Influences of Hydraulic Fracturing on Fluid Flow and Mineralization at the Vein-Type Tungsten Deposits in Southern China

1 Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China 2The Laboratory of Dynamic Digenesis and Metallogenesis, Institute of Geomechanics, CAGS, Beijing 100081, China 3Centre for Geoscience Computing, School of Earth and Environmental Sciences, The University of Queensland, Brisbane, QLD 4072, Australia 4State Key Laboratory of Geological Processes and Mineral Resources, School of Earth Sciences and Resources, China University of Geosciences (Beijing), Beijing 100083, China


Introduction
The Nanling Range in southern China is a world-class tungsten province [1]. Wolframite is the main ore mineral at the vein-type tungsten deposits in this area [2]. One disputed issue on the ore forming processes is how wolframite is precipitated. Three mechanisms have been proposed from fluid inclusion and stable isotopic analysis to cause wolframite deposition: fluid mixing, simple cooling, and fluid immiscibility [3][4][5][6][7][8][9][10][11]. However, the formation of magmatichydrothermal deposits involves complicated mechanical and chemical processes [12][13][14]. Previous work does not consider the links of mechanical processes to ore formation.
This study is organized into three parts. We first introduce the geological background of the vein-type tungsten deposits in the Nanling Range. Based on the geological and geochemical characteristics, then establish a numerical model and investigate the influences of a hydraulic fracturing process on fluid flow and solubility of carbon dioxide (CO 2 ) and quartz. Finally, we discuss the influences of the hydraulic fracturing process on hydrothermal flow and tungsten mineralization.

Geological Background of the Tungsten Deposits in the Nanling Range
The vein-type tungsten deposits in the Nanling Range are dated at an age range of 160∼150 Ma and genetically related to continental crust remelting type granitoids during the Jurassic to Cretaceous (J 2 -K 2 ) [1,25,26]. The mineralized veins are present nearby the roof zone of buried alkalifeldspar granite and extend a depth of 1000 metres [27]. Wolframite is the main ore mineral in the veins ( Figure 1) and the gangue minerals have quartz, feldspar, muscovite, calcite, and tourmaline [2]. Hydrogen, oxygen, carbon, and sulfur isotopic data indicate that the ore fluids have a magmatic origin at the main mineralization stage and then were mixed with meteoric waters at late stages [29]. The mineralized fluids are NaCl-H 2 O ± CO 2 systems with a small amount of CO, CH 4 , N 2 , and H 2 . The fluid inclusions trapped by ore and gauge minerals have homogenization temperatures from 160 ∘ C to 390 ∘ C and salinities from 1 to 10 wt.% NaCl equivalent. The mineralization pressures recorded by fluid inclusions have a range within 20∼160 MPa with maximum range of 75∼160 MPa [3,5,6,9,10,23,24,[30][31][32]. Silicate melt inclusions in wolframite and beryl have a homogenization temperature up to 700 ∘ C and a homogenization pressure of 160∼200 MPa [33].
Previous structural analysis of vein arrays at tungsten deposits in the Nanling Range suggests that high-pressure fluids trigger fracture initiation and propagation [34][35][36]. The high-pressure fluids and the pressure fluctuations are also recorded by fluid inclusions [5,6,23,24]. Polya [37] proposes that a pressure decrease after hydraulic fracturing causes wolframite precipitation from hydrothermal solutions for two reasons. One reason is that wolframite solubility is pressure-dependent. This reason is concluded from quantitative solubility calculations. The other reason derived from qualitative analysis is that dramatic decrease in fluid pressure may cause H 2 O-CO 2 immiscibility and increase pH. The thermodynamic model developed by Wood and Samson [38] suggests that wolframite solubility is only weakly dependent on pressure; therefore, Wood and Samson's model contradicts Polya's first reason. Wood and Samson's model supports that CO 2 loss decreases tungsten solubility because tungsten solubility is strongly dependent on pH, but they do not consider the influence of pressure drop on CO 2 solubility and further impact on tungsten solubility. Therefore, it is necessary to check the links of the pressure drop after hydraulic fracturing to CO 2 solubility. In the next sections, finite element-based numerical experiments are used to quantify the influence of a hydraulic fracturing process on fluid flow and solubility of CO 2 and quartz.

