Numerical modeling of ore-forming processes within the Chating Cu-Au porphyry-type deposit, China: Implications for the longevity of hydrothermal systems and potential uses in mineral exploration

Journal Pre-proofs Numerical Modeling of Ore-forming Processes within the Chating Cu-Au Porphyry-type Deposit, China: Implications for the Longevity of Hydrothermal Systems and Potential Uses in Mineral Exploration Xunyu Hu, Xiaohui Li, Feng Yuan, Alison Ord, Simon M. Jowitt, Yue Li, Wenqiang Dai, Taofa Zhou PII: DOI: Reference:

S0169-1368(19)30588-8 https://doi.org/10.1016/j.oregeorev.2019.103230 OREGEO 103230

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Ore Geology Reviews

Received Date: Revised Date: Accepted Date:

28 June 2019 30 October 2019 11 November 2019

Please cite this article as: X. Hu, X. Li, F. Yuan, A. Ord, S.M. Jowitt, Y. Li, W. Dai, T. Zhou, Numerical Modeling of Ore-forming Processes within the Chating Cu-Au Porphyry-type Deposit, China: Implications for the Longevity of Hydrothermal Systems and Potential Uses in Mineral Exploration, Ore Geology Reviews (2019), doi: https:// doi.org/10.1016/j.oregeorev.2019.103230

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Numerical Modeling of Ore-forming Processes within the Chating Cu-Au Porphyry-type Deposit, China: Implications for the Longevity of Hydrothermal Systems and Potential Uses in Mineral Exploration Xunyu Hua,b,d, *Xiaohui Lia,b, *Feng Yuana,b, Alison Orda,d, Simon M. Jowittc, Yue Lia,b, Wenqiang Daia,b, Taofa Zhoua,b School of Resources and Environmental Engineering, Hefei University of Technology, Hefei 23009, China

a

Anhui Province Engineering Research Center for Mineral Resources and Mine Environments, Hefei University of Technology, Hefei 23009, China

b

Department of Geoscience, University of Nevada Las Vegas,4505 S. Maryland Pkwy., NV 89154-4010, USA

c

School of Earth Science, the University of Western Australia, Perth, Australia, 6009

d

Abstract The Chating Cu–Au deposit is a newly discovered porphyry-type deposit within the Nanling–Xuancheng mining district of the Middle–Lower Yangtze River Metallogenic Belt (MLYRMB), China. This study uses numerical simulation to determine the key characteristics of the mineralizing system that formed the Chating deposit that traditional analysis cannot easily identify, including the duration of the mineralizing events that formed the deposit. We also outline the practical value of numerical simulation in determining the processes that operate during mineral deposit formation and how this knowledge can be used in further mineral exploration. Our simulation interlinks heat transfer, pressure, fluid-flow, chemical reaction, and material migration and indicates the presence of a temperature anomaly and modeled zones of mineralization that match the known distribution of mineralization.

Our modeling further predicts a potentially

mineralized zone at depths below the -1800 m level of the deposit. Combining our numerical modeling with average Cu grades and chemical reaction rates indicates that the Chating deposit formed over a period of 9,600–75,000 years. These data can be used in future prospectivity modeling and mineral exploration as well as to gain

insights into the genesis and duration of the

system that formed the Chating porphyry Cu-Au deposit as well as porphyry mineralization in general. Keywords: Porphyry deposit; Middle-Lower Yangtze River Metallogenic Belt; numerical simulation; duration of ore formation.

1 Introduction Porphyry ore deposits contain the majority of the world’s copper and molybdenum resources as well as a significant amount of gold (Sillitoe, 2010; Weis et al., 2012; Mudd et al., 2013; Mudd & Jowitt, 2018). Research into the genesis of porphyry deposits has not only enhanced exploration for these deposits but has also furthered our understanding of the nature of metallogeny and magmatism within arc-type environments and other geological settings where porphyry deposits develop. The Middle–Lower Yangtze River Metallogenic Belt (MLYRMB) is located in central–eastern China and contains numerous porphyry–skarn copper-gold and magnetite–apatite iron deposits that formed in an intracontinental setting (Chang et al., 1991; Pirajno & Zhou, 2015; Zhou et al., 2012, 2015, 2016; Xiao et al., 2018, 2019; Fig. 1). The Chating Cu–Au deposit is a newly discovered concealed porphyry-type deposit in the northeast of the Nanling–Xuancheng area, one of the eight mining camps within the MLYRMB (Xu et al., 2018; Jiang et al., 2017; Zhou et al., 2017; Xiao et al., 2018, 2019; Figs. 2

3). This deposit has been the focus of a

significant amount of research since its discovery in 2011. However, the complexities involved in hydrothermal systems means that traditional approaches to understanding metallogeny and typical analytical approaches may not yield the information needed to fully understand mineralizing systems such as the system that generated the Chating deposit (Liu & Dai, 2014; Zou et al., 2017). This is especially true when dealing with blind mineral deposits where data is limited to that obtained from either secondary detection methods (e.g. surface geochemistry, geophysics) or samples obtained from drilling. Numerous processes are involved in hydrothermal systems, including fluid flow, heat conduction and convection, pressure variations and distribution, the movement of materials such as metals, ligands, and fluids, and chemical reactions within the system. This interlinked complexity means that determining the longevity of ore-forming systems, identifying deep-seated areas that are prospective for exploration, temporal and spatial variations in ore-forming processes, and identifying the processes that lead to the precipitation of metals within the deposit can be difficult using traditional analytical approaches (Liu et al., 2010a, 2010b; Zou et al., 2017). The addition of numerical simulation to the toolkit applied to understanding mineralizing systems can potentially further our understanding of the complex and interlinked

processes that drive metallogenesis in ways that traditional analytical techniques cannot (Zou et al., 2017). Rapid recent advancements in computing hardware and theoretical and applied computation science have enabled the development of complex and coupled numerical geological models. This has enabled a significant amount of research to be undertaken on the geology of crust- (Zhao et al., 1998, 2008a, 2008b, 2009; Zhao, 2015, 2016; Ord et al., 2010; Lin et al., 2009; Yan et al., 2003; Xing & Makinouchi, 2008; Honda et al., 1993; Hobbs et al., 2007) and deposit-scale geology (Slough et al., 1999; Garven & Freeze, 1984; Reichert & Borg, 2008; Deng et al., 2001; Oreskes et al., 1994; Oliver et al., 2006; Eldursi et al., 2009; Zhao et al., 2008c, 2010; Yang et al., 2004; Cooke & McPhail, 2001; Ge et al., 2006; Zhang et al., 2007; Zou et al., 2017; Hu et al., 2019). This multi-scale research has focused on theoretical or applied geological problems involving one or more of the five main geoscientific factors that are often numerically simulated, namely mechanics, heat, fluid-flow, chemical reaction and material migration. Recent research into the longevity and duration of mineralizing processes (e.g., James & Elderfield, 1996; Zhao et al., 2002; Hobbs et al., 2006; Buret et al., 2016) indicate that pure reaction rate estimates can enable the identification of the time taken for a mineral deposit to form. This in turn has been effectively used in the numerical simulation of the mineralizing processes that occur within hydrothermal systems (Reid et al., 2012a, 2012b; Zou et al., 2017). This study combines this approach with COMSOL Multiphysics software, a software package that allows researchers to customize distributed ordinary differential equations and formulas to calculate variables that allow the simulation of the complex and coupled processes that occur within hydrothermal systems. This approach allows the numerical simulation of the hydrothermal and mineralizing processes that generated the Chating porphyry Cu–Au deposit as well as potentially highlighting areas around the deposit for future exploration. The large Chating porphyry Cu–Au deposit was discovered in 2011 and is the first porphyry-type mineral deposit discovered in the southeastern part of Anhui Province (Jiang et al., 2015). Despite the research and exploration undertaken to date in this area, the prospectivity of this region for both greenfield discovery and brownfield expansion of the deposit remains somewhat unclear (Hong et al., 2017; Qian et al., 2017; Xu et al., 2018; Jiang et al., 2015, 2017). The research that has been undertaken on the deposit to date include determining the geological

