This invention utilizes mechanical vapor compression and / or thermal vapor compression, integrating compression loops across multiple process stages. A sequential network of compressors is used to increase the pressure and
condensation temperature of vapor within each process stage as an internal vapor flow, and as an inter-vapor flow branching between process stages. Because available vapor is shared between compressor stages, the number of compressors can be reduced, improving economics. By separating vapor between compressor stages to balance the vapor
mass flow rate across multiple process stages in the incremental compressor stages, the entire vapor
compression system can be customized to individual process energy requirements and adapt to dynamic fluctuations in
process conditions.