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

Abstract

The Dongguashan skarn copper deposit can be considered as the product of the transport-chemical reaction coupling process of ore-forming materials (for example, complexes of copper) in discrete, parallel fractures in a porous medium system. A mathematical model of metallogenesis has been established and the accurate analytical solutions for depicting the transport of ore-forming materials have been worked out. In establishing the 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 longitudinal mechanical dispersion of ore-forming materials (solutes) along the fracture axis; (3) diffusion of ore-forming materials from the fractures to the wall media; (4) adsorption of ore-forming materials on the surface of wall-rock matrices; (5) adsorption of ore-forming materials within the wall-rock matrices; (6) reduction of the concentrations of solutes due to the chemical reactions between ore fluids and wall-rock matrices and the precipitation 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 case of D = 0 (without dispersion) and of D ¬= 0 (with dispersion), a simple criterion can be established, with which one can assess the importance of longitudinal dispersion along the fracture system. Case studies showed that the developing extent of fractures in the system would exert a great influence on the transport rate and distance of ore-forming materials. In case that fractures are developed at small intervals, ore-forming materials will be transported along the fracture system over larger distance because of the limited capability of the wall rocks to store ore-forming materials. That is to say, larger orebodies would be formed. In the case of higher transport rates of ore fluids along the fracture system the longitudinal mechanical dispersion is negligible, but in the reversed case, the longitudinal mechanical dispersion would exert a great influence on fluid transport. Under such circumstances, the longitudinal mechanical dispersion could not be neglected. In the normal case of D ¬= 0, the steady-state solutions could provide a potential approach to predicting the ultimate distance over which ore fluids of a certain concentration level penetrate along the fracture system, that is, how long an orebody would extend. Analytical solutions can rationally interpret the spatial distribution characteristics of strata-bound skarn copper deposits, the rules governing spatial variations in ore texture and ore grade, as well as other important geological characteristics of the ore deposits. This work will provide a better understanding of the metallogenic mechanism of strata-bound skarn copper deposits widely spread along the Middle-Lower Reaches of the Yangtze River Valley and its adjacent areas in China.