Numerical simulation of compositional flow problems commonly involves the use of 1st- or 2nd-order Euler time stepping. Method of lines (MOL), using highly accurate and efficient ODE solvers, is an alternative technique which, although frequently applied to the solution of two-phase, two-component flow problems, has generally been overlooked for problems concerning more than two components. This article presents the development of a numerical simulator for 1D, compressible, two-phase, three-component, radially symmetric flow using the method of lines (MOL) and a 3rd-order accurate spatial discretization using a weighted essentially non-oscillatory (WENO) scheme. The MOL implementation enables application of the MATLAB ODE solver, ODE15s, for time integration. Simulation examples are presented in the context of $$\hbox {CO}_2$$ CO 2 injection into a reservoir containing a mixture of $$\hbox {CH}_4$$ CH 4 and $$\hbox {H}_2\hbox {O}$$ H 2 O . Following an assumption of constant equilibrium ratios for $$\hbox {CO}_2$$ CO 2 and $$\hbox {CH}_4$$ CH 4 , a ternary flash calculator is developed providing closed-form relationships for exact interpolation between equations of state for $$\hbox {CO}_2$$ CO 2 – $$\hbox {H}_2\hbox {O}$$ H 2 O and $$\hbox {CH}_4$$ CH 4 – $$\hbox {H}_2\hbox {O}$$ H 2 O binary mixtures. The numerical code is successfully tested and verified for a range of scenarios by comparison with an existing analytical solution.