Room acoustic models are used in immersive applications to create convincing virtual environments. The computational cost of full-scale physical models remains prohibitive for most real-time auralisation systems. Scattering delay network (SDN) is a perceptually-motivated and computationally efficient modelling concept that renders the line of sight and first-order reflections accurately, whilst approximating higher order reflections with progressively coarser spatio-temporal resolution. This paper develops a generalised SDN framework capable of rendering reflections up to a selected order accurately. The generalisation requires two issues to be considered: i) spherical spreading attenuation, and ii) placement of scattering nodes, both of which are addressed here. Simulations demonstrate that the proposed model has a similar energy behaviour to that of the image source method (ISM) and improves over standard SDN in terms of normalised echo density and in terms of accuracy of delay, attenuation and direction of early reflections, whilst maintaining the same complexity as standard SDN.