Thermoeconomic optimization of a dual-purpose power and desalination plant

The thermoeconomic optimization of an actual steam power plant coupled with a MSF desalination unit is reported. A global optimization of the whole system is performed based on separated local optimizations of different plant units. The local optimization procedure described herein requires fewer computing resources and deals with simpler mathematical problems than conventional optimization methods. On the other hand, the local optimization method requires a thermoeconomic model providing the exergy and economic costs of all mass and energy flows of a plant, including those corresponding to fresh water and electricity produced. This application can be very useful, either for the plant management in order to achieve a cost-effective operation, and for a better plant design. In the example given, approximately 11% of the total cost was saved according to the optimization results in the nominal operating conditions of the plant.

A complex plant can be optimized by applying local optimization based on thermoeconomic techniques when the devices are isolated enough (i.e., the perturbations in a component only affect its behavior). The most important advantages of the local optimization approach follow: 1. Improvements and optimal design of individual units in highly complex systems are greatly facilitated, as well as of whole systems. 2. The designers can be specialized and their efforts concentrated on designing the variables of single units, while resting assured that these Table 5 Results for the optimization of the dual-purpose plant in the MCR performance case (main exergy flows are described in Fig. 2) Flow Initial Optimum MW C1 S1 B1 B2 S2 W2 B3 S3 W3 B4 S4 W4 B5 S5 W5 B6 S6 W6 B7 S7 W7 B8 S W9 S9 B9 F10 S10 B10 F11 S11 B11 F12 S12 B12 W13 c (10−6 $/kJ) Z (106 $) MW c (10−6 $/kJ) Z (106 $) 481.720 177.721 208.782 53.010 1.992 49.731 24.175 0.619 23.360 21.308 0.796 20.331 21.704 2.357 19.161 8.595 1.880 6.449 7.295 1.761 5.507 7.822 54.310 0.055 0.010 0.043 1.250 0.076 0.994 2.442 0.158 2.005 9.087 1.179 7.997 2.270 2.000 — 6.927 — — 9.632 — — 9.464 — — 9.414 — — 9.989 — — 12.040 — — 11.950 — 1.517 — — 14.420 — — 11.750 — — 10.450 — — 9.781 — — — 31.810 — — 13.780 — — 6.744 — — 5.370 — — 4.590 — — 1.833 — — 1.542 — 3.849 — — 0.072 — — 0.375 — — 0.452 — — 1.593 — 443.798 176.308 206.825 51.913 2.435 48.213 23.785 0.867 22.726 21.267 0.874 20.211 22.253 1.047 21.001 8.507 1.617 6.609 7.040 1.231 5.780 7.422 51.970 0.049 0.006 0.041 1.154 0.071 0.912 2.487 0.166 2.029 9.108 1.174 8.023 2.240 2.000 — 6.642 — — 9.156 — — 8.953 — — 9.010 — — 9.076 — — 11.470 — — 10.990 — 1.453 — — 13.200 — — 9.878 — — 9.206 — — 9.339 — — — 34.340 — — 12.160 — — 5.810 — — 5.200 — — 5.421 — — 2.244 — — 2.000 — 3.662 — — 0.095 — — 0.147 — — 0.203 — — 1.596 — Flow S13 B13 F14 S14 B14 F15 S15 B15 F16 S16 W16 B16 W B ΣZ Initial MW 0.196 2.072 8.765 0.467 8.298 11.776 0.735 11.162 63.664 −133.421 8.000 3.889 122.731 238.862 — Optimum −6 c (10 $/kJ) — 11.720 — — 8.733 — — 8.834 7.485 — — 89.500 9.993 7.237 — Z (10 $) — 0.193 — — 1.243 — — 1.830 — — — 51.950 — — 127.200 efforts yield optimum design and/or improve the overall system. 3. The convergence of the solution is faster. The design variables selected for the optimization process must influence the physical behavior of the plant and the capital cost of the corresponding component. The two terms composing the product cost of each device must be optimized. This optimum value can be used to readapt the design of the existing components. In some cases the optimum set of variables does not correspond to any thermodynamic state of the plant, i.e., the obtained state corresponding to the optimum values of the design-free variables does not correspond with feasible operating conditions of the whole plant. In general, when the number of variables exceeds a limit (>5 variables), conventional global optimization methods have serious convergence problems that can be avoided with the optimization method presented in this paper. On the other hand, the local optimization methods MW 0.190 2.047 8.596 0.454 8.141 10.777 0.704 10.190 63.452 −132.977 8.000 3.889 122.731 235.756 — c (10−6 $/kJ) — 11.090 — — 7.739 — — 7.734 7.109 — — 61.220 9.427 6.865 — Z (106 $) — 0.196 — — 0.497 — — 0.566 — — — 35.542 — — 109.500 suffer also from the feasibility of the optimum solution. Local optimization is a very powerful tool to design plant components of a complex system such as a power plant coupled with a desalination plant. The optimum design point of each component, under the most usual operating conditions and plant loads, can be obtained by locally optimizing. These components should be designed for best efficiency under all operating conditions. The experience of the designers in calculating the capital cost of the components as a function of their capacity and efficiency is essential to find an optimum that coincides with the optimum of the real system.