Analytical solutions for ore fluid transport in fractured rocks: a case study on ore-forming processes of the stratabound skarn copper deposits in China

The Dongguashan skarn copper deposit can be considered as theproduct of the transport-chemical reaction coupling processof ore-forming materials (for example, complexes of copper)in discrete, parallel fractures in a porous medium system. Amathematical model of metallogenesis has been established andthe accurate analytical solutions for depicting the transportof ore-forming materials have been worked out. In establishingthe model of metallogenesis and working out the analytical solutions,the following aspects have been taken into consideration: (1)advective transport along fractures; (2) diffusion and longitudinalmechanical dispersion of ore-forming materials (solutes) alongthe fracture axis; (3) diffusion of ore-forming materials fromthe fractures to the wall media; (4) adsorption of ore-formingmaterials on the surface of wall-rock matrices; (5) adsorptionof ore-forming materials within the wall-rock matrices; (6)reduction of the concentrations of solutes due to the chemicalreactions between ore fluids and wall-rock matrices and theprecipitation of ore-forming materials. The general transient solution takes the form of a double integral,which can be evaluated using the Gauss–Legendre quadrature.By comparing the steady-state solutions in the special caseof D = 0 (without dispersion) and of D 0 (with dispersion),a simple criterion can be established, with which one can assessthe importance of longitudinal dispersion along the fracturesystem. Case studies showed that the developing extent of fracturesin the system would exert a great influence on the transportrate and distance of ore-forming materials. In case that fracturesare developed at small intervals, ore-forming materials willbe transported along the fracture system over larger distancebecause of the limited capability of the wall rocks to storeore-forming materials. That is to say, larger orebodies wouldbe formed. In the case of higher transport rates of ore fluidsalong the fracture system the longitudinal mechanical dispersionis negligible, but in the reversed case, the longitudinal mechanicaldispersion would exert a great influence on fluid transport.Under such circumstances, the longitudinal mechanical dispersioncould not be neglected. In the normal case of D 0, the steady-statesolutions could provide a potential approach to predicting theultimate distance over which ore fluids of a certain concentrationlevel penetrate along the fracture system, that is, how longan orebody would extend. Analytical solutions can rationallyinterpret the spatial distribution characteristics of strata-boundskarn copper deposits, the rules governing spatial variationsin ore texture and ore grade, as well as other important geologicalcharacteristics of the ore deposits. This work will providea better understanding of the metallogenic mechanism of strata-boundskarn copper deposits widely spread along the Middle-Lower Reachesof the Yangtze River Valley and its adjacent areas in China.