Trans-critical CO2 quasi-combined cycles have recently been systematically analyzed, in order that the zero emission fuel-fired power units concept may be promoted. A 0.35-0.49 efficiency of such cycles-based plants were reported, in spite of the power use for O-2 production and CO2 condensation. In this paper, a zero emission CO2 capture power process and plant, COOLENERG (CO2 Loop for Energy and Nature, Enhanced by Refrigeration and Gas-turbines), a patent filed by the author, is thermodynamically modeled. The plant is operated by a CO2 quasi-combined two-stage gas-turbine cycle with CH, gas burning in an O-2/recycled CO2 mixture. It originally uses the advanced thermal absorption technology in cogeneration of power and cooling for its own benefit. Technical calculations show an important benefit of the COOLENERG, expressed by the net power efficiency (0.54), which is more than 1.09 times higher than that of COOPERATE working with same parameters. The increase of the advanced absorption unit efficiency favors the net global efficiency of the power plant and promotes safer and cheaper transport and disposal of the condensed CO2 to the sequestering place. The economic assessment indicates a payback period of 3.5-7 months of the COOLENERG additional investment as compared to COOPERATE.