Processes for preparing diaryl and/or alkylaryl carbonates from dialkyl carbonates

Processes comprising: reacting a dialkyl carbonate and an aromatic hydroxy compound in the presence of a transesterification catalyst in a first reaction column, the first reaction column comprising a top section, a bottom section, a rectifying section in an upper portion of the column and a reaction zone below the rectifying section; feeding a bottom product from the first reaction column to a further reaction column; the bottom product comprising a diaryl carbonate, an alkylaryl carbonate, or both, and residual unreacted dialkyl carbonate and aromatic hydroxy compound; the further reaction column comprising a top section, a rectifying section in an upper portion of the column and a reaction zone below the rectifying section; and reacting the residual unreacted dialkyl carbonate and aromatic hydroxy compound in the further reaction column; feeding a process stream to a distillation column, the process stream comprising a mixture of unreacted dialkyl carbonate and one or more reaction-product alcohols drawn from the first reaction column, the further reaction column, or both, such that the unreacted dialkyl carbonate is separated from the one or more reaction-product alcohols; and recycling the separated, unreacted dialkyl carbonate to the first reaction column; wherein the further reaction column comprises one or more condensers, and heat of condensation from the one or more condensers is fed back into the process.