characteristics and the conditions of ore formation within the study area (Qian et al., 2017; Jiang et al., 2017; Xiao et al., 2018, 2019), genetic connections between the gold and copper mineralization in the study area (Xu et al., 2018), geochronology and the timing of deposit formation (Jiang et al., 2017), and analysis of the temperature and pressure of formation of biotite, indirectly yielding pressures and temperatures of ore formation (Xiao et al., 2018, 2019). All of this research and the complex nature of the mineralizing processes that formed the Chating porphyry deposit means that the study area is an ideal site for the application of numerical simulation to further our understanding of the processes that operate during ore deposit formation as well as the longevity of these processes. This study aims to answer several questions using new numerical simulations combined with the results of previous research, namely: (1) Can results of numerical simulation provide evidence or verification to existing geological fact and implications to porphyry system? (2) Can we calculate the duration of the ore-forming processes that generated the Chating porphyry deposit (as well as other similar deposits)? (3) Can the results of numerical simulation be used to identify prospective areas at depth within the Chating system and guide further exploration in an area that has been drilled to a depth of 1800 m but where considerable Cu mineralization remains open at this depth? All of these points will be assessed during this study and will provide insights not just into the Chating porphyry deposit but also the possible use of numerical simulation in both economic geology research and mineral exploration. This study uses numerical simulation methods and the theory of coupled open flow systems (Ord et al., 2012) to analyze the processes that formed the Chating porphyry Cu-Au deposit. The results indicate the usefulness of mathematical geology and computational geoscience in ore deposit research as approaches that can provide insights into geological processes that cannot be provided by traditional approaches and methods (Zou et al., 2017). Our simulations yield useful data that not only are consistent with the results obtained from previous research using traditional approaches (Hong et al., 2017; Qian et al., 2017; Xu et al., 2018; Jiang et al., 2015, 2017; Xiao et al., 2018; Xiao et al., 2019) but also provides further insight into the mineralizing processes that operated in this area, highlights areas for future exploration, and indicates that numerical simulation is an effective approach for the study of ore-forming systems and the resulting mineral deposits they generate.

2 Regional and Deposit Geology 2.1 Regional geology The MLYRMB (Fig. 1) hosts world-class Cu–Fe polymetallic mineralization and is one of the most important areas of mineralization in China (Tang, 1998; Chang, 1991; Zhai, 1992; Pan & Dong, 1999; Pirajno and Zhou, 2015; Zhou, 2017). The area is cross-cut by a series of major faults and hosts eight large mining camps, namely (from west to east) the southeast Hubei, Jiurui, Anqing–Guichi, Luzong, Tongling, Nanling–Xuancheng, Ningwu, and Ningzhen mining districts (Fig. 1; Chang, 1991; Yuan et al., 2011; Zhai, 1992; Zhao & Tu, 2003; Zhou et al., 2011; Zhou et al., 2017). The mineral deposits in this region contain 13 Mt of contained Cu and 800 t of contained Ag, the majority of which are hosted by porphyry, skarn and epithermal deposits. All of these deposits are genetically associated with Mesozoic magmatism spread over three separate stages at 149–135, 133–125 and 123–105 Ma (Zhou et al., 2015) and the evolution of this area during the associated Yanshanian tectonic event (Ningwu Research Group, 1978). The Nanling–Xuancheng basin is located within the eastern MLYRMB (Fig. 1) and is divided into upper and deeper sections by an unconformity, deformation, magmatism, and the sedimentary stratigraphy of the basin. The deeper part of the basin contains conformable or disconformable Silurian (O) to lower and middle Triassic (T1-2) sedimentary units. The Indosinian orogeny associated with the collision between India and Eurasia generated intense NE–SW oriented folding in these units that are also cross-cut by NW–SE and NE–SW oriented faults. The upper part of the basin contains Jurassic (J) to Quaternary (Q4) units, including the Jurassic volcanic Zhongfencun Formation (J3z). The majority of these formations have unconformable contacts, are variably folded, contain interbedded volcanic units and have been intruded by magmatic units. The majority of the mining camp area is covered by thick Quaternary sediments although this has not prevented the discovery of a number of polymetallic Cu, Au, and Mo deposits. These include the Magushan Cu–Mo and the Shizishan, Qiaomaishan, and Chating porphyry Cu–Au deposits, with the majority of the deposits in this area located within the Chating and Magushan orefields (Fig. 2; Anhui 322 Geological Team, 2016). 2.2 Orefield Geology The Chating orefield is located in the northeastern part of the Nanling–Xuancheng basin and contains NW–SE and NE–SW oriented groups of faults that form a tectonic framework along with

the intense folding that is present across the entirety of the basin. The area is dominated by Triassic and Jurassic units that are associated with the mineralization in this area (Fig. 3) and form the host rocks for the porphyry-related intrusions that in turn host the orebodies that define the Chating Cu–Au deposit (Fig. 4). 2.3 Deposit Geology The Chating Cu–Au deposit is a concealed porphyry copper–gold deposit located in the northern and central part of the Chating orefield. This area contains Cretaceous to Quaternary sediments, with the latter cropping out over more than 60% of the region (Fig. 3). Drillholes in this area indicate that Quaternary sediments in this region cover Triassic, Jurassic and Silurian units that are hosted by a broad anticline that dominates this area, as shown by the stratigraphic column given in Table 1. The intrusions in this area are spatially controlled by the presence of a domal structure (Fig. 4). The majority of the Cu mineralization within the Chating deposit is hosted by a concealed porphyritic quartz diorite (i.e., does not crop out in the study area) that formed from fluid exsolved from mantle-derived magmas, with the single pulse of ore mineral precipitation within the deposit potentially being controlled by the mixing of these fluids with externally derived non-mineralizing fluids (Xiao et al., 2018; 2019). Both spessartine garnet-bearing and porphyritic quartz diorite units are encountered during drilling in the study area where thicknesses of these units range from meters to dozens of meters. The intrusions are overprinted by zoned hydrothermal alteration from an inner K-silicate zone through a pyrite-sericite zone to an outer partially complete propylitic zone. The mineralization within the orebody is dominated by chalcopyrite and typical mineralized intercepts contain 0.19%–1.66% Cu (mean of 0.5% Cu) and 0.28–3.10 g/t Au (mean of 0.85 g/t) across an orebody that is around 1500 m thick. The deposit also contains a smaller orebody with Cu and Au grades of 0.15%–1.66% and 0.12–1.72 g/t, respectively. The overall deposit contains an estimated 1.66 Mt of contained Cu and 240 t of contained Au (Anhui 322 Geological Team, 2016), suggesting this area is highly prospective for further exploration for this type of mineralization.

