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We study the hypothesis of high metallicity clumps being responsible for theabundance discrepancy found in planetary nebulae between the values obtainedfrom recombination and collisionaly excited lines. We generate grids ofphotoionization models combining cold metal-rich clumps emitting the heavyelement recombination lines, embedded in a normal metallicity regionresponsible for the forbidden lines. The two running parameters of the grid arethe metallicity of the clumps and its volume fraction relative to the wholenebula. We determine the density and temperatures (from the Balmer jump and the[OIII] 5007/4363 A line ratio), and the ionic abundances from the collisionaland recombination lines, as an observer would do. The metallicity of thenear-to-solar region is recovered, while the metallicity of the clumps issystematically underestimated, by up to 2 orders of magnitude. This is mainlybecause most of the H$\beta$ emission is coming from the "normal" region, andonly the small contribution emitted by the metal-rich clumps should be used. Wefind that a given ADF(O$^{++}$) can be reproduced by a small amount of richclumps, or a bigger amount of less rich clumps. Finally, comparing with theobservations of NGC 6153 we find 2 models that reproduce its ADF(O$^{++}$) andthe observed electron temperatures. We determine the fraction of oxygenembedded in the metal-rich region (with a fraction of volume less than 1%) tobe roughly between 25% and 60% of the total amount of oxygen in the nebula (afew 10$^{-3} M_\odot$).

Bi-abundance photoionization models of planetary nebulae: determining the amount of Oxygen in the metal rich component