The invention features methods and systems for producing commercial quality carbon dioxide (CO2) of 90% to +99% purity using, wet calcium carbonate lime mud produced in a manufacturing operation, for instance, Kraft pulp mill lime mud (a.k.a., “lime mud”) as a feedstock to a multi-stage lime mud calcination process. This process may be fueled with waste water treatment plant (WWTP), sludge biomass, precipitated lignins, coal, or other low cost solid fuels. High reactivity “soft-burned” lime product (“calcine”) required in the mill's chemical recovery circuit is also produced, and steam and heated boiler feed-water is generated and exported to the mill's steam distribution and generation system as well as hot process water for use in the mill's boiler house and manufacturing operation. The system for calcining calcium carbonate lime mud produced from a re-causticizing manufacturing operation and converting it to re-burned lime and CO2 comprises a calciner and a combustor linked by a moving media heat transfer (MMHT) system or apparatus. The MMHT system or apparatus thermally links separate fluid bed combustion (exothermic) and calcination (endothermic) stages with a solid particulate media. The system further comprises a flash dryer or spray dryer that utilizes exhausted heat from the calcination stage.