3 Methods There are three steps in computation geoscience workflows, namely conceptual geological, mathematical, and simulation modeling (Zhao et al., 2008b; 2009; Zou et al., 2017). Here we construct conceptual geological, mathematical and simulation models for the Chating porphyry

Cu–Au deposit to both advance our knowledge of the processes that control the formation of porphyry copper deposits as well as answering the following specific questions: (1) What changes in temperature and pressure are associated with the formation of the Chating porphyry Cu–Au deposit? (2) Can we determine the time needed for the formation of the Chating porphyry Cu–Au deposit, and what implications does the longevity of this system have for porphyry Cu–Au exploration and genesis? Finally, (3) can our modeling be used in further local and regional exploration? The workflow applied in this paper to reflect the processes involved in ore formation is shown in Fig. 5. 3.1 Conceptual and simulation models for the Chating deposit Reviews of porphyry copper deposits (Sillitoe, 2010) and the energy release that occurs in the subvolcanic environment (Burnham, 1985) form the basis of our conceptual geological model, and the relationship between porphyry Cu stocks, underlying plutons, overlaying comagmatic volcanic rocks, and the lithocap environment is shown in Fig. 6. The conceptual model of the Chating deposit is based on previous research in the porphyry Cu-Au mineralizing environment (Sillitoe, 2010; Burnham, 1985; Weis et al., 2012; Weis, 2015) combined with the geological characteristics of the deposit (as shown in the cross-section A–B in Fig. 4 and the spatial relationship model shown in Fig. 6). The area of mineralization shown in Fig. 4 combined with the results of drillcore analysis indicates that the mineral deposit in the study area remains open with ore-grade Cu mineralization at depths of -1800 m. We incorporate the open nature of the deposit in our modeling, setting a maximum depth of -3000 m and a width of 3800 m, some five times the width of the deep-seated deep porphyritic quartz diorite intrusion in the study area. Previous calculations of the temperature and pressure of formation of the deposit based on the analysis of mineralization-related biotite (Xiao et al., 2018; 2019) indicated that the deposit formed at pressures of 44–85 MPa, yielding calculated depths of 1.7–3.3 km (mean of 2.47 km). These biotites were sampled at a relatively shallow depth of –110 m, so we add a 2.36 km layer to the surface of our model to represent ancient sedimentary units that were subsequently denuded and eroded away. The stratigraphic data given in Table 1 indicates a Quaternary to Jurassic sedimentary thickness of 2.24–10.59 km, indicating that the use of 2.36 km thick overlying layer in our model is reasonable. The previous research in the study area also indicated that the

porphyritic quartz diorite crystallized at temperatures of 746C–773C, with the porphyry-type mineralization forming at 260C–310C and the skarn-type mineralization in this area forming at 270C–410C (Ji, 2018; Xiao et al., 2018; 2019). Our modeling reflects this by giving the porphyritic quartz diorite a set temperature of 500C with a constant heat source of 500C at the base of the intrusion, reflecting the fact that this igneous body must have a higher temperature than the ore-forming fluids derived from these magmas (Liu et al., 2011; Liu & Dai, 2014; Zou et al., 2017). The model has initial Cu2+, Fe2+, and S2– concentrations of 0 mol/m3 and the other parts of the model have a temperature gradient of 25C/km with a surface temperature of 20C, reflecting average surface temperatures. Our model incorporates a pressure gradient of 26.5 MPa/km reflecting the average density of the rocks in this area and a surface pressure that is equal to atmospheric pressure. We used a calculation time of 100,000 years with a time step of 40 years and our model was setup to yield transient results. The simulation model was constructed using the boundary conditions and conceptual model outlined above (Fig. 7) and the resulting subdivision model used is shown in Fig. 8, with relevant rock material parameters given in Table 2. The boundaries of the model are open and the boundary temperature is the same as the geothermal gradient whereas the temperature at the base of the porphyritic quartz diorite is fixed at 773.15 K (i.e. 500C). Boundary pressures are the same as the lithostatic pressure gradient, automatically generating Darcy speed values. The hydrostatic pressure is not taken into consideration because the reaction zone is at a depth of more than –2 km below the surface, meaning it is unlikely to be affected by near-surface hydrostatic pressures. The fact that the Cu2+, Fe2+ and H2S within the ore-forming fluids are derived from the magmas within porphyry systems (Heinrich, 2005; Richards, 2014) means that we use inlet concentrations of 1760 ppm Cu2+, 3323 ppm Fe2+, and 2500 ppm S2-, using average fluid compositions derived from previous research on porphyry systems (Rusk et al., 2004; Vanko et al., 2001). The concentrations of Cu2+, Fe2+ and S2are set to be zero along all other boundaries. 3.2 Mathematical modeling of the Chating deposit The main driving force that enables the release and subsequent evolution of exsolved magmatic–hydrothermal fluids from a magma body is dynamic porosity and permeability, fluid-flow driven by temperature and pressure differences, and chemical reactions within pore

spaces. The entire magmatic-hydrothermal system involves a number of physical and chemical processes that are controlled by fluid-flow, heat transfer, mechanics, chemical reactions and material migration. These factors affect each other and combine in various ways in the overall process of ore formation (Fig. 9). The main associated processes and their formulas and equations are given below. (1) Heat transfer and the body force Temperature and pressure gradients are calculated using: 𝑇 = 𝑇0 ―𝑦 ∙ 𝐺𝑇

(Eq. 1)

𝑃 = 𝑃0 ―𝑦 ∙ 𝐺𝑃

(Eq. 2)

where 𝑇 is temperature in C, 𝑇0 is room temperature (normally 20C under 1 atmospheric pressure, i.e. 0.1013 MPa), 𝑦 is depth in m, 𝐺𝑇 is the temperature gradient within the geological units in the model (25C/km; Bickle, 1978; Lister, 1963), 𝑃 is pressure in MPa, 𝑃0 is the atmospheric pressure, and 𝐺𝑃 is the pressure gradient within the geological units in the model, reflecting the average density of these units (26.5 MPa/km; Anderson, 1989; Hart et al., 1995; Hu et al., 2003; Table 3). The equations that describe the conservation of energy are given below and are default equations used by the Comsol software package: ∂𝑇

𝑑𝑧(𝜌𝐶𝑝)𝑒𝑓𝑓 ∂𝑡 + 𝑑𝑧𝜌𝐶𝑝𝜈 ∙ ∇𝑇 + ∇ ∙ 𝐪 = 𝑑𝑧𝑄 + 𝑞0 + 𝑑𝑧𝑄𝑣𝑑

(Eq. 3)

𝐪 = ― 𝑑𝑧𝑘𝑒𝑓𝑓∇𝑇

(Eq. 4)

(𝜌𝐶𝑝)𝑒𝑓𝑓 = 𝜃p𝜌p𝐶𝑝,p +(1 ― 𝜃p)𝜌𝐶𝑝

(Eq. 5)

𝑘𝑒𝑓𝑓 = 𝜃p𝐶pr + (1 ― 𝜃p)𝐶𝑚 + 𝑘𝑑𝑖𝑠𝑝 𝜃p = 1 ― 𝜀

(Eq. 6) (Eq. 7)

where 𝑑𝑧 is the thickness of the section (set as 800 m), 𝜌 is fluid density, 𝐶𝑝 is the heat capacity of the mixture of fluid and chemical reactants (details are given in section 3 below), 𝑇 is temperature, 𝑡 is time, 𝜈 is the speed of fluid flow, 𝐪 is heat dissipation, 𝑞0 is generalized inward heat flux, 𝑄 is reaction heat, 𝑄𝑣𝑑 is the heat transferred from the surrounding environment, 𝜌p is the density of porous rock, 𝜃p is the volume fraction of porous rock, 𝐶𝑝,p is specific heat capacity, 𝑘𝑒𝑓𝑓 is effective heat conductivity, 𝐶pr is the heat conductivity of porous

rock, 𝐶𝑚 is the heat conductivity of the mixture of fluid and chemical reactants (details are given in section (3) below), 𝑘𝑑𝑖𝑠𝑝 is the coefficient of initial heat dissipation to the surrounding environment, and 𝜀 is porosity. (2) Fluid-flow driven by pressure differentiation Fluid-flow in our model is governed by Darcy’s law (Mandl, 1988; Zhang et al., 2011; Kumar et al., 2016): 𝑘

