The dissipativity-based observer design approach is extended to a class of coupled systems of 1-D semi-linear parabolic partial differential equations (PDEs) of diffusion-convection-reaction type with in-domain point measurements. This class of systems covers important application examples like tubular or catalytic reactors. By combining a dissipativity (sector) condition for the nonlinearity with a modal measurement injection for the linear differential operator sufficient conditions for the exponential convergence of the observer are derived in the form of a linear matrix inequality (LMI). The performance of the proposed approach is illustrated for an exothermic tubular reactor model. (C) 2018 Elsevier Ltd. All rights reserved.