The abundances derived from permitted lines run from similar to about an order of magnitude higher than those derived from forbidden lines (see the review by Liu 2001). By assuming that collisional deexcitation is not important (low density limit) and that the objects are chemically homogeneous it is possible to reach agreement between both types of determinations adopting a t2 > 0.00.
The t2 values determined from observations are in the 0.00 to 0.09 range, while those values predicted by chemically homogeneous photoionization models, CHPM, are in the 0.005 to 0.025 range. We can divide the well observed PNe in three groups: a) those that have t2 values smaller than 0.025, they can be fitted with CHPM and comprise about a third of the well studied cases, b) those with intermediate t2 values, in the 0.025 to 0.045 range, and c) those with t2 larger than 0.045, most of these objects are of Type I (Peimbert 1978; Peimbert et al. 1995) and show complex velocity fields reaching velocity differences of many hundreds of km s-1, for these objects the deposition of mechanical energy might be significative. A lot of effort has been put into the determination of t2 and special attention has been given to those objects with the largest t2 values.
To explain the t2 differences between the predicted values from CHPM and the observed values at least eight possible causes have been suggested in the literature (see the review by Esteban 2001): a) large density variations, b) chemical inhomogeneities, c) deposition of mechanical energy due to shocks or dissipation of turbulent motions, d) enhanced dielectronic recombination (Garnett & Dinerstein 2001), e) shadowed regions ionized by indirect radiation from the nebula rather than direct radiation from the ionizing star (Mathis 1995), f) magnetic reconnection (Ferland 2001), g) observational errors, and h) errors in the atomic parameters.
Some of these causes might be present in some objects and not in others. Only a careful analysis of a given object will indicate the relative importance of each of them.
One question that we want to answer is: which are the representative abundances for the whole nebula, those provided by the forbidden lines or those provided by the recombination lines? The answer is fundamental to constrain the evolution of intermediate mass stars and the chemical evolution of the Galaxy. If the effects due to b) and d) dominate then the representative abundances for the bulk of the mass ejected are those given by forbidden lines (see Liu et al. 2000; Liu 2001; Péquignot et al. 2001), alternatively if effects due to a), c), and e) dominate then the representative abundances are those given by the permitted lines. Carigi (2001) has constructed models of the chemical evolution of the Galaxy based on observational yields of carbon derived from recombination lines and from forbidden lines of planetary nebulae, she finds that the models that use the yields based on permitted lines agree better with the observational constrains provided by H II regions and stars of the solar vicinity, than the models based on the yields derived from forbidden lines.