the Majiagou aquifer in the Liyazhuang coal mine. Furthermore, the hydraulic relationship between them is poor. Observational data of water inrush from the floor of the No. 2 coal seam and the water level of the confined aquifer in the Liyazhuang coal mine, including the water quality test data of different Ordovician ash aquifers, show that the source of water inrush from the floor of the No. 2 coal seam is the aquifer of the Fengfeng Formation. This finding is consistent with the results of the numerical simulations of the flow field. The results demonstrate that, in mining areas subjected to high pressures, numerical simulations of the flow field can serve as an effective tool for determining the location of hidden hydraulic contact points.

Failure of the Conventional Expression of Tortuosity in Granular Porous Solids

The tortuosity of porous solids has been widely used as a basic concept in understanding the fluid flow capacity of these media. Starting from a geometric expression of the tortuosity, different relationships have been developed over time to estimate it from different perspectives as hydraulic, electrical, and molecular diffusion, making necessary an exhaustive analysis of these developments. In this study, evidences for the lack of the true hydrodynamic sense of the conventional expression of tortuosity are shown. As a first sign of its failures, the disparity of results between the different relationships of tortuosity–porosity derived from this conventional expression is shown. Next, the presentation of several examples directly shows that the value obtained with that conventional expression is the same in cases where the actual tortuosity is obviously different. Likewise, a routine physical analysis of the flow in this study shows that the use of the capillary analogue is erroneous for one-dimensional flow analyses. Another inconsistency has been encountered in the widely used equality between the volumetric porosity and the product of free cross-sectional area by the length representing the path of the fluid through the pores. The last key showing the deficiencies of these estimations of the tortuosity is the constraint of the use of constant section ducts in the electrical analogy. As a new expression of tortuosity, an alternative ratio is proposed which can be included in known hydraulic and electrical relationships, in the same way than the conventional tortuosity. This tortuosity ratio constitutes a rethinking of the knowledge and understanding of flow in granular porous media.

An optimization model for joint power generation dispatching of the cascade hydropower stations on the lower reaches of Jinsha River and the Yangtze River

The Xiluodu, Xiangjiaba, Three Gorges and Gezhouba cascade hydropower stations, which located at the lower reaches of Jinsha River and the upper reaches of Yangtze River, plays a very important role in the electrical power system in China. To optimize and solve the joint power generation problem of the cascade system with highly complex constraints, hydraulic relationship and multiple dispatching objectives, this research focus on: (1) a mid-and-long term power generation optimization model for the cascade system is established, considering hydraulic and electricty connections, as well as the flood control, water supply and ecology objectives; (2) an improved LSSDC-DDDP hybrid optimization framework, based on the theory of large-scale system decomposition coordination (LSSDC) and the discrete differential dynamic programming (DDDP), is designed to well solving the proposed optimization model. In the optimization framework, a relative coefficient is used to calculate the coordination factor among subsystems (a single hydropower station); meanwhile, an adaptive corridor and a bias corridor are adopted to enhance convergence speed of DDDP. The optimization model is applied in the dispatching calculation of the cascade system using the 2015-2017 actual runoff conditions, respectively. The results indicate that joint optimal dispatching of the cascade system can theoretically increase its yearly total power generation benefit about 2.73 billion yuan on average, simultaneously satisfying the requirements of downstream water supply and improving the total firm output guarantee rate of the system.

Clearing Model for Day-ahead Market Considering Hydraulic Coupling Relationship of Multi-operator Cascade Hydropower Stations

There is a hydraulic coupling relationship between the upstream and downstream of cascade hydropower stations, and they usually belong to different stakeholders. Traditional clearing mechanism may lead to the mismatch between the bid-winning power and the actual power generated by the downstream power stations, and the low-cost downstream power stations may lose some chance to generate, resulting in damage to social welfare. This paper analyzes the problems faced by multi-operator cascade hydropower stations participating in the day-ahead market. By deducing the generation coupling relationship between upstream and downstream cascade hydropower stations, it is found that the output of downstream hydropower stations can be divided into four parts: fixed part, adjustable part, the part coupled with the output of the upstream power station, the part coupled with the output of the upstream power station and the adjustable output. At last, day-ahead market clearing mechanism and settlement mechanism for downstream power stations to participate in bidding are proposed.

