Treatments of naturally fractured carbonate formations typically involve acid injection when damage of natural fractures (NFs) occurs mechanically and chemically. Coupled modeling of both mechanisms is often neglected. We build a quantitative model of damageable reservoir, where the permeability depends on the shear and tensile activation of NFs, as well as acid transport and reaction. Simulations demonstrate model applicability to NF acidizing and acid fracturing. Particularly, we show that strong pressure drawdowns in tight carbonates result in steep production declines because of NF pinching.

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