This paper focuses on the derivation of analytical formulae to estimate the effective capacity at freeway merges. It extends previous works by proposing a generic framework able to account for (i) heterogeneous vehicle characteristics and (ii) refined description of the physical interactions between upstream waves and downstream voids created by inserting vehicles within the merge area. The provided analytical formulae permit to directly compute the capacity values when the merge is self-active, i.e. when both upstream roads are congested while downstream traffic conditions are free-flow. They show that accounting for vehicle heterogeneity is not necessary when only the mean capacity is targeted. Calculations with the proper mean value for all parameters provide accurate estimates. This result is appealing because the shape of the parameter distributions does not need to be calibrated. However, this paper also shows that vehicle heterogeneity plays a major role in the flow dynamics just upstream of the merge.