This is the first of a series of papers devoted to derive the metallicity of old open clusters in order to study the time evolution of the chemical abundance gradient in the Galactic disk. We present detailed iron abundances from high resolution (R~40000) spectra of several red clump and bright giant stars in the open clusters IC 4651, NGC 2506 and NGC 6134. We observed 4 stars of NGC 2506, 3 stars of NGC 6134, and 5 stars of IC 4651 with the FEROS spectrograph at the ESO 1.5 m telescope; moreover, 3 other stars of NGC 6134 were observed with the UVES spectrograph on Kueyen (VLT UT2). After excluding the cool giants near the red giant branch tip (one in IC 4651 and one in NGC 2506), we found overall [Fe/H] values of -0.20 +/- 0.01, rms = 0.02 dex (2 stars) for NGC 2506, +0.15 +/- 0.03, rms = 0.07 dex (6 stars) for NGC 6134, and +0.11 +/- 0.01, rms = 0.01 dex (4 stars) for IC 4651. The metal abundances derived from line analysis for each star were extensively checked using spectrum synthesis of about 30 to 40 Fe I lines and 6 Fe II lines. Our spectroscopic temperatures provide reddening values in good agreement with literature data for these clusters, strengthening the reliability of the adopted temperature and metallicity scale. Also, gravities from the Fe equilibrium of ionization agree quite well with expectations based on cluster distance moduli and evolutionary masses.
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