Operational optimization of industrial waste heat recovery systems: a comparison of linear, quadratic and nonlinear formulations

Computer-aided modeling and optimization are essential for realizing the efficiency potential of industrial waste heat recovery, where the dominant modeling challenge is the nonlinear nature of heat transfer. The choice of optimization formulation trades physical accuracy against computational effort, and mixed-integer quadratically constrained programming (MIQCP) has emerged as a potential compromise between linear and fully nonlinear models. This work presents a systematic comparison of linear, quadratic and nonlinear formulations (LP, MILP, QCP, MIQCP, NLP and MINLP) for the operational optimization of an industrial waste heat recovery system with two instrumented heat exchangers, in order to assess the potential of MIQCP. Heat transfer surrogates of each class are parameterized and validated on hourly measurement data covering a summer and a winter period, embedded into a common system optimization model, and evaluated with respect to accuracy, implementation complexity, computational time and the deviation in the calculated optimum. The latter is obtained by transferring each result to a common nonlinear reference model. The logarithmic mean temperature difference is found to be the dominant error source. MIQCP reproduces it more accurately than the linear and even the most advanced piecewise linear models at a fraction of their model size and combinatorial effort. The quadratic and nonlinear formulations reach the best dispatch, and MIQCP attains it within a relative optimality gap of 1e-4 certified by a global solver, where the nonlinear formulation admits only a local solution. The piecewise linear models return a costlier dispatch. Its cause is not the heat transfer surrogate but the linearized energy balance, which leaves an unpriced decision variable free. MIQCP is therefore an effective compromise for waste heat recovery optimization.