High energy consumption is a major challenge currently threatening many industrial processes. This has made industrial processes such as absorptive CO2 capture expensive and energy intensive. However, research has shown that the application of Heat Exchanger Networks has the potential of minimizing energy demands in many industrial processes due to its energy recovery advantage. In this study, a sequential procedure is presented for the synthesis of heat exchanger network for multi-period operations with specified uncertainties in flow rates and variations in inlet and outlet temperatures of process streams. The synthesis task in this study was sequentially decomposed into three stages. Temperature interval method was used to determine the loads and minimum utilities required by the network in the first stage. Determination of the minimum number of units was considered in the second stage while the third stage was dedicated to the derivation of a network configuration and sizing of heat exchangers to determine the capital cost using area targeting technique. Efficacy of the proposed methodology was tested using an example from literature. A new heuristic rule was established and the network topologies obtained using the proposed approach testifies to the applicability of HENs for energy minimization during absorptive CO2 capture.