Влияние засоления на устьичную и гидравлическую проводимость, а также на уровень аквапоринов в клетках листьев растений ячменя, различающихся по солеустойчивости

We studied participation of aquaporins in the regulation of leaf hydraulic conductivity and relationship of hydraulic conductivity with accumulation of ABA and stomatal closure during salt stress. Using the method of immunohistochemical localization we showed that salinity led to greater decline in the level of aquaporins in the region of the vascular leaf bundles of the more salt-tolerant Prairia cultivar, accompanied by a noticeable decrease in hydraulic conductivity of the leaf. In the less salt-tolerant plants of the Mikhailovsky cultivar, significant changes in the level of aquaporins under the influence of salt stress were not found. The degree of decrease in the hydraulic conductivity of the leaf in plants of two cultivars under the influence of salt stress correlated with a decrease in transpiration. Immunohistochemical localization of abscisic acid (ABA) in leaf cells showed that during salt stress this hormone accumulated in leaf mesophyll cells and stomata. The uptake of exogenous hormone from the nutrient solution and its entry into the leaf through the vascular bundles was accompanied by an increase in staining for aquaporins and the hydraulic conductivity of the leaves, which is characteristic of the ABA action. Differences in the localization of exogenous and endogenous hormones were obviously the cause of the opposite directions of changes in hydraulic conductivity: its increase under the influence of an exogenous ABA and a decrease - under the influence of salt stress. ABA concentration assessment in xylem showed the absence of its increase during salt stress, which explains the absence changes of staining for this hormone in the region of the leaf vascular bundles and indicates that accumulation of ABA in a short-term salt stress is not the result of its delivery from the roots, but the result of its synthesis in the shoot itself.

Use of Multidimensional Models to Investigate Boundary Shear Stress through Meandering River Channels

Three-dimensional hydraulics were simulated through a wide range of synthetically generated meandering river channels to determine how channel curvature and width would correlate with the maximum boundary shear stress. Multidimensional models were applied, similar to a computational flume to simulate a wide range of 72 meandering channels, developed from sine-generated curves. Cannel sinuosity ranged from 1.1 to 3.0 and included five consecutive meander bends. Longitudinal slopes of the various channels spanned four orders of magnitude, while bankfull discharges spanned three orders of magnitude. Using results from one-half of the simulation sets, an empirical correlation was found to predict the maximum boundary shear stress as a function of dimensionless ratios of channel curvature and width. The remaining simulation sets were used for verification. Multidimensional models were used to simulate channel hydraulics to efficiently investigate a wide range of channel sinuosity, width/depth ratios, bankfull discharges, and valley slopes. When simulating such a wide range of channel conditions, multidimensional models offer a more efficiency method of generating consistent datasets than either field studies or physical modeling. This paper demonstrates how multidimensional models can be used to identify important hydraulic relationships that are otherwise difficult to determine.

Equilibrium sediment transport, grade and discharge for suspended-load-dominated flows on Earth, Mars and Titan

Recent surface observations have emphasised the importance of bedload transport by rivers and streams on Mars and Titan. Previous “hydraulic” analysis, however, has also shown that transport as suspended load should be possible, if not more prevalent due to lower critical shear stresses, under reduced gravity conditions compared with Earth; where the dominant mode of sediment flux by rivers is as suspended load. A new suspended-load equilibrium condition (zero net erosion and deposition) constraint is advanced, using a flux-balance model applicable to transport (capacity) limited alluvial channels. The theory unifies Gilbert's relation for slope and flow capacity model with the Shields criterion for incipient motion. Shields-stress analysis shows that sediment transport thresholds on Earth, Mars and Titan are dynamically similar. Thus, despite large differences in dimensional shear stresses, variations in the critical slopes and flow depths required for threshold and equilibrium conditions are comparatively modest. Under reduced gravity conditions, there exists a slightly higher potential for sediment transport as suspended load; except for systems involving high particle-fluid density ratios, as may apply to the transport of organic particles on Titan. Critically we show that graded suspended-load channels should develop gentler slopes under reduced gravity, and not steeper slopes as previously inferred based on generalized hydraulic geometry relationships of terrestrial river and submarine channels. We further argue that the use of submarine channels as analogues for channels formed under reduced gravity is not physically justified. Finally, compared with bedload channels, suspended-load channels should also have markedly higher discharges, with implications for mechanistic-based discharge predictions and precipitation models.

Hydraulic and Mechanical Relationship of Individual Fracture in Rock under Compression and Shearing: Theoretical Study

In this paper, a new approach has been developed for predicting the hydraulic and mechanical relationship of individual fractures subjected to normal stress and compression-shear stress. Considering that the closure process of rough fracture subjected to normal stress can be divided into two phases (linear behavior and nonlinear behavior), a relationship between normal stress and fracture aperture is derived through the minimum potential energy principle. Then, a formulation for calculating fracture permeability during shearing and compression processes is developed. Furthermore, a formulation for determining fracture aperture during the crack growth process is obtained, which is further implanted into the permeability model to predict the hydraulic behavior of fractured rock during fracture propagation. This new model not only considers the normal deformation of the fracture but also, and more importantly, integrates the effect of fracture propagation and shear dilation. Theoretical studies demonstrate that fracture permeability increases nonlinearly during fracture propagation. At last, experimental results and analytic results are compared to demonstrate the usefulness of the proposed models, and satisfactory agreements are obtained.

