There has been tremendous recent interest in Direct Air Capture (DAC) systems. A key part of any DAC system are the multiple air intake units. In particular, the arrangement of such units for optimal capture and sequestration is critical. Accordingly, this work develops an easy to use model for a modular unit system, where an approximate flow field is computed for each unit and the aggregate flow field is developed by summing the fields from each unit. This allows for a modular framework that can be used for rapid simulation and design of an overall DAC system. The rapid rate at which these simulations can be completed enables the ability to explore inverse problems seeking to determine which parameter combinations can deliver the maximum sequestration of tracer plume particles for the minimum amount of energy input. In order to cast the objective mathematically, we set up an inverse as a Machine Learning Algorithm (MLA); specifically a Genetic MLA (G-MLA) variant, which is well-suited for nonconvex optimization. Numerical examples are provided to illustrate the framework.