Natural methane hydrate has often been observed in sand layers that contain no particulate organic carbon (POC), but are surrounded by organic-rich, fine-grained marine muds. In this paper, we develop a reactive transport model (RTM) of a microbially-mediated set of POC degradation reactions, including hydrolysis of POC driven by extracellular enzymes, fermentation of the resulting high-molecular weight dissolved organic carbon (HMW-DOC), and methanogenesis that consumes low-molecular weight dissolved organic carbon (LMW-DOC). These processes are mediated by two groups of microbes, fermenters and methanogens that are heterogeneously distributed in different lithologies, with the largest numbers of microbes in the large pores of coarse-grained layers. We find that the RTM can reproduce methane hydrate occurrences observed in two different geological environments, at Walker Ridge Site 313-H (Gulf of Mexico) and IODP Site U1325 (Cascadia Margin). We also find that microbes can degrade POC even if they are physically separated, as extracellular enzymes and DOC can diffuse away from where they are produced by microbes. Microbial activity is highest at relatively early times after burial at shallow depths and near lithological boundaries, where concentration gradients transport solutes to intervals that contain the most microbes.