ν = - 𝜇（∇𝑃 + 𝑔𝜌𝑙）

(Eq. 8)

∂

𝑄𝑚 = ∂𝑡(𝜀𝜌𝑙) +∇ ∙ (𝜌𝑙ν)

(Eq. 9)

where ν is the speed of fluid flow, 𝑘 is the permeability, 𝜇 is viscosity, 𝜀 is porosity, 𝑄𝑚 is the fluid source term (fluids are modeled as vectors in the COMSOL software package so they only have a direction and a value but no entity), 𝑄𝑚 is used to describe the total of the fluid flow in/through the model system (this term would be a sink term when fluids are flowing out of the model; Zhao et al., 2009), 𝑡 is time, ∇𝑃 is pressure gradient, and 𝑔𝜌𝑙 is the body force (gravity and liquid density) where 𝑔 is the gravitational constant and 𝜌𝑙 is the density of the liquid in question. (3) Chemical reaction, entropy, enthalpy, and coupling equations with heat transfer The chemical reaction component of our modeling used typical chalcopyrite formation equation and enthalpy and entropy variation equations to describe chemical reactions during ore-forming processes at temperatures of 260C–310C (Xiao et al., 2018, 2019) as follows (Eq. 11 to 14 are default equations in the Comsol software): 𝐶𝑢2 + + 𝐹𝑒2 + + 2𝑆2 ― →𝐶𝑢𝐹𝑒𝑆2 (𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒:𝑅𝐶𝑢𝐹𝑒𝑆2)

(Eq. 10)

𝐻 = ― ℎ𝐶𝑢2 + ― ℎ𝐹𝑒2 + ― 2ℎ𝑆2 ― + ℎ𝐶𝑢𝐹𝑒𝑆2

(Eq. 11)

𝑆 = ― 𝑠𝐶𝑢2 + ― 𝑠𝐹𝑒2 + ― 2𝑠𝑆2 ― + 𝑠𝐶𝑢𝐹𝑒𝑆2

(Eq. 12)

𝐶𝑝,𝑖

𝑐𝑖𝑀𝑖

𝐶𝑝 = ∑𝑤𝑖 𝑀𝑖 , 𝑤𝑖 = ∑𝑐 𝑀 𝑖

(

( ) 𝑥𝑖

𝐶𝑚 = 0.5 ∑𝑖𝑥𝑖𝐶𝑐,𝑖 + ∑𝑖𝐶𝑐,𝑖

―1

), 𝑥 = 𝑖

(Eq. 13)

𝑖

𝑐𝑖 ∑𝑖𝑐𝑖

(Eq. 14)

where 𝑅𝐶𝑢𝐹𝑒𝑆2 is the reaction rate during the simulated process, 𝐻 is total reaction enthalpy, ℎ𝐶𝑢2 + is the enthalpy of 𝐶𝑢2 + , ℎ𝐹𝑒2 + is the enthalpy of 𝐹𝑒2 + , ℎ𝑆2 ― is the enthalpy of 𝑆2 ― and ℎ𝐶𝑢𝐹𝑒𝑆2 is the enthalpy of 𝐶𝑢𝐹𝑒𝑆2, all with units of J/mol, S is the total reaction entropy,

𝑠𝐶𝑢2 + is the entropy of 𝐶𝑢2 + , 𝑠𝐹𝑒2 + is the entropy of 𝐹𝑒2 + , 𝑠𝑆2 ― is the entropy of 𝑆2 ― and 𝑠𝐶𝑢𝐹𝑒𝑆2 is the entropy of 𝐶𝑢𝐹𝑒𝑆2, all with units of J/(mol ∙ K). In addition, 𝑤𝑖 is the ratio fraction of material 𝑖, 𝐶𝑝,𝑖 is the heat capacity of material 𝑖, 𝑀𝑖 is the molar weight of material 𝑖, 𝑐𝑖 is the concentration of material 𝑖; 𝑥𝑖 is the concentration fraction of material 𝑖, and 𝐶𝑐,𝑖 is the heat conductivity of material 𝑖, where 𝑖 can be 1, 2, 3…. (4) Changes in porosity and permeability The deposition of chalcopyrite changes porosity as well as other factors such as heat transfer, fluid flow, material migration and the body force. The ordinary differential equation of porosity is given by the following equation (COMSOL case library, 2015): ∂2𝜀

∂𝜀

𝑒𝑎∂𝑡2 + 𝑑𝑎 ∙ ∂𝑡 = ― 𝑘𝜀 ∙

𝜀𝑟𝑀𝐶 𝜌𝐶

(Eq. 15)

where 𝑒𝑎 is the mass coefficient (equal to 0 in our model), 𝑑𝑎 is the damping coefficient (equal to 1 in our model), 𝑘𝜀 is a constant (equal to 104 in our model), 𝑀𝐶 is the molar weight of chalcopyrite, 𝜌𝐶 is the density of chalcopyrite, 𝜀 is the dynamic porosity of the background media and 𝑟 is the chemical reaction rate. This equation can be rearranged as follows: ∂𝜀

𝑓 = ∂𝑡 = ― 𝑘𝜀 ∙

𝜀𝑟𝑀𝐶 𝜌𝐶

(Eq. 16)

where the initial value of 𝑓 is 0. Porosity changes can also cause changes in permeability, with these changes described using the Kozeny-Carman relationship (Carman, 1937): 𝐾 𝐾0

=

𝜀3𝐶0

(Eq. 17)

𝜀30𝐶

where 𝐾0 is initial permeability, 𝐾 is dynamic permeability, 𝜀0 is initial porosity, 𝜀 is dynamic porosity, 𝐶0 is the initial specific surface area, and 𝐶 is the dynamic surface area. Later, Ives and Pienvichitr (1965) simplified the Kozeny-Carman relation by assuming 𝐶 ∝ 𝜀𝑥 as follows: 𝐾 𝐾0

𝜀

= (𝜀0)𝜂

(Eq. 18)

where 𝜂 is a fitting factor that makes the formula more adaptable than the original Kozeny-Carman relation. This adaptability and the fact that this formula only requires porosity 𝜀 and initial porosity 𝜀0 values combined with the fitting factor 𝜂 has meant that this formula has been widely used to describe the relationship between dynamic permeability and dynamic porosity. Previous research has also made this formula even easier to use by defining a relationship between

different values of 𝜂 and the circumstances these values most often apply to (Bernabe et al., 2003), where 𝜂 values of 2.5–3 apply to plastic compression, 𝜂 =

8 applies to mineral

precipitation, 𝜂 > 10 applies to chemical (i.e. hydrothermal in our case) alteration, and 𝜂 > 20 applies to mineral dissolution (Bernabé et al., 2003; Hommel & Coltman, 2018). Here we use an 𝜂 value of 8 given out modeling is focused on mineral precipitation (Hommel & Coltman, 2018) yielding the following permeability formula that was used in our modeling: 𝜀 8

𝐾 = 𝐾0 ∙ (𝜀0)

(Eq. 19)

(5) Transport of dilute minerals in porous rock The transportation of the fluids that precipitate minerals through rocks using Darcy’s law is implicitly related to the nature of the porous media, as reflected by the fluid-flow equation used for porous rocks as follows: ∂𝑐𝑖 ∂𝑡

+∇ ∙ ( ― 𝐷𝑖∇𝑐𝑖) +ν ∙ ∇𝑐𝑖 = 𝑅𝑖 𝑁𝑖 = ― 𝐷𝑖∇𝑐𝑖 +𝜈𝑐𝑖

(Eq. 20) (Eq. 21)

where 𝐷𝑖 is the diffusion coefficient of reactant 𝑖 in fluid, ν is the speed of fluid flow, 𝑅𝑖 is the reaction rate of reactant 𝑖, and 𝑁𝑖 is the amount of reactant 𝑖 that takes part in the chemical reaction. A summary of all of the important symbols used in this study is given in Table 4.

