Conclusiones

4.2.1 Energy integration

Process integration aims at reducing energy consumption and its corresponding operating costs.

The detailed methodology has been described in Chapter 3. With the help of the case study on a dairy process, the complete approach has been illustrated. The following list summarizes this approach:

1. Process analysis: This begins from the definition of the actual energy consumption of a given process, through the analysis of the process unit operations up to the final definition of the process heat requirements and the corresponding hot and cold streams.

2. Minimum energy requirement (MER): The maximum heat recovery is calculated with the

∆T_min assumption and the corresponding minimum hot and cold utility requirements are computed.

3. Integration of utilities: From the grand composite curves, the required temperature levels for hot and cold utilities can be defined. With a certain knowledge and experience, adequate utilities can be chosen. The optimal flow-rates are then calculated by solving a mixed linear programming problem (MILP), in order to minimize the operating costs.

The simple application of this approach leads to one optimal solution, depending strongly on the chosen utilities and optimization parameters defined by the user. For example, for a process with heat pump opportunity, the optimal integration depends on the temperature for the condensation and evaporation chosen by the user.

But it is interesting to optimize the temperature levels and to compare different heat pump solutions depending on their operating conditions. Those solutions will be different in terms of operating costs and investment costs.

4.2.2 Multi-objective optimization

In this section, a multi-objective optimization strategy will be described. Instead of one optimal resulting solution, it provides several optimal solutions. The best solution can then be determined applying financial or other criteria.

ˆ Input: A range of validity for each decision variable (in this approach linked to the tempera-ture levels of the heat pump), fixed optimization parameters (e.g. the value of the isentropic efficiency of a given compressor type)

ˆ Output Pareto curves with associated results

In engineering, several conflicting objectives are often pursued simultaneously. In the case of two different objectives, it is possible to represent the results on a Pareto curve that represents one objective on each axis.

The applied multi-objective optimization strategy is based on an evolutionary algorithm. This term is coming from its analogy with the Darwin law: ”survival of the fittest”.

It starts with an initial population of a given number of individuals. Each individual in the system is defined by a set of decision variables. As each of these variables can vary in a certain range, it is possible to generate randomly several individuals. Once the number of initial population size has been found, the real optimization is started.

The optimization evaluates for each individual the objective functions, which allows to compare individuals between each other. Then, the individuals which gave the best performances are kept (i.e. they are the ”fittest”) and new individuals are created from their decision variables.

The optimization is finished when the maximum number of evaluation is reached.

4.2.3 Master and slave problem

The goal is to identify optimal heat pump technologies with their operating conditions for a given process.

The optimization strategy chosen in this work is based on the decomposition of the optimization problem in master and slave sub-problems (Figure 4.1) (Gassner and Mar´echal, 2009). A similar two stage optimization approach has also be applied by Colmenares and Seider (1989b): In their outer problem (master problem), the pressure and temperature levels are optimized, whereas the

72 CHAPTER 4. HEAT PUMP TECHNOLOGIES AND THEIR INTEGRATION

inner problem (slave problem) optimizes the flow-rates. The inner problem can be linear when the objective function and the constraints are linear.

In the same way, in the presented approach the temperature levels will be optimized in the master problem (non-linear multi-objective optimization) and the utility flow-rates will be optimized in the inner problem (formulated as MILP). Additionally, the interest rate is included as a decision variable of the master problem, in order not to penalize more expensive equipments from the beginning, when estimating the annualized investment costs.

The two objectives are minimizing the operating costs of the industrial process and the investment costs related to new heat pump installations. At the master level, the values of the decision variables are chosen by the evolutionary algorithm and the operating conditions of the heat pumps (condensation and evaporation temperatures) are known, enabling the thermodynamic model to calculate the heat pump cycles and consequently to establish the enthalpy-temperature profiles of heat pumps hot and cold streams, the consumed mechanical power and the annualized investment costs for a nominal size (nominal flow-rate).

Multi Objective

Utilization rates of the utility (f_u) according to process requirements - i (annualization interest rate) Generation of new values for

the set of decision variables

Minimize

Using the operating conditions of the heat pumping cycles, the slave problem solves the energy integration problem, which aims at minimizing the total cost. It includes the yearly operating costs of hot and cold utilities and the annualized investment costs of heat pump installations. All utility flow-rates are optimized simultaneously, using the mixed integer linear programming (MILP) formulation of the heat cascade (Chapter 3.4.4.1). With the selected technologies and the optimized utility flow-rates, the corresponding operating and investment costs can be computed.

The master problem is solved with an evolutionary algorithm. This allows using complex heuris-tics in the heat pump selection procedure and process integration, without difficulties related to constraints and non-differentiable equations.

The presented optimization approach results in a set of optimal solutions laying on a Pareto front.

Considering that the goal is to help the engineers in their final decision, this method gives the advantage that the final solution can be chosen among the optimal solutions by applying financial, environmental or other criteria.