The energy receiving-conversing devices are mainly composed of wind turbines, photovoltaic generators, and transformer station. Wind turbines and photovoltaic generators convert the wind and solar power into electricity, respectively. Their power P w and P s can be expressed by (Boumaaraf et al., 2018; Pali and Vadhera, 2018; Yesilbudak, 2018) P w = 1 2 c t ρ a π R 2 u a 3 , (1a) P s = α A J s η s o ( 1 − η L ) , (1b) where c t is the efficiency of wind turbines capturing the wind. ρ a represents the air density. R is the length of the blades on the wind turbines and u a is the wind velocity. α , η s o , and η L are solar fraction, efficiency of photovoltaic generator, and heat loss rate.   J s is the solar radiation intensity in W/m². η L is the heat loss rate of photovoltaic generator. Before using the electricity with hydraulic pumps, electricity transmission is necessary to obtain an appropriate voltage, which may cause some electricity losses (Han et al., 2017). P t m = η t m ( P w + P s ) , (2) where η t m is the comprehensive efficiency of the electricity transmission. P t m and η t m are the output and overall conversion efficiency of the electricity transmission station.

The energy transferring devices include hydro-pump/turbine and penstock. The input power of a pump P h p ,   i n is related to the excess energy transmitted via the transmission station. The water flow pumped from lower reservoir to upper reservoir can be calculated by (Novara and McNabola, 2018) P t m = P h p ,   i n   = Q h p ρ w g H a v η h p , (3) where ρ w and g are water density and gravitational acceleration, respectively. H a v is the lifting height, i.e., the elevation difference between the two reservoirs. Q h p and Q h t are the flow rates. η h p is the efficiency of hydro-pumps.

The hydraulic turbine converts the potential energy of water in the upper reservoir into electricity, in which output power P h t ,     o u t can be evaluated by P h p ,   o u t = η h t ρ w g H a v Q h t . (4)

The efficiency of a hydro-pump/turbine normally varies from 0.86 to 0.95, with water flow, head, etc. In this paper, for simplicity, it is considered constant and equal to 0.91.

Transmission over long distances results in loss of hydraulic energy, due to the friction between the fluid and pipe wall. The pressure loss P of water flow in the penstocks can be evaluated by (Fan et al., 2018b; Fan et al., 2019a) ΔP L = λ d ρ w u w 2 2 , (5a) λ = 0.11 ( R u d ) 0.25 , (5b) where λ is the drag efficiency and can be calculated using absolute friction. u w represents the water velocity inside the pipes. L and d are the length and diameter of the penstock. R u is the absolute roughness of penstock interior walls.

As coal is mined, the remained space in goafs was filled with rubbles from proof and floor surrounding rocks (Figure 3). Above the rubbles, the rock formations generate a large number of fractures and cracks due to the large displacement (Li et al., 2018). In the further rock, small displacement just induces deformation without fractures forming. The three overlaying rock zones of different fractures above the mined coal seam are known as “vertical three zones,” namely, the caving zone, the fissure zone, and the displacement zone (Jiang et al., 2016; Shu et al., 2019). After coal mining, massive fissures and pores, capable of storing water, form in the goaf. The caving zone and fissure zone contain massive pores and fissures, capable of storing water. The rock in the displacement zone only displays some micro-fractures, which has no storage capability, but has a considerable permeability due to the formation of micro-fractures (Liu et al., 2020).

The range of the caving zone and the fissure zone would vary with lithology of the overlying rock and thickness of the mined coal seam and can be estimated with numerical simulations (Dong et al., 2016), physical detection (Deng et al., 2018; Ren and Wang, 2020), or empirical models (Peng, 1984). To facilitate calculation, an empirical model was used. If the overlaying rocks are hard rocks, the height of the caving zone ( h 1 ) and the height of the fissure zone ( h 2 ) can be evaluated by Eqs. 6a,b (Peng, 1984), h 1 = 100 M 2.1 M + 16 + 2.5 , (6a) h 2 = 100 M 1.6 M + 3.6 + 5.6 , (6b) where M is the thickness of the mined coal seam. The storage space ( V s g ) in the caving zone and the fissure zone can be estimated by V s g = ∫ 0 h 2 F n m L g L t f d h , (7) where n m , L g , and L t are the number, the length, and the width of the goaf. F is a usability coefficient for the reservoir, while f represents the goaf storage coefficient, determined by the capacity of pores and fissures.

