The transformation of hydrated clay minerals (smectite) to anhydrous forms (illite) occurs in the diagenesis of shales in sedimentary basins. The released pore water can lead to excess pore pressures and is of concern in oil drilling operations. Most simply, the process can be modeled as a first-order thermally activated reaction, but an alternative interpretation is that diagenesis occurs via dissolution of smectite in free pore water and subsequent precipitation of illite. We show how such a realistic model of diagenesis can be included in a compactive model of the sediment/pore water system, and by using the limit of weak solubility (also known as solid density asymptotics), we show how an explicit expression can be derived for the smectite dissolution rate, even when this is mediated by feldspar dissolution and other reactions. In certain circumstances, the reaction rate reduces to that of a simple first-order model. By solving the model we also show that shale diagenesis provides a mechanism for the generation of fractures at depth in rapidly deposited sediments. When sedimentation is slow (or compaction is fast), the smectite to illite transition occurs over a reaction window which typically lies below the equilibrated normally pressured part of the profile, but it does not generally contribute significantly to the overpressuring.