Modeling and simulating the transport of oxygen in blood provides critical insight on the planning of cardiovascular surgeries. Mathematical simulation provides a quantitative angle on the understanding of changes in hemodynamics. Due to the complexity of the cardio- vascular circulation, this is a computationally challenging task. Further, oxygen transport is coupled to the velocity field of blood. Thus, the numerical solution of the transport equation requires either the specification or the computation of the velocity field of blood. The latter approach is expensive when the three-dimensional Navier Stokes equations are considered, and the a-priori specification of the velocity does not account for changes in the velocity field. To counteract these difficulties, we propose a model reduction of the convection diffusion equation of oxygen in a compliant vessel with varying radius. We ob- tain a one-dimensional equation coupled to the reduced model of blood flow. We employ discontinuous Galerkin methods to efficiently solve the resulting system in one vessel. We show stability of the proposed numerical scheme for a general nonlinear convection diffusion equation. We verify the model using the method of manufactured solutions. We extend the numerical method to a bifurcation of vessels, and we simulate oxygen transport in a three vessel network