4 Results 4.1 Temperature The numerical simulations undertaken during this study used the model outlined in the Methods section (Section 3.1 and section 3.2) of the paper. The results of this simulation include the distribution of temperature, pressure, chalcopyrite precipitation and reaction rates as discussed below. The distribution of temperature over time in our is shown in Fig. 10A1–A5, with the distribution of areas with temperatures of 260C–310C shown in Fig. 10B1–B5, reflecting the temperatures of formation of the porphyry-type mineralization within the Chating deposit (Ji, 2018; Xiao et al., 2018; 2019) Previous research has determined that temperature is a key control on the localization of mineralization within hydrothermal systems (Zhao et al., 2008a, 2009), with areas with increased fluctuations in temperature and greater fluid flow rates representing zones that are more

favourable for the generation of mineralization (Ord et al., 2002; Zhao et al., 2002, 2008a; Sillitoe, 2010; Zou et al., 2017; Richards, 2018). This means the distribution of temperatures within our model (Fig. 10) can be used to delineate locations that are more prospective for mineralization. This highlights a deeper part of the system that appears prospective, matching the known geology in this area (Fig. 11) and indicating that there may be a 614 m thick zone beneath existing geological cross-sections (and therefore the extent of current drilling) that is highly prospective and should be considered a key target for future mineral exploration. 4.2 Pressure The modelled distribution of pressure in our simulation is shown in Fig. 12(A–B). The pressure within the mineralizing systems appears to be nearly identical to the lithostatic pressure gradient and seems to have very little direct influence on the mineralizing processes in this area. This indicates that factors other than the lithostatic pressure regime have very little impact on pressure variations despite the fact that pressure drives fluid flow, as evidenced by the fact that the overall pressure within our model remains basically invariant throughout the entire simulation. There is a minor pressure anomaly within the centre of Fig. 12(A) that may reflect a pressure change as a result of chemical reactions, but the overall simulation does not provide any evidence of major pressure changes within the system over time. Smaller changes may be present in the system but the resolution of this model does not allow these changes to be identified and assessed, and these smaller changes are likely to have little impact on the overall mineralizing system unlike the larger temperature changes discussed above. 4.3 Distribution of mineralization The distribution of chalcopyrite predicted by our modeling is shown in Fig. 13. The low concentrations of chalcopyrite within the system meant that we used logarithmic values to define the color gradient that depicts the distribution of this ore mineral within Fig. 13. This identification of areas containing chalcopyrite used inlet Cu2+, Fe2+ and S2– concentrations that were conceptually set based on fluid inclusion data, meaning that the chalcopyrite concentrations in our model are only relative. This in turn means that our modelling can predict areas with high and low concentrations of chalcopyrite but cannot identify actual mineral abundances, although normalizing our data to known chalcopyrite concentrations may make this possible during future research. The results of our simulation matches areas of known mineralization and again suggests

that more Cu mineralization may be present within the periphery of and deeper than areas of known mineralization, consistent with the results of our temperature modelling discussed above. A minor area of mineralization in the eroded area within our model (0 to –2360 m) may also be associated with ascending ore-forming fluids. Although this area of mineralization was most likely low grade, it may have provided evidence for exploration if these overlying units were not eroded away; equally the erosion of these weakly mineralized units may suggest that some surficial geochemical evidence of mineralization might be present in this area despite the fact that the deposit is currently blind. This suggests a role for surface geochemistry in the exploration for blind or deep-seated deposits in this area providing these deposits have similar erosional histories. This also suggests that any other orebodies discovered in this region may have undergone supergene enrichment, increasing their economic potential. However, the equilibrium coefficient of the chemical reaction is unknown, meaning that the entire reaction remains in some form of an unknown equilibrium. This in turn means that the values of chalcopyrite concentrations and the associated natural logarithmic values determined from these concentrations are relative, indicating the values are qualitative rather than quantitative and not have any practical use in e.g. resource estimation (Hu et al., 2019). 4.4 Estimation of the Duration of Ore-Forming Processes Our simulation automatically calculates the distribution and variations in chemical reaction rates as shown in Fig. 14. This modelling predicts chemical reaction rates between 3.06  10-14 mol/(m3·s) and 2.38  10-13 mol/(m3·s) which can be combined with average measured Cu grades within the deposit to predict the duration of the processes that formed the Chating Cu–Au deposit as follows (Zou et al., 2017): 𝑇𝐷 = 𝑇𝐴 =

𝑊𝐶𝑢𝐹𝑒𝑆2 ∙ 𝜌𝑝𝑜𝑟𝑝ℎ𝑦𝑟𝑦 𝑅𝐶𝑢𝐹𝑒𝑆2 ∙ 𝑀𝐶𝑢𝐹𝑒𝑆2 𝑇𝐷

60 × 60 × 24 × 365

where 𝑇𝐷 is the duration of the ore-forming event with a unit of s, 𝑊𝐶𝑢𝐹𝑒𝑆2 is the Cu grade of chalcopyrite (0.5%), 𝜌𝑝𝑜𝑟𝑝ℎ𝑦𝑟𝑦 is the density of the mineralized porphyry (2650 kg/m3), 𝑅𝐶𝑢𝐹𝑒𝑆2 is the chemical reaction rate, 𝑀𝐶𝑢𝐹𝑒𝑆2 is the molar weight of chalcopyrite (183.5 g/mol), and 𝑇𝐴 is the duration of the ore-forming processes in the study area (in years). This modelling yield results between 9,600 and 75,000 years, indicating that the deposition of chalcopyrite within

Chating porphyry Cu–Au deposit occurred over a period between 9,600 and 75,000 years.

5 Discussion Modern geochronological analysis (e.g. Ar–Ar, U–Pb, Re–Os) can typically yield results with an internal precision of around 0.1%–0.2%, meaning that in absolutely ideal circumstances the duration of the hydrothermal systems that form mineral deposits can be constrained to around this precision (e.g. Chiaradia et al., 2013). However, although these absolutely ideal circumstances do exist in some areas, enabling the precise determination of specific events within mineralizing (and associated magmatic) systems (e.g. Large et al., 2018; Von Quadt et al., 2011; Rohrmeier et al., 2013; Buret et al., 2017), a significant proportion of mineral deposits are non-ideal. These deposits have constraints such as a lack of dateable minerals, non-ideal samples (e.g. post-mineralization resetting by metamorphism), are affected by increasing in absolute uncertainties with age (i.e. 0.1% uncertainty at 10 Ma is 10,000 years, 0.1% uncertainty at 100 Ma is 100,000 years, and so on), the presence of multiple pulses of mineralization and uncertainties over what minerals are related to mineralization and what minerals reflect geological processes that are not related to mineralization (e.g. Hou et al., 2019). This often means that determining the longevity of mineralizing systems is difficult, indicating that the numerical modeling of hydrothermal processes within mineralizing systems can provide extra constraints on the duration of these systems. Advances in the quantification of geological processes as a result of the rapid development of computer science and technology and research in branches of mathematical geology such as advanced numerical modeling of geological and geochemical processes at micro-, macro-, and regional scales, two and three-dimensional prospectivity modeling, and machine learning have also enhanced the insights into geological systems that can be provided by numerical modeling. This is exemplified by previous research into the numerical simulation of geological processes that has taken this type of modeling from purely theoretical into more applied approaches (Weis et al., 2012; Ord et al., 2012; Hobbs et al., 2000; Zou et al., 2017). This study provides another example of this numerical quantification of geological processes, defining a workflow to quantitatively study the ore-forming processes of a porphyry copper deposit based on the formers. Our modeling indicates that the simulated distribution of temperature and mineralization within the Chating porphyry Cu-Au deposit matches the known geology and areas of mineralization within the study area, indicating the validity of our approach to modeling the

