We have constructed a 3D photoionization model of a planetary nebula (PN) similar in structure to NGC 7009 with its outer pair of knots (also known as FLIERs - fast, low-ionization emission regions). The work is motivated by the fact that the strong [NII]λ6583 line emission from FLIERs in many PNe has been attributed to a significant local overabundance of nitrogen. We explore the possibility that the apparent enhanced nitrogen abundance previously reported in the FLIERs may be due to ionization effects. The model is constrained by the results obtained by Gonçalves et al. from the analysis of both Hubble Space Telescope (HST) [OIII] and [NII] images, and long-slit spectra of NGC 7009. Our model is indeed able to reproduce the main spectroscopic and imaging characteristics of the bright inner rim of NGC 7009 and its outer pairs of knots, assuming homogeneous elemental abundances throughout the nebula, for nitrogen as well as all the other elements included in the model. We also study the effects of a narrow slit on our non-spherically symmetric density distribution, via the convolution of the model results with the profile of the long slit used to obtain the spectroscopic observations that constrained our model. This effect significantly enhances the [NII]/Hβ emission, more in the FLIERs than in the inner rim. Because of the fact that the (N+/N)/(O+/O) ratio predicted by our models is 0.60 for the rim and is 0.72 for the knots, so clearly in disagreement with the N+/N = O+/O assumption of the ionization correction factor (icf) method, the icfs will be underestimated by the empirical scheme, in both components, rim and knots, but more so in the knots. This effect is partly responsible for the apparent inhomogeneous N abundance empirically derived. The differences in the above ratio in these two components of the nebula may be due to a number of effects including charge exchange - as pointed out previously by other authors - and the difference in the ionization potentials of the relevant species - which makes this ratio extremely sensitive to the shape of the local radiation field. Because of the latter, a realistic density distribution is essential to the modelling of a non-spherical object, if useful information is to be extracted from spatially resolved observations, as in the case of NGC 7009.