In this study, we introduce a stochastic method to delineate the mineral effective surface area (ESA) evolution during a re-cycling reactive flow-through transport experiment on a sandstone under geologic reservoir conditions, with a focus on the dissolution of its dolomite cement, Ca_1.05Mg_0.75Fe_0.2(CO_3)_2. CO_2-enriched brine was circulated through this sandstone specimen for 137 cycles (~270 hours) to examine the evolution of in-situ hydraulic properties and CO_2-enriched brine-dolomite geochemical reactions. The bulk permeability of the sandstone specimen decreased from 356 mD before the reaction to 139 mD after the reaction, while porosity increased from 21.9% to 23.2% due to a solid volume loss of 0.25 ml. Chemical analyses on experimental effluents during the first cycle yielded a dolomite reactivity of ~2.45 mmol~m^-3~s^-1, a corresponding sample-averaged ESA of ~8.86× 10^-4~m^2/g, and an ESA coefficient of 1.36× 10^-2, indicating limited participation of the physically exposed mineral surface area. As the dissolution reaction progressed, the ESA is observed to first increase, then decrease. This change in ESA can be qualitatively reproduced employing SEM-image-based stochastic analyses on dolomite dissolution. These results provide a new approach to analyze and upscale the ESA during geochemical reactions, which are involved in a wide range of geo-engineering operations.