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analyzing how the process is affected by ππ3, it is assumed that ππ3 is always optimal with respect to energy consumption, which is the case if the set pressure of the throttling valve is operated by an intelligent control system. Similarly, if the exchangers are designed for a particular set of operating That is, ππ , h , h , h are optimized for each case and not directly explored in the sensitivity studies. In 2456 conditions, it can be assumed that the exchanger sizes to some extent can be optimized for the task. this approach the temperature pinch becomes the most important factor describing the heat exchanger sizes. The 14 parameters in ππ can be divided into two categories: β’ Optimized variables (ππ) related to process control (ππ3) and heat exchanger design (ππ2, h4, h5, h6). β’ Variables (ππ) contain the other operating conditions and equipment variables (ππ = ππ β ππ). A list of the optimization parameters, and the constraints applied, are shown in Table 1. 2.2.1 Optimization Parameters and Constraints Table 1. Optimized parameters and constraints for heat pump ABC. Heat pump AB and BC are modelled with one less parameter since these systems only have two gas coolers, h = h and h = h respectively. Parameters (ππ) Constraints ππ3 ππ3 β₯ ππ2 ππ ππβππ β₯ππβ₯ππ 4365 2 6 min,pinch 2 h4 h3 β₯ h4 β₯ h5 h5 h4 β₯ h5 β₯ h6 h6 h5 β₯ h6 β₯ h7 1 ππβ₯ππ+ππ 7 1 min,pinch ππpinch β₯ ππmin,pinch The objective function, in the minimization problem, is therefore defined as: min{βCOP( ππ)}, for given ππ, (9) which has ππ = 11 constraints (the inequalities are shown in Table 1). In particular, the requirement ππpinch β₯ ππmin,pinch complicates the optimization problem, because all the optimization parameters are directly related to pinch temperatures. However, a direct optimization approach is possible by implementing all the constraints in a penalty function: ππ(ππ) = βCOP(ππ) + βππ ππ β [max(0, ππ (ππ))]2, ππ=1 ππ ππ where ππππ are penalty factors and ππππ constraints function listed in Table 1. The pinch constraint is e.g. (10) (11) defined as: ππ (ππ)=ππ βππ 11 min,pinch pinch (ππ). 2.2.2 Optimization Algorithm There are multiple optimization algorithms available in MATLAB, and the current code optimizes the processes with a hybrid method combining multiple fminsearch and genetic algorithm (ga) searches (Eiksund et al., 2018). Fminsearch is a deterministic solver based on the Nelder-Mead simplex algorithm which can find a local minimum with a few function evaluations (Nelder and Mead, 1965), while ga is a stochastic optimization technique suitable to compute the global minimum (Goldberg, 1989). 2.2.3 Selection of Temperature Pinch Constraints Although pinch constraints are not generally reported in earlier studies, Stene (2005) presents experimental data sets for a similar integrated CO2 heat pump, from which an estimate of the pinch temperature can be determined. 9PDF Image | CO2 Heat Pump Performance
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