Numerical Modelling of Tungsten Deposits in the Nanling Range
3.1. Hydromechanical Theories. The mechanics of hydraulic fracturing is first synthesized by Hubbert and Willis [39] using the concept of effective stress. The technique of artificial hydraulic fracturing has been successfully developed to increase oil and gas reservoir production; therefore, most of our knowledge about hydraulic fracturing comes from those fields [40][41][42]. Hydraulic fracturing is a fluid-to-solid coupling where a change in fluid pressure or fluid mass alters the volume of a porous material and produces strains [43]. Several conceptual models have been proposed to understand how hydraulic fracturing involves formation of hydrothermal veins [44][45][46][47][48][49]. There are also numerous numerical models developed to clarify hydraulic fracturing and further hydrothermal flow in magmatic-hydrothermal systems [12,13,16,19,[50][51][52][53][54][55][56]. However, many of those models do not solve the constitutive relation of rock deformation; therefore, the hydraulic fracturing processes are not well captured.
Various yield criteria are implanted in PANDAS including the Maximum Tensile Stress Criterion and the Drucker-Prager Criterion [66] used in this paper. The three principle stresses 1 , 2 , 3 satisfy the inequality: 1 ≥ 2 ≥ 3 . Positive normal stresses mean compression and negative normal stresses represent tension. Extensional failure is produced once the tensile minimum principle stress exceeds the uniaxial tensile yield strength. Extensional fracture is normal to 3 and aligned with 1 . Shear fractures are produced when the shear stress reaches the shear strength. Both shear failure and extensional failure form an anisotropic permeability tensor.

Key Assumptions.
The following assumptions were made to conduct numerical experiments at a reasonable computational cost: (1) high temperature did not alter the rock constitutive relation. The deformation regime of rocks changes from brittle to ductile around 400 ∘ C [21,67]. A background temperature of 350 ∘ C was set in the model. It was assumed that this temperature would not alter the deformation regime from brittle to ductile. (2) Hydrothermal fluid flow was driven by a constant pressure. The timescales of abrupt rock deformation like crack initiation are significantly smaller than those of other subsets of ore forming processes [68]. It was assumed that the supply of magmatic fluids maintained the fluid pressure at a constant level. (3) Heat transport was not calculated by the simulator codes because the temperature field would change little during the short timescales of fracturing. (4) The model was set in a deep depth and the fluid flow was single-phase; otherwise, fluid flow may be two-phase in a shallow depth [51].

A Two-Dimensional Numerical Model of Tungsten
Deposits in the Nanling Range. A 2D numerical model at a depth of 4 km was built based on the structural and geochemical characteristics of tungsten deposits in the Nanling Range. This depth was determined from the mineralization pressure of the tungsten deposits (see Section 2). This depth is also the emplacement depth of many typical tungsten-tin and porphyry copper systems elsewhere [15,19,[69][70][71]. The model has only one unit with a size of 100 m × 100 m (Figure 2).
-axis represents the orientation normal to veins and -axis is vertical. The rock model was discrete into 39200 elements with 59643 nodes in total ( Figure 3). The parts close to the fluid source had much finer meshes than the other parts of the model.
Operation of the numerical experiments had two steps. At the first step, a vertical stress of 100 MPa was loaded at the top and a horizontal stress of 60 MPa was loaded on the left and right sides of the model. The bottom was fixed vertically. Assuming a lithostatic gradient of 25 MPa/km, these boundary conditions formed an initial extensional stress field at a depth of 4 km. At the second step, the loaded stresses at the first step were removed but the displacement boundary conditions were held. At this step, a fluid pressure of 200 MPa was fixed at the bottom to represent the highpressure fluids released from magma at depth. An initial  fluid pressure of 40 MPa was set to form an initial pressure field at the depth of 4 km assuming a hydrostatic pressure gradient of 10 MPa/km. Table 1 shows the rock's hydraulic and mechanical parameters. The fluid density, viscosity, and compressibility of NaCl solutions at the temperature of 350 ∘ C with a salinity of 10 wt.% NaCl equivalent were reproduced from the empirical models in [64,72]. The mineralized veins at tungsten deposits in the Nanling Range are hosted by metamorphosed sandstone and slate, granite [73,74]. The mechanical parameters of sandstone and granite in [75] were used in the model. A reference point was selected to show the evolution of stresses and fluid flow during hydraulic fracturing ( Figure 3). The fluid pressure was the only variable controlling solubility of CO 2 and quartz in the model. It is a controversial issue whether the mineralized fluids contain CO 2 at tungsten deposits in the Nanling Range. The existence of CO 2 is identified in fluid inclusions in gauge minerals like quartz, beryl, and topaz that can reflect the temperature and salinity conditions at an early mineralization stage [6,10,11,76,77]. In contrast, the infrared microthermometry of fluid inclusions in wolframite suggests that the mineralized fluids are NaCl-H 2 O systems [3,4,9,11]. High concentrations of W, Mn, and Fe are found in fluid inclusions in quartz [78]. This indicates that the fluid inclusions in quartz have trapped the mineralized fluids at some mineralization stages, although whether the mineralized fluids trapped in quartz are the same with those in wolframite is still enigmatic. Thus, results from fluid inclusions in quartz still have some reference value and CO 2 is still considered to be involved in tungsten mineralization as a control of pH.