formation of the deposit. Our modeling has also enabled the identification of the duration of the mineralizing system within the study area based on chemical reaction rate estimates, suggesting that the Chating deposit formed over a period of 9,600 to 75,000 years. Although our numerical modeling approach is relatively simple and conceptual, the consistency of these results with the known geology of the region indicates that this is a valid approach that can be used to further our understanding of mineralizing systems. This simple and conceptual approach admittedly does not simulate the entirety of the processes involved in mineral deposit formation, an approach that would require the development of extremely complex modelling and access to supercomputing facilities. Our estimates of the duration of ore-deposit formation are significantly shorter than some estimates based on traditional approaches such as those for the Khetri copper belt (about 7 Ma; Li et al., 2018a) and Quellaveco copper formation (whole porphyry system for about 3.25 Ma; Sillitoe & Mortensen, 2010). However, our predicted duration of formation of the Chating deposit is similar to the results of numerical modeling of the formation of the Bingham Canyon, Yerington and Batu Hijau deposits, all of which seemed to have formed over periods ranging from 50,000 to 100,000 years (Weis et al., 2012). The longevity of the Chating mineralizing system is also similar to the duration of the mineralizing processes that formed the Hutouya skarn Pb–Zn deposit predicted by numerical simulation, suggesting that the galena in this deposit was deposited over a period of 10,000–60,000 years whereas the sphalerite in this deposit was deposited over a span of between 30,000 and 100,000 years (Zou et al., 2017). Our predicted duration of the mineralizing event at Chating is similar to the timespan of porphyry deposit formation predicted by high precision geochronological analysis, as evidenced by research by Large et al. (2018), who suggested that the mineralization within the Ok Tedi deposit in Papua New Guinea (and the majority of other porphyry systems) formed over tens of thousands of years, much shorter than the lifetime of the upper crustal magma reservoirs that have lifespans of a few hundred thousand years (as predicted by cooling rates and consistent with the longer timespans estimated by Li et al., 2018a, and Sillitoe & Mortensen, 2010). These much shorter duration mineralizing events are also consistent with other research, predicting that porphyry copper deposits may form in timespans of less than a few tens of thousands to a hundred thousand years (Buret et al., 2016; Von Quadt et al., 2011). This change in apparent timing reflects the pulses of activity within porphyry systems, as

shown by recent research on the Qulong porphyry Cu–Mo deposit that documented the formation of the system over a span of ~0.266 Ma split into shorter stages of 76,000, 60,000, and 120,000 years (Li et al., 2018b), although the initial pulse formed some ~60% of the mineralization within this system. This contrasts with the Chating system, which our modeling and the research of Xiao et al. (2019) suggests formed in a single short-lived period of metallogenesis rather than as a result of multiple stages over a longer more protracted period of ore deposit formation. This may reflect the mixing of porphyry-type magmato-hydrothermal fluids with external fluids during the formation of the Chating deposit (Xiao et al., 2019) a process that caused a single pulse of mineralization rather than the gradual decrease in magmato-hydrothermal fluids within the system documented in the multiple pulse Qulong system (Li et al., 2018b). This suggests that multiple end-members may exist within the porphyry copper class of mineral deposits, ranging from single pulse deposits, such as the Chating deposit that formed over 9,600–75,000 years to those deposits that form as a result of multiple pulses of ore formation over a span of several hundred thousand years. Future research should focus on determining the implications of these end-members for the size and grade of porphyry systems. Our numerical modeling also provides useful information for exploration below the currently open maximum depth of drilling at Chating and indicates the potential use of this approach for exploration in deeper parts of mineralized systems. Identifying deep-seated areas for mineral exploration has been problematic for a number of years as near-surface targets are identified and brought into production, requiring exploration to proceed to deeper levels over time. The deep nature of this exploration means that only certain types of exploration tools can be used, such as geophysics and drilling based on structural and geophysical targeting (Emmermann & Lauterjung, 1997; Liu et al., 2006; Yang et al., 2006; Huerta et al., 2009; Nykänen & Salmirinne, 2007). Recent advances in three-dimensional prospectivity modeling for mineral exploration has highlighted the potential use of numerical modeling in this type of exploration targeting (Porwal et al., 2010; Porwal and Carranza, 2015; Li et al., 2015; Mao et al., 2011). However, the simulation undertaken during this study provides another method of predicting the location of areas that are prospective for deep exploration, supplementing more traditional exploration approaches and removing risks related to the verification of conditional independence. Our modeling of temperatures during mineralization and the distribution of ore minerals within the Chating system

indicates that areas deeper than the current extent of exploration should be considered highly prospective, as indicated by the fact that mineralization remains open at depths of -1800 m. Our modeling also correctly predicts the location of areas of known mineralization despite being based on modeling rather than any training of our dataset using areas of previously known mineralization. This indicates that our simulation approach provides independent identification of highly prospective targets for future exploration as well as having potential use in exploration for deep-seated mineralization elsewhere. This is consistent with the results of Li et al. (2019), who used a numerical simulation within a three-dimensional prospectivity analysis of the skarn-dominated Yueshan orefield in China. This research indicated that the incorporation of numerical simulation enhanced the results of prospectivity modeling, indicating the usefulness of numerical simulation in exploration at depth, where traditional geological and geophysical approaches may be less effective. This study used numerical simulation to identify areas for future exploration deeper and within the periphery of areas of known mineralization within a porphyry-type deposit, but the effectiveness of this approach on larger scales, such as entire orefields, needs to be assessed. The Chating orefield is located within the northern part of the newly discovered Nanling–Xuancheng mining district, an area rated as highly prospective after the discovery and exploration of the Chating porphyry deposit (Anhui 322 Geological Team, 2016). However, the majority of the area is covered by Quaternary sediments (Fig. 3), meaning very few outcropping older rocks that may host or be associated with mineralization are present in this region. This presents a significant challenge to traditional approaches to exploration, meaning that the construction of a simplified orefield-scale numerical model and the associated numerical simulation of mineralized processes based on the Chating deposit and the existing geological and geophysical data for this area may increase exploration success in this region. This approach is far more economical than the significant amount of drilling that is needed to test the entire area, which covers some 23 km  16 km. This situation emphasizes the increasing challenges facing exploration globally, not just within this region. This reflects the gradual increase of exploration depth as the majority of outcropping and near-surface mineralization has been identified and exploited over time, indicating that mathematical/numerical and quantitative approaches to mineral exploration will become more important over time, indicating that this type of numerical simulation will be more

