Temperature–enthalpy curve for energy targeting of distillation columns

The temperature–enthalpy (T–H) diagram of a distillation column at practical near-minimum thermodynamic condition (PNMTC) or the column grand composite curve (CGCC) is a useful representation for energy targeting studies and may be generated from a converged simulation of a base-case column design. The calculation procedure for the CGCC involves determination of the net enthalpy deficit at each stage by generating envelopes from either the condenser end (top-down approach) or the reboiler end (bottom-up approach). However, the values calculated by the two approaches differ for stages with feeds because existing procedures for CGCC generation do not consider the enthalpy balances at the feed stages. In fact, the net enthalpy deficits at feed stages calculated by both approaches are erroneous even for the simplest case of binary distillation. A feed stage correction (FSC) that rigorously considers the mass and enthalpy balance equations at feed stages is proposed in this work to resolve the discrepancy. Instead of assuming that the compositions obtained from the converged simulation for a feed stage will remain unchanged at PNMTC, the pinched compositions for the feed are determined by the intersection of the equilibrium curve and the feed q-line. Rather than perform an additional flash calculation to establish the pinched feed compositions, a quadratic approximation is developed here for column targeting purposes by assuming the relative volatility obtained from the simulation to remain constant in the neighborhood of the feed stage. The proposed FSC ensures that the CGCC is identical whether the calculations are performed by the top-down approach or the bottom-up approach. The effect of the FSC on the targets for energy conservation by reflux modification, feed conditioning, and introduction of side reboilers/condensers is discussed. As the energy target for reflux modification is determined by the CGCC pinch which typically occurs at or close to the feed location, the significance of the FSC on the reflux modification target is highlighted through several case studies including a complex column featuring multiple feeds and consequently multiple pinch points. The CGCCs for these case studies are generated by a computer program based on the FSC and a single analytical equation for the calculation of the net enthalpy deficits that allows every stage to have a feed, liquid product, vapor product, and side exchanger. The studies show that the reflux modification targets may be erroneous in many cases, if the FSC is ignored.