Steam system heat exchanger network optimisation using degenerate solutions : a focus on pressure drop and boiler efficiency

Abstract

This work presents a revised methodology to minimise pressure drop through a steam system heat exchanger network (HEN). This is based on previous work where network pressure drop is minimised after utility flow through the network has been reduced to its minimum. With the minimum utility flow as a parameter, the proposed methodology enlarges the solution space of the problem in an attempt to find a better pressure drop solution. The resulting minimum pressure drop found using this method is an improvement of 1.1 % and 7.4%, in two case studies respectively, on the current HEN minimisation problem formulation. The method is then extended to maintain boiler efficiency with the same minimum steam flowrate. Due to the simpler nature of the problem of maintaining boiler efficiency the proposed methodology did not yield improvements to the steam flowrate however a wider variety of network configurations was found. The steam flowrate to a HEN can be substantially reduced with the application of process integration. Reducing the steam flowrate to the HEN involves creating series heat exchanger connections, which ultimately increase the pressure drop to the system. The reduced steam flowrate also compromises the return condensate temperature and consequently reduces the efficiency of the steam boiler. A HEN optimisation and design methodology exists whereby the minimum steam flowrate to a heating utility system can be found and the pressure drop through the HEN can be minimised. This methodology does not however incorporate the full solution space of potential network configurations. This is as a result of network conditions of optimality which fix the outlet temperature of condensate streams leaving heat exchangers in order to achieve a globally optimal minimum steam flowrate. The minimum steam flowrate can still be achieved by relaxing the optimality conditions and allowing for variable heat exchanger outlet temperatures. Solutions of this nature are referred to as degenerate and are formulated with bilinear terms forming part of the energy balance constraints. The presence of bilinear terms results in a nonlinear, nonconvex mixed integer nonlinear programming (MINLP) problem. The bilinear terms are catered for in the methodology by the reformulation and linearisation technique of Quesada and Grossmann (1995) as well as the transformation and convexification technique of Pörn et al (2008). The reformulation and linearisation approach proved to be the most successful for the proposed problem. By utilising the larger solution space created by incorporating degenerate solutions into the HEN design process, many HEN design variables can potentially be further optimised once a minimum steam flowrate has been achieved. Consequently, this thesis concerns the optimisation of a steam system HEN by finding the minimum steam flowrate to the system and using it as a parameter while relaxing the conditions of network optimality to create solutions which can be degenerate. The complexities of MINLPs in the degenerate solutions are explored and a methodology to further optimise network pressure drop through heating networks is proposed. The methodology was also used to maintain boiler efficiency with a reduced steam flowrate which was achieved, but not improved upon from previous methodologies. While this methodology does not guarantee an improved HEN pressure drop, solutions adhering to the conditions of network optimality also fall within the solution space of the proposed methodology, therefore solutions achieved with current techniques from literature will not be compromised.