Due to the stress release in the process of mining, the rock volume would expand with the formation of new fractures and pores. After mining, the rubbles and fracture rocks will be re-compacted under the gravity of overlying strata. But there is no way to completely restore the volume. The expansion coefficient K of rock mass is defined as the ratio of the expanded rock volume to the original volume, to characterize the volumetric expansion behavior of the surrounding rock after fracturing. Coefficient K and the zone range vary with the pressure, lithology, and distance to the mined coal. The storage coefficient therefore can be calculated using K , f = 1 − 1 K . (8)

The expansion coefficient K of the rock mass at different positions can be evaluated by (Meng et al., 2016a) K = { K u t + λ 1 h , λ 1 = K m a x − K u t h 1 , 0 ≤ h ≤ h 1 K m a x − λ 2 ⁡ ln ( h − h 1 + 1 ) , λ 2 = K m a x − 1 ln ( h 2 − h 1 + 1 ) , h 1 ≤ h ≤ h 2 . (9)

Mining activities also influence its underlying rocks, which will move toward the remained space after the coal is excavated, leading to new fractures. Compared with caving zone and fissure zone, the new space created within underlying rock is relatively small, thus not included in the storage space. But its permeability changes a lot, enhancing the water seepage. The influence depth h 3 in underlying rocks is estimated by (Fan et al., 2019b) h 3 = x a ⁡ cos ⁡ φ 2 ⁡ cos ( π 4 + φ 2 ) e ( π 4 + φ 2 ) tan ⁡ φ , (10a) x a = M ⁡ ln ζ γ h 0 + C ⁡ cot ⁡ φ m ξ C ⁡ cot ⁡ φ m 2 ξ ⁡ tan ⁡ φ m , (10b) ξ = 1 + sin ⁡ φ m 1 − sin ⁡ φ m , (10c) where C and φ are the cohesion and friction angle of the underlying rock. φ m is the friction angle of coal. ζ , γ , and h 0 are respectively the coefficient of stress concentration, unit weight of overlying rock, and depth of the mined coal seam.

Water and air seepage in the goafs through rocks are assumed to be slow and follow the Darcy’s law. The water flow velocity v is determined by v = k μ w a d p d r , (11) where r is the distance, k is the permeability, and p is the water pressure. Using the finite element method, the seepage velocity of water through the upper reservoir boundary can be determined.

Expansion coefficient K characterizes the volumetric expansion of the rock mass overlying the coal seam after mining. It varies with the pressure, lithology, and mining activities. Based on the K behavior obtained from the literature (Meng et al., 2016a), Figure 4 shows the goaf volume of a single goaf 200 m wide and 3,500 m long vs water level. As the coal seam thickness increases, the total volume V1 rises almost linearly. Considering the resistance of waterproof walls surrounding the water reservoirs, an admissible capacity V2 is calculated according to the suggested maximum water head (17.8 m) (Fan et al., 2020). Storage ratio R1, defined as the ratio of total capacity to the volume of excavated coal, shows a deceleration downtrend.

Based on the production history of the shutdown coal mines issued by the State Administration of Coal Mine Safety and China Coal Industry Association, the storage space of the abandoned coal mine goafs could be calculated. It reaches a considerable value of 4.70 × 108 m³. Figure 1 shows its distribution in the Mainland China. Taking a typical abandoned (shut down) coal mine, Yima Qianqiu coal mine in Henan province, with a dimension 3 × 5 km² and a coal thickness of 6 m as an example, the goaf storage capacity with a water level of 17.8 m is calculated at 1.97 × 106 m³.

To efficiently pump/inject water during charging/discharging, water‐collecting wells are made at the center of the goaf reservoir bottom. Water/air flow velocity within the reservoir is determined by pressure gradient and permeability. To ensure sufficient outputs of turbine and pumps, the maximum water flow should be guaranteed. The water saturation lines within the goafs were marked when the water flow in penstocks was constant at 6.25 m³/s. The maximum water level in the WCWs was set at 17.8 m in similar consideration of the maximum water head restriction [48, 49]. The minimum water level is 0. Figure 5A, B show the highest saturation line during water injection and the lowest saturation line during water releasing. As the permeability decreases, the saturation line tends to decline during injection and rise during releasing, implying a less water volume injected during filling and released during draining the reservoir, and hence a smaller usable capacity of the goaf reservoirs. Subtracting the corresponding saturation lines in Figures 5A, B, the usable coefficient relying on the permeability would be obtained for the goaf reservoirs, which are shown in Figure 6. It can be calculated that the permeability should be above 10⁻⁷ m² to have a considerable usable capacity ( ≥ 80 % of storage capacity). Literatures (Konicek et al., 2013; Meng et al., 2016b) reported that the goaf permeability within the overburden rocks above 0–17.8 m ranges from 10⁻¹⁰ to 10⁻⁶ m² which suggests that goafs are highly likely to be able to serve as PHS reservoirs and have a considerable usable capacity.

