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Carbonate grainstones from Apulia in Italy with varying degree of dolomitisation and calcite cementation have a wide range of porosity, permeability and elastic moduli. In general, elastic moduli increase with decreasing porosity and stiffening frame. By using the effective medium iso-frame model, the effect of frame stiffening due to cementation may be quantified independently of mineralogy and porosity. We find that for carbonate samples with less than 15% porosity, variation in elastic moduli is rather due to change in porosity than in change in pore stiffness. For samples with porosity over 20%, we rather find that for variation in elastic moduli, changes in pore stiffness plays a distinct role.