Results
The principle stresses ( 1 , 3 ) at the reference point decreased as the high-pressure fluids flew into the host rock ( Figure 4). The minimum principle stress ( 3 ) at the reference point reached the tensile strength after 7.7 seconds when the maximum principle stress ( 1 = 13 MPa) was still compressive and the differential stress was 18 MPa. In PANDAS, the stresses become zero once they reach the shear or extension strength.
The fluid pressure at the reference point kept increasing and the fluid velocity decreased gradually before yield (Figure 5). The tensile failure increased the permeability of the reference point and caused a sharp decrease of fluid pressure from 168 MPa to 148 MPa. The fluid velocity increased significantly to approximately 0.09 m/s. After that, there were also several smaller fluctuations of fluid pressure and velocity at the reference point because the surrounding nodes were fractured. The fluid pressure decreased to 115 MPa and the fluid velocity increased to 0.004 m/s at the last fluctuation.
The solubility model in [79] was used to calculate CO 2 solubility in aqueous NaCl solutions. Because CO 2 solubility in aqueous NaCl solutions increases with fluid pressure at a temperature of 350 ∘ C, the fluid pressure fluctuations during hydraulic fracturing caused a similar change on CO 2 solubility ( Figure 6). CO 2 solubility at the reference point reached up to 11 mol/kg before yield and decreased to 7 mol/kg after hydraulic fracturing. Quartz is the main gauge mineral at the vein-type tungsten deposits [2]. Its dissolution and precipitation alter rock permeability and hence influence fluid flow and heat transfer in hydrothermal systems [80][81][82][83][84][85]. The predictive model proposed by Akinfiev and Diamond [86] was employed to calculate quartz solubility in aqueous NaCl solutions. Figure 7 shows that solubility of quartz in aqueous NaCl solutions   increases with increasing fluid pressure. Quartz solubility decreased from 0.0248 mol/kg to 0.0226 mol/kg during hydraulic fracturing.

Comparisons between Numerical Experiments and the Griffith Criterion.
In the numerical experiments, extension failure forms when the minimum principle stress reaches the tensile strength and the differential stress is less than four times the tensile strength. This is consistent with the Griffith criterion for extension failure [88][89][90].

