Expanding upon on the frequent use of reactive transport models to understand processes related to the formation of hydrothermal alteration zones and mineral deposits we introduce here a methodology that allows to infer the fluid composition from measurements of mineralogical or chemical compositions. An expectation maximisation algorithm is deployed to objectively solve the joint problem of identifying alteration zones in the measured data and estimating the fluid composition based on the fit between the mineral abundances in the measured and predicted alteration zones. Using Greisenisation, the hydrothermal alteration of Granite as a test case we present a range of synthetic tests to illustrate how our methodology allows for objective inference of the mineralising fluid. For the East Kemptville tin deposit in Nova Scotia, our from normative mineral compositions made inference about the fluid composition compares favourably with previous independent estimates, thereby demonstrating the feasibility of the proposed calibration methodology.