The search for fast, secure, and reliable solutions intensifies the use of computational tools to support the decision-making process and, in many cases, operational research (OR) methods play a fundamental role. OR is a branch of engineering focused on solving real problems focusing on decision-making, using mathematical, statistical features, and algorithms. The use of methods such as linear programming, network flow, integer programming, non-linear programming, mixed integer linear (and non-linear) programming, among others, is a reality in the search for optimal solutions mainly when the amount of data is huge and complex [1-3].
In industry, OR is used in many areas from control and production planning to logistics and product distribution. Various industrial processes may also be modeled and optimized using OR. In general, spreadsheets and specific computer programs are used.
Obtaining accurate solutions becomes impractical with increasing the number of problem variables. In such cases, heuristics to specific OR problems have been formulated and implemented to search for good (but not always optimum) solutions. In the heuristic, it is desirable that computer programs are equally efficient.
OR methods have been successfully applied to cogeneration problems, which is a complex process that depends on many variables and does not always operate optimally .
Cogeneration is a process in which certain fuel generates heat and power, thus avoiding losses widespread. It has great potential both in the industrial (mainly in the sugar and alcohol, pulp and paper, chemical, and petrochemical facilities) and in the residential sectors [4-7].
Energy is a recurring and strategic issue for Brazil as well as for the world. In São Paulo state, this issue has become more evident with the water management crisis of recent years since the Brazilian electricity generation is largely dependent on hydropower . In this scenario, the cogeneration presents a great alternative to increase the capacity and reliability of the electrical power system.
Reduction of uncertainties and risks in the long-term planning of energy resources is the result of the multi-criterion ranking developed in, the model finds that the resources next to the demand side appear as lower fuel costs .
Biomass residues can be a potentially sustainable source of energy. It is estimated that nearly one-third of the energy available from the sugarcane plant is contained in its tops and leaves (trash), which are generally either burnt before harvesting or are left in the field. Experts estimate 1.353 million tons of trash in South Africa is available annually for cogeneration, which could potentially produce 180.1 MW during a 200-day milling season . Other examples are found around the world, such as Pakistan, which has a potential to generate electricity from sugarcane bagasse estimated in 1598 GWh up to 2894 GWh . Okello et al.  presented a review of the efforts and progress made by different organizations in promoting improved bioenergy technologies in Uganda.
The use of biomass residues for energy generation through cogeneration has been increasingly adopted by many industries, as it can reduce energy costs and even increase their profit by selling the energy excess in the market. The forestry industry has been increasingly investing in cogeneration processes using the residue generated during the mechanical, physical and chemical processing of the wood logs [13-14]. Others promising bioenergy conversion technologies are also found in the literature, such as biomass conversion with anaerobic digestion .
Cogeneration plays an important role in reducing CO2 emission to the atmosphere, fulfilling goals of the Kyoto Protocol, in which market-based mechanisms for buying and selling carbon credits are used [16-18]. These credits are certificates generated by reduction projects or absorption of greenhouse gases. They are also found in other carbon markets outside the Kyoto Protocol .
Regenerative cycle with open feed-water heater
The problem presented consists in a work production system, here considered as electrical power, and heat through multi-stage turbines and condenser, respectively.
In this system, the sugarcane grinding residue, called sugarcane bagasse, is burned in boiler generating superheated steam at 8 MPa. This steam will pass through turbines producing work or electrical power, leaving as steam or liquid-steam mixture in the streams 2 and 3. After leaving through flow 3 at 0.008 MPa, passed through a condenser wherein steam heat is removed making it saturated liquid (stream 4). As the water need to be pumped at 0.7 MPa, it is important that the water is saturated or compressed liquid in stream 4 because if steam may cause cavitation in the pump decreasing its life. Finally, the streams 2 and 5 are mixed in an open feed water heater, and then returning to the boiler, thus closing a cycle.
The goal is to calculate the minimum cost of energy production through a flow of steam and a great amount of sugarcane bagasse for each of the superheated steam temperature in the boiler output.
It is possible to write the objective function and constraints based on the process data and assuming that the sugarcane bagasse has no cost. The first will be based on the cost per unit mass of steam, electrical power contracted from the power grid and penalty, while constraints involve the mass and energy balances, also the process boundaries.
Solution via MATLAB©
It is observed that with the increase in the high-pressure line temperature, the exergetic efficiency of the process also increases. This temperature rise can be achieved by increasing the amount of sugarcane bagasse in the boiler which leads to a consequent increase of the amount of heat produced.
The result of the minimum cost for each temperature of the high-pressure line. Note that with the temperature increase process cost decreases.
The total amount of electrical power generated and the steam produced in the process, respectively. Note that by increasing the amount of heat in the boiler the mass of steam required for the process decreases. On the other hand, the electrical power generated increases as the available steam energy entering the turbine increases.
With the decrease of steam need and electricity contracted always being the minimum (the model always find the lowest cost for this term) and, thus, constant, the profit function will be changed only due to the steam mass.
In general, with increasing outlet temperature of the high-pressure steam boiler, the system operation is improved achieving higher efficiency and lower cost. In this temperature rise, it is necessary to burn a larger quantity of sugarcane bagasse, thus providing more heat to the process.
To the problems analyzed and studied in this work, the following conclusions are made:
- Through the analyzed problem, it was noted that a power generation plant has an improved performance (greater exergetic efficiency) with increasing temperature of the steam line leaving the boiler. This increase is due to an increased quantity of sugarcane bagasse burned in the boiler and also less need for steam in the process. Thus, the costs have become smaller and the electrical power generated increased;
- In order to have an improvement in process efficiency, vary only the amount of sugarcane processed (or sugarcane bagasse burned) is not sufficient. For this, it is need to increase the output temperature of the boiler steam or get turbines and boilers with higher efficiencies;
- Finally, it was possible to note that the computational tools, mainly the MATLAB© codes, combined with operational research have proven effective in solving industrial cogeneration problems.
These findings are described in the article entitled Computational tools and operational research for optimal design of co-generation systems, recently published in the journal Renewable and Sustainable Energy Reviews. This work was conducted by Fabiano Fernandes Bargos, Wendell de Queiróz Lamas, and Gabriel Adam Bilato from the University of São Paulo.
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