widely applied during future mineral exploration. The numerical modeling undertaken during this study can also provide other insights beyond the duration of mineralizing systems. These include the type and location of phase changes, variations in stress within the system, rates of fluid flow, and variations in the composition of material within the system (provided that researchers have identified the nature of the material within the system and the reactions that can affect their composition). Developing more detailed numerical models during future research will provide deeper insights into ore- and rock-forming processes that operate within porphyry systems as well as other types of hydrothermal deposits, providing key insights into mineralizing systems that can be used to inform future approaches to exploration. However, there are some limitations involved in the use of finite element simulations such as those undertaken using Comsol software during this study. These models cannot completely express all of the characteristics of some of the variables involved in mineral deposit formation (e.g. chalcopyrite precipitation), causing slight mismatches between the results of our simulations and the known geology within the study area, even though the latter is also not completely known (Figs 13 and 14). This issue can only be resolved by either significant modification to the existing computational methods or by the use of an approach involving a new series of calculations. However, the rapid development of computer hardware and computational methods and continued theoretical research into the numerical simulation of nonlinear geological processes means that this issue is likely to be resolved in the near future. One other issue with the numerical modeling undertaken during this study is that it is a 2D model of the 3D environment, meaning any influences from the surrounding environment (i.e. both sides of the modeled cross-section) are ignored. The 3D shape of the contact between geological units in the study area (i.e., sedimentary units and the intrusion) may also influence the distribution of the concentration of chalcopyrite and associated mineralization in this region. Finally, it is also currently not possible to determine the equilibrium coefficient of the chemical reaction that was used to model the precipitation of chalcopyrite in the study area. Although all of these issues are outside of the remit of this paper, further research into resolving one or all of these issues will certainly not only improve this type of modeling but will also increase the practical significance of the results of this type of numerical simulation.

6 Conclusions The Chating Cu-Au deposit is a porphyry copper deposit that was discovered in 2011. This study numerically modelled the processes that formed the deposit, producing the following key findings: (1) The simulated distribution of temperature and chalcopyrite mineralization match areas of known mineralization identified during drilling, indicating that our modelling can potentially be used to predict areas of hitherto unknown mineralization as well as verifying the potential use of this type of approach in economic geology research and mineral exploration. (2) The chemical reaction rates predicted during our simulation can be combined with known grades of Cu within the deposit to determine the duration of metallogenesis in the study area. This calculation suggests that the chalcopyrite within the Chating Cu-Au deposit was deposited over a duration between 9,600 and 75,000 years, similar to the duration of pulses of mineralization identified within other porphyry systems using traditional geochronological approaches. (3) The modelled distribution of temperatures within the mineralizing system and the predicted locations of chalcopyrite deposition suggests that there may be deeper zones of Cu mineralization at depths greater than the current -1800 m depth of drilling in the Chating area. This suggests that these deep-seated prospective areas represent key targets for future exploration down to depths of -2414 m, indicating that deeper drilling to investigate these potential extensions to the known deposit (which is open at depth) is warranted. (4) The computational methods used during this study have some limitations that are reflected in the slight mismatch between the actual and predicated locations of mineralization within the study area. Further research and development into computational methods, theoretical geochemistry, and the geochemistry and numerical simulation of nonlinear geological processes will undoubtedly improve both the results of numerical simulations such as the model presented in this study but also the practical significance of this type of research.

Acknowledgements This research was financially supported by funds from the National Natural Science Foundation of China (Grant No. 41820104007, 41702353, 41672069, 41872247), the National

Key R&D Program of China (Grant No. 2016YFC0600209，2016YFC0600206), the Scientific and Technological Program of Land and Resources of Anhui province (Grant No. 2016-K-4), the Fundamental Research Funds for the Central Universities (Grant No. JZ2016HGTA0710), China Scholarship Council, and the Fundamental Research Funds for the Central Universities (Grant No. JZ2018HGTB0249, PA2019GDZC0093). We thank Miss. Xuanxuan Li, Miss Qingling Xiao, Dr. Shiwei Wang, the Anhui Quanxin mining company, the Anhui 812 Geological Team, and the Geological Exploration Technology Institute of Anhui Province, all of whom undertook fieldwork examining and exploring the Chating Cu–Mo deposit, for their input into our modeling of this porphyry deposit. We also thank two anonymous reviewers for constructive comments on an earlier version of this article.

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Captions Fig. 1. Map showing the location of major volcanic basins and intrusions within the Middle and Lower Yangtze River Valley. Modified from Zhai (1992) and Zhou et al. (2017).

Fig. 2. Map showing the geology and mineral deposits of the Nanling-Xuancheng mining camp (Anhui 322 Geological Team, 2016). Fig. 3. Map showing the geology and mineral deposits of the Chating orefield; box shows the location of Fig. 4 (Anhui 322 Geological Team, 2016). Fig. 4. Map showing the geology of the area around the Chating copper deposit (Quaternary sediments are omitted for clarity) and a cross-section across the main orebody (Anhui 322 Geological Team, 2016). Fig. 5. Workflow used in the numerical modeling of the formation of the Chating ore deposit during this study (Hu et al., 2019). Fig. 6. Generalized schematic diagram showing the spatial relationship between porphyry Cu stocks, underlying plutons, overlaying comagmatic volcanic rocks and the lithocap environment (Sillitoe, 2010) Fig. 7. Simulation model used during this study constructed using the conceptual model outlined in the text. Fig. 8. Diagram showing the subdivision of the study area used for numerical modeling during this study. Fig. 9. The coupled relationship of fluid-flow, mechanics, heat transfer, material migration and chemical reactions during mineralization and mineral deposit formation (Hu et al., 2019). Fig. 10. Diagrams showing variations in the distribution of temperature over time (A) within the entire model and (B) focusing on areas with temperatures of 260C–310C, reflecting the temperature of formation of the porphyry-type mineralization within the Chating system. Fig. 11. Cross-sections based on our modelling (A) and the known geology (B) showing the location of prospective regions below current drilling that appear highly prospective based on the modelling of temperatures within the mineralizing system and knowledge of the key temperatures of ore formation (260C–310C). Fig. 12. Modeled pressure distributions (A) throughout the entirety of our simulation compared to (B) the normal lithostatic pressure gradient in this area, showing only minor changes in the pressure within the system during ore deposit formation. Fig. 13. The modelled distribution of chalcopyrite (A; shown in logarithmic form to enhance the differences in color gradient within the figure) based on the simulations undertaken during this study compared with areas of known mineralization (B). Note that the distribution shown in (A) is relative and predicts areas with low and high concentrations of chalcopyrite rather than absolute abundances. Fig. 14. Modeled distribution of variations in chemical reaction rate within our simulation; these rates vary between a maximum of 2.38  10-13 mol/(m3·s) and a minimum of 3.06  10-14 mol/(m3·s). Table 1. Stratigraphy of the study area (Geological exploration technology institute of Anhui province, 2016).

Table 2. Rock material parameters used in our simulation model (adapted from Geological exploration technology institute of Anhui province, 2016) Table 3. Pressure gradients within different layers in the lithosphere (Hu et al., 2003; where 𝑑𝑝 is pressure increment, 𝑑ℎ is depth increment, 𝑔 is the gravity constant, and 𝜌 is the density of the object). Table 4. Description of symbols (listed in order of appearance).

Conflict of interest statement No conflict of interest exists in the submission of this manuscript, and it’s approved by all authors for publication.

Table 1. Stratigraphy of the study area (Geological exploration technology institute of Anhui province, 2016).

