Fractured rocks are essential for flow, solute transport and energy production in geosystems. Existing studies on mineral reactions in fractured rocks mostly consider single mineral systems where reactions occur at the fracture wall without changing rock matrix properties. This work presents multicomponent reactive transport numerical experiments in a fractured rock from the Brady's field, a geothermal reservoir at a depth of 1,396 m in the Hot Springs Mountains, Nevada. Initial porosity, permeability, mineral composition (quartz, clay, and calcite), and fracture geometry are based on microscopy characterization and X-ray tomography. The model was calibrated using a CO2-saturated water flooding experiment. Three numerical experiments were carried out with the same initial physical properties however different calcite content. Although total dissolved masses are similar among the three cases, abundant calcite (50% (v/v), calcite50) leads to a localized, thick zone of large porosity increase while low calcite content (10% (v/v), calcite10) creates an extended and narrow zone of small porosity increase resulting in surprisingly larger change in effective transport property. After 300 days of dissolution, effective matrix diffusion coefficients increase by 9.9 and 19.6 times in cakite50 and calcite10, respectively, inducing corresponding 2.1 and 3.2 times rise in the slopes of power law tailing, a measure of transport properties. This counterintuitive results suggest that lower abundance of reactive minerals leads to greater alteration in the fractured media. Detailed analysis show that the effective rates of the fast-dissolving calcite are limited by diffusive transport in the altered matrix and the shape of the altered zone. In contrast, the while effective dissolution of slow-dissolving quartz depends on effective diffusion within the entire rock matrix. Calcite dissolution only occurs at the thin altered unaltered matrix interface of tens of micrometers thickness occupying less than 1% of the total calcite content. In contrast, all quartz are effectively dissolving. This work highlights the importance of mineralogical complexity in determining mineral dissolution and rock matrix property evolution.