We develop mathematical models to investigate anhydrite precipitation in hydrothermal recharge zones at ocean ridge axes. We first consider constant flow during hydrothermal recharge to estimate the depth, the depth interval over which anhydrite precipitation would occur, and the initial rate of porosity reduction. We find that the smaller the downward mass flux, the shallower and more broadly distributed the region of precipitation. For values of downward mass flux similar to that for high-temperature black smoker systems, the porosity would be clogged significantly in a matter of months to years depending upon the initial porosity. We then consider anhydrite precipitation in a buoyancy-driven single-pass model in which the reduction in permeability resulting from anhydrite precipitation exerts a feedback on the flow rate. This model gives results similar to the constant flow model for the initial depth, depth interval, and rate of porosity reduction. The effect of the permeability clogging on the flow rate, however, is twofold. First, the zone of anhydrite precipitation shallows and broadens as the flow rate decreases, thus allowing deeply deposited anhydrite to be preserved temporarily. Second, if the recharge area of the same size as the discharge area, anhydrite precipitation rapidly reduces the flow rate and the heat output of the hydrothermal system. If the initial porosity of the recharge zone is 1%, the area of the recharge zone must be ~10--100 times that of the discharge zone to maintain near steady state conditions for time periods of decades to hundreds of years. This result implies that recharge zones may be quite large and extend off axis as well as along axis.