Age

Unit Code

Lithological description

Unit (m)

Chishan Formation Xuannan Formation Pukou Formation Gecun Formation Zhongfencun Formation

Q N E K2c K2x K1p K1g K1z

1-30 0-25 0-20 1055-7605 50-700 379 >700 20-300

Jurassic

Zhongfencun Formation

J3z

Triassic

Nanlinghu Formation Helongshan Formation

T1n T1h

Clay Breccia, mudstone Breccia, mudstone Sandstone Quartz sandstone Sandstone, breccia Mudstone, sandstone Limestone, sandstone, andesite Limestone, sandstone, andesite Limestone Limestone

Quaternary Neogene Paleogene Cretaceous

Lithostratigraphic unit

20-300 160-645 130-220

thickness

Permian

Carboniferous Devonian Silurian

Yinkeng Formation Dalong Formation Longtan Formation Gufeng Formation Qixia Formation Chuanshan Formation Huanglong Formation Gaolishan Formation Wutong Formation Maoshan Formation Fentou Formation Gaojiabian Formation

T1y P3d P2-3l P2g P1q P1c C2h C1g D3w S1-2m S1f S1g

Limestone Quartz sandstone Quartz sandstone Shale Limestone Limestone Limestone Siltstone Quartz sandstone Quartz sandstone Lithic sandstone Fine-grained sandstone, mudstone, shale

200-300 10-50 100-300 200-300 160-300 30-50 30-50 60-90 85-176 600-900 800-1500 700-1300

Table 2. Rock material parameters used in our simulation model (adapted from Geological exploration technology institute of Anhui province, 2016) Rock type

Rock

Density

description

(Kg/m3)

Specific heat

Porosity

Permeability

Thermal

Heat

(/1)

(10-12)

expansion

conductivity

capacity

coefficient

(W/m K)

(J/Kg

(10-6/K)

K) Wall rock

Sandstone

2660

880

0.28

8.0

7

3.1

Intrusion

Porphyritic quartz diorite

2650

680

0.22

8.6

8

2.9

Denuded and

Sandstone and limestone

2540

720

0.27

8.5

7

3.5

overlying sedimentary units

Table 3. Pressure gradients within different layers in the lithosphere (Hu et al., 2003; where 𝑑𝑝 is pressure increment, 𝑑ℎ is depth increment, 𝑔 is the gravity constant, and 𝜌 is the density of the object).

Formula

Layer classification

Pressure gradient (MPa/km)

Calculated depth (km)

Lithostatic gradient: 𝑑𝑝 =𝑔∙ 𝜌 𝑑ℎ

Upper crust Middle crust Lower crust Crust (average) Lithosphere (average)

26.5 29 33.75 30 33

0-15 15-24.4 24.4-115 Whole crust Whole lithosphere

Table 4. Description of symbols (listed in the order of appearance).

Symbol

Description

Unit or value if a constant

𝑇

Temperature

C

𝑇0

Room temperature

𝑦

Depth

C m

𝐺𝑇

Temperature gradient

𝑃

Pressure

C/km MPa

𝑃0

Atmospheric pressure

MPa

𝐺𝑃

Pressure gradient

MPa/km

𝑑𝑧

Thickness

m

𝜌

Density

Kg/m3

𝐶𝑝

Heat capacity

J/(kg∙K)

𝑡

Time

s

𝜈

Speed of fluid flow

m/s

𝐪

Heat dissipation

J

𝑞0

Generalized inward heat flux

W/m2

𝑄

Reaction heat

J

𝑄𝑣𝑑 𝜌p

Heat transferred from surroundings

J

Density of porous rock

kg/m3

𝜃p

Volume fraction of porous rock

𝐶𝑝,p

Specific heat capacity

J/(kg∙K)

𝑘𝑒𝑓𝑓 𝐶pr

Effective heat conductivity

W/(m∙K)

Heat conductivity of porous rock

W/(m∙K)

𝐶𝑚

Heat conductivity of the mixture of fluid and chemical reactants

W/(m∙K)

𝑘𝑑𝑖𝑠𝑝

Coefficient of initial heat dissipation to the surrounding environment

𝑘

Permeability

𝜀

Porosity

𝜇

Viscosity

m2 Pa∙s

𝑄𝑚

Source term of fluid

∇𝑃

Pressure gradient (in Darcy’s law)

Pa/m

𝑔

Gravitational constant

m/s2

𝜌𝑙

Density of the object liquid

kg/m3

𝐻

Total reaction enthalpy

J/mol

S ℎ𝑖

Total reaction entropy

J/(mol∙K)

Reaction enthalpy of material i

J/mol

𝑠𝑖

Reaction entropy of material i

J/(mol∙K)

𝑤𝑖 𝐶𝑝,𝑖

Ratio fraction of material 𝑖 Heat capacity of material 𝑖

J/(kg∙K)

𝑀𝑖

Molar weight of material 𝑖

g/mol

𝑐𝑖

Concentration of material 𝑖

mol/m3

𝑥𝑖 𝐶𝑐,𝑖

Concentration fraction of material 𝑖 Heat conductivity of material 𝑖

W/(m∙K)

𝑒𝑎

Mass coefficient

0

𝑑𝑎

Damping coefficient

1

𝑘𝜀

Constant value

104

𝑀𝐶

Molar weight of chalcopyrite

g/mol

𝜌𝐶

Density of chalcopyrite

kg/m3

𝑟

Chemical reaction rate

mol/(m3∙s)

𝐾0

Initial permeability

m2

𝐾

Dynamic permeability

m2

𝜀0 𝐶𝑐,𝑖

Initial porosity Heat capacity of material 𝑖

W/(m∙K)

𝜂

Fitting factor

𝐷𝑖

Diffusion coefficient of reactant 𝑖 Reaction rate of reactant 𝑖

m2/s

Reacted amount of reactant 𝑖

mol

𝑅𝑖 𝑁𝑖

Graphical Abstract:

Fig. 1. Workflow used in our study

mol/(m3∙s)

Fig. 2. The modelled distribution of chalcopyrite (A; shown in logarithmic form to enhance the differences in color gradient within the figure) based on the simulations undertaken during this study compared with areas of known mineralization (B). Note that the distribution shown in (A) is relative and predicts areas with low and high concentrations of chalcopyrite rather than absolute abundances.

Fig. 3. Modeled distribution of variations in chemical reaction rate within our simulation; these rates vary between a maximum of 2.38  10-13 mol/(m3·s) and a minimum of 3.06  10-14 mol/(m3·s).

Here we present our workflow and results of the distribution of mineralization and reaction rate of the Chating deposit. The workflow is the core guiding ideology of our work. During the numerical modeling research, we tried to couple heat transfer, fluid-flow, mechanics, chemical reaction and material migration. The results provides useful information for exploration below the currently open maximum depth of drilling at Chating and indicates the potential use of this approach for exploration in deeper parts of mineralized systems as well as enables the identification of the duration of the mineralizing system within the study area based on chemical reaction rate estimates, suggesting that the Chating deposit formed over a period of 9,600 to 75,000 years. This study outlines the practical value of numerical simulation in determining the processes that operate during mineral deposit formation and how this knowledge can be used in

further mineral exploration.

1. This study presents a new coupled numerical model for the genesis of the deep-seated and unexposed Chating porphyry-type copper-gold deposit. This approach furthers our understanding of the key processes that led to the formation of this deposit and enables the identification of areas prospective for future exploration that would be difficult or impossible to identify using traditional deep exploration techniques and in a significantly more economical fashion. 2. Our modeling has enabled the identification of the duration of the mineralizing system within the study area based on chemical reaction rate estimates 3. Our numerical modeling also provides useful information for exploration below the currently open maximum depth of drilling at Chating and indicates the potential use of this approach for exploration in deeper parts of mineralized systems.