In this paper we show how the powerful ODE-based fluid-analysis technique for the stochastic process algebra PEPA is an approximation to the first moments of the counting processes in question. For a large class of models this approximation has a particularly simple form and it is possible to make qualitative statements regarding how the quality of the approximation varies for different parameters.\r\n\r\nFurthermore, this particular point of view facilitates a natural generalisation to higher order moments. This allows modellers to approximate, for instance, the variance of the component counts. In particular, we show how systems of ODEs facilitating the approximation of arbitrary moments of the component counting processes can be naturally defined. The effectiveness of this generalisation is illustrated by comparing the results with those obtained through stochastic simulation for a particular case study.