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Abstract In the oil industry chemical products are often injected during fluid transport either to modify the rheological characteristics, i.e. viscosity, or to stabilize crude oil composition by inhibition of phase separation. The effects are generally related to the dosed product concentration so it is important to study the transient variation in the amount of fluid incorporated to a stream mainly for cases where there is no mechanical pre-mixing of phases when the main flow is in the laminar regime. This paper presents a theoretical model based on the conservation equations of mass and momentum that prescribes the temporal evolution of the spatial concentration profiles under different conditions. An analytical solution to the model is proposed that shows how the behavior is dependent on the injection method. The theoretical results can be considered as a basis to predict how the injection method affects these profiles.