Ventilation shafts are excavated to connect the atmosphere with goafs for air smooth exchange during water pumping and injecting (Figure 7). The location of the shaft is selected at the center of the goaf and its bottom is 2 m above the maximum water level in the reservoir. The shaft dimension closely effects pressure loss of passing air. The length is determined by the nature of goaf (depth of coal seam). Figure 8 shows the pressure loss (the pressure difference between Point P0 and P1) decreases dramatically by five orders of magnitude, as the diameter of the ventilation shaft increases from 0.5 to 5 m with the concrete shaft wall lining material. When the shaft diameter is 0.8 m, pressure loss decreases to a negligible value (∼1 KPa). As the permeability increases from 10⁻¹⁰ m² to 10⁻⁷ m², the pressure loss (between P1 and P2) of air passing through the goaf diminishes, as shown in Figure 8. It is suggested that goafs should have a permeability larger than 3 × 10⁻⁹ m² to bring about an acceptable pressure loss during the air passing. This, however, is hardly feasible according to the estimation in Ref. (Alehossein and Poulsen, 2010; Poulsen et al., 2018) that the permeability within the goaf above 19.8 m varies between 10⁻¹⁰ and 10⁻¹³ m². Dendritic horizontal ventilation tubes (Figure 2) are, therefore, advised for the safety and smoothness of water-air exchange.

Except for system efficiency η s y s , the following parameters are defined as in Eqs 1 2, the power type, α w representing the share of imported wind energy in the total imported energy, and the regulated-energy per volume ( R E P V ) representing the regulation ability of the goaf-PHS system. α w = ∫ 0 T P w d t ∫ 0 T P w d t + ∫ 0 T P s d t , (12a) R E P V = ∫ 0 T P L d t V s g , p k − V s g , t r , (12b) where P w and P s are the outputs of wind power generator and solar collector. T is a calculation period. V s g ,   p k and V s g , t r represent the peak and the trough value of water volume in the reservoir.

Based on the above analysis, the pressure loss during water-air exchange in the goaf is negligible and the storage capacity of one goaf reservoir is temporarily set at 1.97 × 106 m³ and the usable coefficient is 0.8. The altitude difference between the upper and lower reservoir is 100 m. The initial water level inside the upper and lower reservoirs is zero and 17.8 m, respectively.

The load profile, wind velocity, and solar radiation intensity for 1 year or 1 day in Inner Mongolia, a typical richest area in wind and solar energy resources in north China, were used in the following performance evaluations. Detailed data can be seen in Refs. (Xiaolin et al., 2009; Ruichun and Bin, 2014; Wang et al., 2015).

PHS plants usually have several time scales of operation modes, among which the yearly case and daily case are the most representative. The performance of the goaf-PHS system in both yearly and daily operation cases is shown in Figure 9. The model of the goaf-PHS system is detailed.

Based on the wind and solar electric capacity generated in 2017 (wind, 2.70 × 10¹⁰ kW·h, and solar, 9.67 × 10⁹ kW·h, respectively), we could see that the type of energy emplaced in the goaf-PHS consists of 74% of wind generated electricity and 26% of solar electricity. Using the parameters of a typical abandoned coal mine as the standard, the evaluation results for a yearly operations case are shown in Figure 9. Regarding the share of component supply and consumption of the goaf-PHS system over 8,760 h in 1 year, the goaf-PHS is charged every day throughout the 1 year (Figure 9B), while the discharge stage is mainly from the middle of May to October (Figure 9A), indicating that the system stores the surplus energy every day, while releasing that from May to October, during the period of energy deficit. The average regulated load is 275 kW as the altitude difference between the two reservoirs is 100 m. The maximum output of the PHS system is delivered in August, when energy supplied by wind is the weakest (Figure 9A). The maximum input of the PHS system appears in January (Figure 9B).

The details of several selected days (January 1^st–4^th for winter, April 1^st–4^th for spring, August 1^st–4^th for summer, and October 1^st–4^th for autumn) are shown in Figure 10. It can be seen that the pump units work every day in the hours around noon to stores surplus electricity, even in August (Figure 10B), when the wind energy is seriously inadequate. In January, the pump units work full time, while the turbine units stay inoperative. The turbine units provide the maximum work output 19 h in 1 day, except for 11:00 to 15:00, in August (Figure 10A). In April and October, the turbines and pumps work with roughly the same period. It is therefore the water variation in the reservoirs that changes slowly in April and October, rapidly in January, and especially in August (Figure 11). The water volume in the upper reservoir increases from October to May, reaching a peak of 1.22 × 106 m³ and then decreases, down to a trough value of −3.6 × 105 m³ (Figure 12). The average system efficiency in 1 year is 82.8%. The calculated REPV is 2.82 kW·h/m³.