The Bayes Recognition Model for Mine Water Inrush Source Based on Multiple Logistic Regression Analysis

Accurate recognition of water inrush sources is important in mine water hazard control. In this study, 118 water samples of four water types in the Qinan coal mine were analysed by multiple logistic regression, and the 12 water samples that did not meet the requirements were removed. The remaining 106 were used as training samples to establish a Bayes recognition model (BRM). In addition, the BRM was used to complement multiple logistic regression analysis (MLRA) to discriminate other water samples in the mining area. The recognition accuracy of the combined model was 95.28%. The results from the model were consistent with the field water samples and showed that the combined MLRA-BRM approach fully considers the hydraulic relationships between different aquifers and a mixed water inrush source. Moreover, the MLRA-BRM combination improved water inrush source recognition accuracy and was more reliable than using MLRA or BRM alone.

New insights into the hydrogeology and groundwater flow in the Great Barrier Reef catchment, Australia, revealed through 3D modelling

Study regionThe Great Barrier Reef catchment is located adjacent to the world's largest coral reef system, the Great Barrier Reef, in eastern Queensland, Australia. Study focusThis study characterized the geologic and hydrogeologic settings and evaluated the influence of regional faults on groundwater flow. 3D geological models of six regions within the catchment were constructed using drill-log data from >49,000 wells, digital elevation models and surface geological maps. The 3D models were then integrated with potentiometric surface maps and faults data to conceptualize the hydraulic relationships of aquifer units and estimate groundwater development potentials. Potentiometric surfaces and fault orientations were used to conceptualize groundwater flow directions. New hydrological insights for the regionThe 3D geological and hydrogeological characterizations revealed previously unknown faults and aquifer units in the study area. The study found that the central regions consisted of fractured and porous-unconfined aquifers, while confined aquifers, which extend to the coast and likely beyond, were also found in the northern and southern most regions. The orientations of the faults trended in NW-SE directions and could form conduits for south-easterly groundwater flow as opposed to the predominate easterly flow in the porous-unconfined and confined aquifers. The 3D models, aquifer connectivities and geometries provided crucial information to determine groundwater development potentials and offer a first step in developing local and regional groundwater flow and contaminant transport models.

Numerical method for identifying the flow model in the line pipe

With high availability of measuring tools and wide opportunities of modern computer technology, the existing methods of predictive estimations of hydraulic parameters for the fluids’ pipeline transport seem to be too approximate. Due to this, it is relevant to adapt the most accurate relationships available in the scientific and technical literature to real conditions. Based on the review of analytical solutions for calculating friction losses in the pressure lines, the structure of relationships most accurately reflecting the experimental data of I. Nikuradze is determined, where the hydraulic drag coefficient ? is described by the piecewise-continuous relations, given by O. M. Ayvazyan. The hydraulic drag coefficient structural relationship shall be selected with the highest capability to summarize the experimental data available in the scientific and technical literature. Using the pressure measurement data, free parameters included in the selected relationship for the hydraulic drag coefficient shall be identified. The numerical computation algorithm is proposed that enables to recover the values of parameters in the structural relationship of hydraulic drag coefficient ? through multiple application of the well-known method of sensitivity functions and pressure measurement data in the line pipe. The procedure is described for generating the computing system of ordinary differential equations that enables for every fixed set of experimental data (pressure and flow rate) to determine (or correct, if necessary) the corresponding parameters in the unified structural relationship for hydraulic drag coefficient ?. The feature of the proposed algorithm is the absence of embedded cycles. Dynamic control of variable parameters in the hydraulic drag coefficient ? based upon the proposed approach enables to improve the predictive estimations accuracy of flow parameters while pumping fluids and to acquire additional data on the state of the fluids filling the inner pipeline space.

Reach‐scale bankfull channel types can exist independently of catchment hydrology

AbstractReach‐scale morphological channel classifications are underpinned by the theory that each channel type is related to an assemblage of reach‐ and catchment‐scale hydrologic, topographic, and sediment supply drivers. However, the relative importance of each driver on reach morphology is unclear, as is the possibility that different driver assemblages yield the same reach morphology. Reach‐scale classifications have never needed to be predicated on hydrology, yet hydrology controls discharge and thus sediment transport capacity. The scientific question is: do two or more regions with quantifiable differences in hydrologic setting end up with different reach‐scale channel types, or do channel types transcend hydrologic setting because hydrologic setting is not a dominant control at the reach scale? This study answered this question by isolating hydrologic metrics as potential dominant controls of channel type. Three steps were applied in a large test basin with diverse hydrologic settings (Sacramento River, California) to: (1) create a reach‐scale channel classification based on local site surveys, (2) categorize sites by flood magnitude, dimensionless flood magnitude, and annual hydrologic regime type, and (3) statistically analyze two hydrogeomorphic linkages. Statistical tests assessed the spatial distribution of channel types and the dependence of channel type morphological attributes by hydrologic setting. Results yielded 10 channel types. Nearly all types existed across all hydrologic settings, which is perhaps a surprising development for hydrogeomorphology. Downstream hydraulic geometry relationships were statistically significant. In addition, cobble‐dominated uniform streams showed a consistent inverse relationship between slope and dimensionless flood magnitude, an indication of dynamic equilibrium between transport capacity and sediment supply. However, most morphological attributes showed no sorting by hydrologic setting. This study suggests that median hydraulic geometry relations persist across basins and within channel types, but hydrologic influence on geomorphic variability is likely due to local influences rather than catchment‐scale drivers. © 2020 John Wiley & Sons, Ltd.

