Addressing climate change constitutes one of the major scientific challenges of this century, and it is widely acknowledged that anthropogenic CO2 emissions largely contribute to this issue. To achieve the "net-zero" target and keep the rise in global average temperature below 1.5 °C, negative emission technologies must be developed and deployed at a large scale. This study investigates the feasibility of using membranes as direct air capture (DAC) technology to extract CO2 from atmospheric air to produce low-purity CO2. In this work, a two-stage hollow fiber membrane module process is designed and modeled using the AVEVA Process Simulation platform to produce a low-purity (≈5%) CO2 permeate stream. Such low-purity CO2 streams could have several possible applications such as algae growth, catalytic oxidation, and enhanced oil recovery. An operability analysis is performed by mapping a feasible range of input parameters, which include membrane surface area and membrane performance metrics, to an output set, which consists of CO2 purity, recovery, and net energy consumption. The base case for this simulation study is generated considering a facilitated transport membrane with high CO2/N2 separation performance (CO2 permeance = 2100 GPU and CO2/N2 selectivity = 1100), when tested under DAC conditions. With a constant membrane area, both membranes' intrinsic performances are found to have a considerable impact on the purity, recovery, and energy consumption. The area of the first module plays a dominant role in determining the recovery, purity, and energy demands, and in fact, increasing the area of the second membrane has a negative impact on the overall energy consumption, without improving the overall purities. The CO2 capture capacity of DAC units is important for implementation and scale-up. In this context, the performed analysis showed that the m-DAC process could be appropriate as a small-capacity system (0.1-1 Mt/year of air), with reasonable recoveries and overall purity. Finally, a preliminary CO2 emissions analysis is carried out for the membrane-based DAC process, which leads to the conclusion that the overall energy grid must be powered by renewable sources for the technology to qualify within the negative emissions category.