A method includes obtaining a model associated with production of natural gas from a well, where the well has a choke valve that controls flow of material including natural gas from the well. The method also includes identifying, using the model, a solution that increases an amount of natural gas obtained from the well over a specified time horizon. In addition, the method includes adjusting operation of the choke valve based on the identified solution. The model could be generated using geological data associated with the well and/or historical data associated with natural gas production from the well. A natural gas reservoir can be modeled as a continuous stirred bed with a rock or shale void fraction using mass or volumetric unit balances. Gas content versus pressure for the well can be plotted, and Langmuir adsorption parameters for the well can be identified using the plotted gas content versus pressure.