Field scale reactive transport models of CO and HS mineral sequestration in basalts were developed with a focus on Reykjavik Energy's ongoing CarbFix and SulFix sour gas re-injection tests at Hellisheidi geothermal power plant, SW-Iceland. Field data, such as drill cuttings and a calcite cap-rock overlying the high-temperature geothermal reservoir, suggest that mineral CO and HS sequestration already plays an important role within Hellisheidi geothermal system. The data indicate CO sequestration to be most intensive from 550-800-m depth below surface, while HS sequestration is most intensive below 800-m depth. Injecting and precipitating CO and HS into nearby formations with the objective of imitating and accelerating natural sequestration processes should therefore be considered as an environmentally benign process. Reactive transport simulations predict rapid and efficient mineralization of both CO and HS into thermodynamically stable minerals, with calcite, magnesite, and pyrrhotite being the favored carbonate and sulfide minerals to form. At intermediate depths and low temperatures (25-90 C), calcite is the main CO sequestering carbonate predicted to form, while magnesite is the only carbonate predicted to form at high temperatures (250 C). Despite only being indicative, it is concluded from this study that the capture and sequestration of CO and HS from geothermal power plants are a viable option for reducing their gas emissions and that basalts may comprise ideal geological CO and HS storage formations.