  (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.
