A method incorporating the full diffusion-governed solidification kinetics and the ternary phase diagram into a multiphase volume average solidification model is presented. The motivation to develop such a model is to predict macrosegregation in castings. A key feature of this model, different from most previous ones which usually assume an infinite solute mixing in liquid (e.g. lever rule, Gulliver–Scheil), is that diffusions in both liquid and solid phases are considered. It is known that models with assumption of an infinite liquid mixing lead to erroneous estimation of the solidification path at the initial stage. Here solidification of a ternary alloy (Fe–0.45 wt.%C–1.06 wt.%Mn) is examined. As the two chosen alloy elements (C and Mn) have large differences in the solute partition coefficient, liquidus slope and liquid diffusion coefficient, the solidification path shows differently from those predicted by infinite liquid mixing models. The first part of this two-part investigation evaluates the full diffusion-governed kinetics and its influence on solidification path and microsegregation. Applications of the model for the calculation of solidification and macrosegregation are presented in the accompanying paper [Part 2].