Analysis of chemical abundances in planetary nebulae with [WC] central stars. II. Chemical abundances and the abundance discrepancy factor

(Abridged) We present the abundance analysis of 12 PNe ionized by [WC]-type stars and wels obtained from high-resolution spectrophotometric data. Our main aims are to determine the chemical composition of the PNe and to study the behaviour of the abundance discrepancy problem (ADF) in this type of planetary nebulae. The detection of a large number of optical recombination lines (ORLs) and collisionally excited lines (CELs) from different ions were presented previously. Most of the ORLs were reported for the first time in these PNe. Ionic abundances were derived from the available CELs and ORLs, using previously determined physical conditions. Based on these two sets of ionic abundances, we derived the total chemical abundances in the nebulae using suitable ICFs (when available). In spite of the [WC] nature of the central stars, moderate ADF(O^++), in the range from 1.2 to 4, were found for all the objects. We found that when the quality of the spectra is high enough the ORLs O^++/H^+ abundance ratios obtained from different multiplets excited mainly by recombination are very similar. Possible dependence of ADFs with some nebular characteristics were analysed, finding no correlation. Abundances derived from CELs were corrected by determining the t^2 parameter. O abundances for PNe, derived from ORLs, are in general larger than the solar abundance. We derived the C/O ratio from ORLs and N/O and alpha-element/O ratios from CELs and found that these PNe are, in average, N-and C-richer than the average of large PN samples. About half of our sample is C-rich (C/O>1). The alpha-elements grow in lockstep with O abundance. Comparing the N/O and C /O ratios with those derived from stellar evolution models, we estimate that about half of our PNe have progenitors with initial masses > 4 M_sun. No correlation was found between the stellar [WC]-type and the nebular abundances.