To solve the problem of water carryover in the supercritical CO2 separation and mining process in the CO2 plume geothermal system, a three-dimensional shell-tube hollow fiber membrane absorption separator is designed in this study. A coupled species transport model, a porous medium model, and an absorption mathematical model are established, and the flow field and separation characteristics in the circular and flat tubes are analyzed using numerical simulation. The results show that the membrane separation efficiency increases with an increase in the flatness and membrane tube length. When the inlet velocity of the mixture is 0.1 m/s, the separation efficiency can reach 75.92%. Selecting a smaller flow Reynolds number and a more significant membrane tube flatness will reduce the water mass fraction at the outlet. When adding baffles of different shapes to the membrane tube, the mixture fluid in the membrane tube meanders forward and flows in the shape of “Z” under the blocking effect of the arcuate baffles. With an increase in the number of arcuate baffles in the membrane tube, the membrane separation efficiency of the separator increases continuously. The mixture fluid flows in the membrane tube with the built-in torsional baffles in a spiral manner, and the separation efficiency of the membrane separator increases with a torsion ratio reduction in the membrane tube.