One approach for cleaning up aquifers contaminated with organic chemicals is to stimulate biological degradation in situ by addition of gases such as oxygen or hydrogen, which can be introduced into the groundwater using novel hollow-fiber membrane gas transfer systems. In this research, pilot-scale experiments were performed using a 1 m × 2 m × 1 m model sand aquifer to evaluate the effects of membrane system design and operation on the zone of influence of the dissolved gas plume about a vertical narrow bore (2.54 cm inner diameter) well installed in the aquifer. Two membrane systems were evaluated: (1) a membrane module installed directly in the narrow bore slotted well (“in-well” design) which was operated passively and with addition of water pumped from a downgradient extraction well and (2) an “external” module located above the ground surface which was operated in pumped mode only. In addition to the physical experiments a two-dimensional MODFLOW-MT3D simulation model was created using commercial software, calibrated and verified using the experimental data, then used to evaluate additional operational strategies not investigated experimentally. The simulated zones of influence from the calibrated MODFLOW-MT3D model were in good agreement (−1.3 to 14.4%) with experimental observations. Simulations of various well configurations (i.e., locations of extraction and injection wells), pumping rates, and dissolved gas consumption rates suggested that these factors can have a significant effect on the zone of influence and hence the cost of installation and operation of a membrane gas transfer system.