Different power types would bring about a different system performance. As seen from Figure 13, with the wind contribution increasing ( α w rising), the R E P V for the yearly regulation case increases and then declines, reaching a peak around α w = 0.25 .

For a typical abandoned coal mine, the system performance was evaluated on two selected days (one in winter, 15th January, shown in Figure 14A; the other one in summer, 15th July, shown in Figure 14B). The chosen energy type is α w = 0.8 for 15th January and α w = 0.5 for 15th July, according to the daily generated electricity capacity. The comprehensive system efficiency of the goaf-PHS is 73.6 and 77.5%, respectively, which are notably lower than that in yearly operation case, since the water flow is faster in daily regulation mode and more friction produces more energy loss. The average regulated load in 15th January is 160.4 MW, while it is 70.5 on the 15th July. The REPV representing the regulatable energy of a unit volume is 2.50 kW·h/m³ and 1.07 kW·h/m³, respectively, which result from different energy types.

Using the load profile and wind and solar parameters in summer, 15th July, the REPV with various energy types calculated is shown in Figure 13. When the wind contribution increases ( α w changing from 0 to 1), the R E P V for the daily regulation case increases monotonically. It can be observed that in daily time scale, the pure wind electricity supply is the most suitable energy type for the goaf-PHS system under the load profile and climate conditions in Inner Mongolia.

Goaf water quality, especially the pH value, is another major substantial concern on the construction of the goaf-PHS system. With a low pH value, acid goaf water can corrode equipment, release metal ions, even some heavy metals, damage the underground structures (like waterproof wall), and pollute the surrounding water bodies (González et al., 2018). As already known, most coal contains various amounts of (0.5–3%) sulfide that exists mainly (60–70%) as pyrite minerals. The elevated pH level can cause the precipitation or co-precipitation of metal ions such as aluminum (Al), cadmium (Cd), cobalt (Co), chromium (Cr), copper (Cu), iron (Fe), manganese (Mn), nickel (Ni), lead (Pb), and zinc (Zn) contained in the mine water and result in sediments in the seepage channels and reduce the permeability of rock mass, thus blocking the fluid exchange within the goaf (Pujades et al., 2019).

As already known, most coal contains various amounts of (0.5–3%) sulfide that exist mainly (60–70%) as pyrite minerals. After repeated pumping and injection, mine water is exposed to oxidation conditions and acidizes following the chemical reaction R1–R3: FeS 2 + 3.75 O 2 ( aq ) + 7.5 H 2 O = Fe ( O H ) 3 ( s ) + 2 SO 4 2 − + 4 H + , (R1) Fe 3 + + 2 H 2 O = FeOOH + 3 H + , (R2) 8 Fe 3 + + 12.5 H 2 O + 1.75 SO 4 2 − = Fe 8 O 8 ( OH ) 4.5 ( SO 3 ) 1.75 + 20.5 H + . (R3)

With a hypothesis of geological medium (residual coal and gangue) containing 1% pyrite, Pujades et al. conducted numerical simulations and show that the pH value would decrease continuously to 3.1–3.3 in both surface reservoir and underground goaf reservoir (which is considered as a porous medium in the study) during 30 days of repeated pumpings and injections (Pujades et al., 2018). Under the condition of 10% carbonate such as calcite and 1% pyrite in the initial goaf environment, the research shows calcite would mitigate and precipitate around the surface reservoir (Pujades et al., 2016). Many underground mine reservoirs using coal goafs from Shennan coal mine district, northwest China, have been constructed. The quality analysis shows that the original well water is weakly alkaline (pH = 7.1–7.8) and there is any substantial difference from natural water, except some obvious increases in permanent hardness and sulfate radical (Wang et al., 2018). A long-term water monitoring shows that with the circulation of water resources, several harmful elements have shown a significant remobilization, in spite of ultra-low sulfur deposited in Jurassic coal of the Shennan coal mine district. Taking purification measures, the value of the mine water could be controlled above the utilization standard (pH = 6.9–7.1).

In consequence, hydrogeology and hydrochemistry investigations are also indispensable in the feasibility demonstration of goaf-PHS system. Necessary purification treatments are very important to the water safety. The coal gangue packed in goaf reservoirs, which contain clay mineral contents such as illite and kaolinite, could act as a useful adsorbent to reduce the contents of organic compounds and nitrogen in mine water (Liu et al., 2019). In one word, the environmental influence of goaf reservoirs should be a point of concern but also a solvable problem when developing the hybrid-PHS plants using abandoned coal mine goafs.