Simulation on the stochastic evolution of hydraulic geometry relationships with the stochastic changing bankfull discharges in the Lower Yellow River

Extreme weather is an important noise factor in affecting dynamic access to river morphology information. The response characteristics of river channel on climate disturbances draw us to develop a method to investigate the dynamic evolution of bankfull channel geometries (including the hydraulic geometry variables and bankfull discharges) with stochastic differential equations in this study. Three different forms of random inputs, including single Gaussian white noise and compound Gaussian/Fractional white noise plus Poisson noise, are explored respectively on the basis of the classical deterministic models. The model parameters are consistently estimated by applying a composite nonparametric maximum likelihood estimation (MLE) method. Results of the model application in the Lower Yellow River reveal the potential responses of bankfull channel geometries to climate disturbances in a probabilistic way, and, the calculated average trends mainly run to synchronize with the measured values. Comparisons among the three models confirm the advantage of Fractional jump-diffusion model, and through further discussion, stream power based on such a model is concluded as a better systematic measure of river dynamics. The proposed method helps to offer an effective tool for analyzing fluvial relationships and improves the ability of crisis management of river system under varying environment conditions.

Investigating the interaction of hydraulic fracture with pre-existing joints based on lattice spring modeling

Abstract Pre-existing joints have a significant influence on the geometry of the fracture network induced by hydraulic fracturing. Understanding the interaction between hydraulic fractures (HF) and pre-existing joints is of great importance to optimize the design of hydraulic fracturing operations in many applications. A three-dimensional hydro-mechanical coupled lattice-spring code was employed to investigate the interaction mechanisms under different pre-existing fracture shear strength (cohesion and friction angle), in-situ stress, angle of approach, and varying treatment parameters (fluid viscosity and injection rate). Simulation results indicate that hydraulic fractures tend to cross pre-existing joints for high magnitudes of assumed of fracture cohesion, friction angle, stress difference, approach angle, fluid viscosity, and injection rate. Three basic model hydraulic fracture-joint relationships were noted which were termed zero-joint crossing, 1-joint crossing and 2-joint crossing. For varied assumed shear strength, in-situ stress, approach angle and treatment parameters, the contribution of tensile-failure in intact rock and shear-failure on pre-existing joints tends to be enhanced or reduced, which controls the dominant observed interaction behavior (slip or crossing) as well as the variation in the resulting stimulated reservoir area.

Validation of the operation efficiency criteria for geothermal probes in flooded mine workings

Purpose. To develop and test the energy and cost criteria for evaluating the operation efficiency of a closed geothermal system using coaxial or U-shaped probes that can be installed in flooded workings of mines. Methodology. To justify the energy and cost criteria, we applied thermodynamic, hydraulic and cost-efficiency relationships, conducted the engineering analysis of closed geothermal systems, studied hydrogeological settings and geothermal conditions of the mines of the Selidovo group in Donbas. The developed criteria were examined within the ranges of key parameters such as the flow rate of the heat transfer fluid and the probe submerged length. Findings. We quantified the influence of the probe submerged length and the heat transfer fluid flow rate on the energy balance and the net present value NPV and identified the parameter combinations that allow achieving efficient heat recovery in terms of energy balance and cost-efficiency. The produced/spent energy ratio may reach 1.52.2 and the NPV a few dozen thousand when increasing the submerged depth to 500 m at the flow rate of 20m3/d. A higher flow rate may lead to a negative energy balance but the NPV remains positive within some ranges of the probe submerged length, thus, indicating the system profitability. The payback period can be shortened to a few years. Originality. The proposed energy criterion balances the thermal energy produced and the thermal equivalent of electric energy generated using fossil fuel and spent on system operation. This ratio as distinct from the usually applied COP parameter allows comparing the energies of the same nature and drawing more adequate conclusions on environmental acceptability of a geothermal system. Practical value. The proposed criteria can be used for prioritization of geothermal system installation and the operation efficiency evaluation among the number of potential sites in post mining areas.