Influences of Hydraulic Fracturing on Fluid Flow and Ore
Precipitation. In the numerical experiments, high-pressure fluids crack low-permeability rock and enhance its local permeability. This allows transient high-velocity hydrothermal flow. Such fluid pulses are also identified by other numerical models [22,50,52,91,92].
Quartz crystallization after fracture opening can decrease rock permeability and alter rock strength [87,[93][94][95]. In the numerical experiments, the quartz solubility decreases by 9% after hydraulic fracturing. This amount of quartz precipitation may be insufficient to decrease rock permeability significantly. Other factors like flow rate and supersaturation can be incorporated in further improvement of the models [96][97][98].
The fluid pressure and velocity fluctuate repeatedly once hydraulic fracturing occurs in the numerical experiments. This may promote chemical disequilibrium and cause mineral deposition reactions [99,100]. Tungsten solubility is weakly dependent on fluid pressure [38]. However, the fluid pressure drop during a hydraulic fracturing process decreases CO 2 solubility significantly. This could cause effervescence of CO 2 and increase pH and facilitate precipitation of ores like wolframite and cassiterite [37,[101][102][103][104][105][106][107][108][109]. Therefore, fluid pressure drop accompanying hydraulic fracturing is a trigger for increasing pH and could cause wolframite precipitation at tungsten deposits in the Nanling Range. Wood and Samson [38] do not consider the links of pressure drop to CO 2 loss and further influence on tungsten solubility in their thermodynamic model. Our numerical experiments provide a supplement to their model. Fluid immiscibility characterized by CO 2 escaping is recorded by the fluid inclusions in quartz, beryl, and topaz at tungsten deposits in the Nanling Range [6,10,11,76,77]. However, evidence of fluid immiscibility has not yet been found in fluid inclusions in wolframite [3]. Phase separation of immiscible fluids in NaCl-H 2 O ± CO 2 systems is more difficult to occur at deeper levels than at shallower levels [110]. The relatively deep emplacement may be an important reason why phase separation is uncommon at the vein-type tungsten deposits in the Nanling Range [23].
Fluid mixing and simple cooling are also proposed to cause wolframite deposition at tungsten deposits in the Nanling Range [3,9]. It is recently reported that the irons contributed by the host rock are decisive for wolframite (dominantly FeWO 4 ) precipitation at the Panasqueira deposit in Portugal [111]. These mechanisms for tungsten deposition do not contradict findings from the numerical experiments. Hydraulic fracturing cracks impermeable rocks and creates channels for later heat transfer and reactions between hydrothermal fluids and the host rock, which could last for a much longer timescale [49,112]. Our numerical experiments do not eliminate other possible mechanisms for wolframite precipitation at tungsten deposits in the Nanling Range.

Hydraulic Fracturing and Emplacement
Depth Estimation. The fluid pressures recorded by fluid inclusions are commonly used to estimate the emplacement depth of ore deposits [113][114][115][116]. However, it is indefinite whether these pressures are lithostatic or hydrostatic [117]. Engelder [118] analyzed the links between fracture mechanics and fluid inclusion barometry. In the numerical experiments, the fixed pressure at the bottom is higher than the pressure recorded by fluid inclusions. The fluid pressures both before and after hydraulic fracturing are superlithostatic at the depth of 4 km. Actually, hydraulic fracturing occurs because a pressure gradient changes the volume of a porous material and creates strains [43]. Thus, hydraulic fracturing depends on the initial stress field, the existence of faults, and the fluid pressure filed. The fluid pressure is very dynamic when coupled with rock deformation. Given that fluid inclusions may record some pressures after hydraulic fracturing, the fluid pressure fixed at the bottom of the model is higher than those recorded in fluid inclusion. Also, it requires some cautions before calculating the emplacement depth from the fluid pressures recorded by fluid inclusions. Combinations of refined models and fluid inclusion studies may offer better constraint on the emplacement depth of ore deposits.

Conclusions
The mechanisms precipitating wolframite is one of the most disputed issues on the ore forming processes at tungsten deposits in the Nanling Range. Previous studies for this focus on fluid inclusion and stable isotopic analysis but no one has yet evaluated the influences of mechanical processes on fluid flow and mineralization. Assuming fluid pressure is the only variable influencing solubility of CO 2 and quartz, we investigate the influences of a hydraulic fracturing process on fluid flow and solubility of CO 2 and quartz by using finite element-based numerical experiments. The numerical experiments provide the following implications for the mechanisms precipitating wolframite at tungsten deposits in the Nanling Range: (1) Rock could be fractured by high-pressure fluids in a short time scale. Such a hydraulic fracturing is followed by significant fluctuations of fluid pressure and high-velocity hydrothermal pulse.
(2) The fluid pressure drop during the hydraulic fracturing process could result in a 9% decrease of quartz solubility. This amount of quartz crystallization may not cause a significant decrease in rock permeability.
(3) The fluid pressure decrease after hydraulic fracturing could reduce CO 2 solubility by 36% and increases pH. Because tungsten solubility is strongly negatively correlated to pH, the fluid pressure drop accompanying hydraulic fracturing favours wolframite precipitation.
(4) The numerical experiments provide insight into the mechanisms precipitating wolframite at tungsten deposits in the Nanling Range as well as other metals whose solubility is strongly dependent on pH.

Conflicts of Interest
The authors declare that they have no conflicts of interest.