(abridged) In the inner regions of AGB outflows, several molecules have been detected with abundances much higher than those predicted from thermodynamic equilibrium (TE) chemical models. The presence of the majority of these species can be explained by shock-induced non-TE chemical models, where shocks caused by the pulsating star take the chemistry out of TE in the inner region. Moreover, a non-uniform density structure has been detected in several AGB outflows. A detailed parameter study on the quantitative effects of a non-homogeneous outflow has so far not been performed. We implement a porosity formalism for treating the increased leakage of light associated with radiation transport through a clumpy, porous medium. The effects from the altered UV radiation field penetration on the chemistry, accounting also for the increased reaction rates of two-body processes in the overdense clumps, are examined. We present a parameter study of the effect of clumping and porosity on the chemistry throughout the outflow. Both the higher density within the clumps and the increased UV radiation field penetration have an important impact on the chemistry, as they both alter the chemical pathways. The increased amount of UV radiation in the inner region leads to photodissociation of parent species, releasing the otherwise deficient elements. We find an increased abundance in the inner region of all species not expected to be present assuming TE chemistry, such as HCN in O-rich outflows, H$_2$O in C-rich outflows, and NH$_3$ in both. Outflows whose clumps have a large overdensity and that are very porous to the interstellar UV radiation field yield abundances comparable to those observed in O- and C-rich outflows for most of the unexpected species investigated. The inner wind abundances of H$_2$O in C-rich outflows and of NH$_3$ in O- and C-rich outflows are however underpredicted.
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