Carbon conversion processes (where carbon dioxide is not only captured and stored, but converted to commercially-valuable products) have high barriers to sustained and large-scale commercial viability. Mass algae production as a means to carbon emissions reductions is considered to have great commercial potential, but the viability of deployment is going to rely on technological leaps supported by strong public and private investment. Presented in this Design Report is a novel pilot-scale microalgae cultivation system that successfully converts over 50% of the carbon dioxide (CO2) present in a stream of flue gas from a coal-red power plant flue gas into valuable biomass. The process operates at a carbon dioxide input rate of 200 kilograms per day from a 10% carbon dioxide by volume flue gas stream. A 9-15% Return on Investment over a 4-5 year period is reported. The project met a set of highly ambitious carbon conversion goals, and contributes to a positive outlook for the future of algae production for sustainable carbon emissions reduction and value-added product creation. This presented design should encourage investment into pilot-scale and demonstration facilities in a move towards large-scale operation. The presented process can be used to convert high volumes of CO2 to valuable biomass that can be sold for many applications ranging from feed to nutraceuticals to biofuels. The innovative "Hybrid Petal Reactor" design incorporates a central gas exchange column with a horizontal tubular photobioreactor system that harnesses sunlight during the day, and an internally- illuminated nighttime tank that involves innovative use of optics. The outdoor system was designed to scale with a series of tubes that branch out like petals" from the central gas exchange column. The tube design is optimized for high productivity and low costs. An emphasis was placed on designing a process highly considerate of biological constraints. The presented final design offers great flexibility and opportunity for scale-up.