مدل سازی احتمالاتی فازی و تجزیه و تحلیل حساسیت برای برنامه ریزی سوخت گاز بهینه در پالایشگاه

In refinery, fuel gas which is continuously generated during the production process is one of the most important energy sources. Optimal scheduling of fuel gas system helps the refinery to achieve energy cost reduction and cleaner production. However, imprecise natures in the system, such as prediction of production rate of fuel gas, prediction of energy demand of the equipments and cost coefficient in the objective function, make the deterministic optimization method which requires well-defined and precise data cannot be competent for the fuel gas scheduling problem. In this study, fuzzy possibilistic programming (FPP) method is proposed to deal with these imprecise natures by triangular possibility distributions. The fuzzy possibilistic model is transformed into usual mathematical model by definition of necessity measure and the α-level method. Although FPP models have been widely applied to modeling, few research works have been reported on the performance evaluation, namely sensitivity analysis, of these models. Marginal value analysis, which is always used to provide additional economic information, is proposed to give the sensitivity analysis in the paper. This method is demonstrated to be much more flexible than the simulation method. Particularly, the analytical method is adopted to examine how the imprecise natures in the fuel gas system affect the scheduling results.

Refining process is one of the most energy-intensive industries, whose energy cost is the second-largest cost component after crude and intermediate products. Among all kinds of the consumed energy sources, fuel gas which is continuously generated during the production process contributes most of the primary energy source to the energy needs of the refinery. Furthermore, fuel gas can be converted into other forms of energy, such as steam, electricity and heat. Therefore, the effective scheduling of the fuel gas system plays a central role in energy cost reduction and cleaner production in refinery process. Little research work has been reported on the optimal scheduling of the fuel gas system in refinery. It is always referred as an important part in the analysis of the whole refinery energy system. Frangopoulos et al. (1996) presented a method for the thermoeconomic operation optimization of a refinery combined-cycle cogeneration system. By the analysis of the interrelationships among various energy sources, such as fuel gas, fuel oil, steam and electricity, an energy system planning model was formulated. Nevertheless, the capacity of the fuel gas drum and the gas vessels was not considered because of the large time granularity. White (2005) proposed the concept of the fuel gas balance and recommended to model the planning model of the site-wide energy system integrating fuel gas, steam and electricity. Zhang and Hua (2007) embedded the Mixed Integer Linear Programming (MILP) model of utility system which included the fuel gas system into the plant-wide planning model for overall optimization and better energy efficiency, and the proposed approach was executed in an example provided by a real refinery. Li et al. (2006) developed a plant-wide multi-period planning model for a refinery complex. By considering the fuel oil and fuel gas produced in the refinery plant and the steam and electricity generated in utility plant, the interaction of utility plant and other plants in the complex is taken into account. Therefore, the plant-wide optimization can be achieved. Zhang and Rong (2008) proposed an MILP model for multi-period optimization of fuel gas system scheduling in refinery, and then gave a marginal value analysis of the system. Some suggestions are also made by the analysis to assist the engineering operation in refinery. Some research works related with the optimal scheduling of fuel gas system in iron- and steel-making process have been reported. Akimoto et al. (1991) proposed a multi-period MILP model which considered the drum level control and the optimal distribution of fuel gas in the power plant of steel works. Based on his research, Bemporad and Morari (1999) proposed a framework for modeling and controlling the Mixed Logical Dynamical (MLD) systems, and a simulation case study on a complex fuel gas supply system was reported. Kim et al. (2003) presented a further consideration on the problem. They took the cost of turn on/off of the burner into consideration and proposed a plant-wide multi-period MILP model to determine the optimal energy supply to meet the varying energy demands. However, these researches constructed the model of fuel gas system without considering its imprecise natures. In fact, input data and related parameters, such as available supply, forecast demand and cost coefficients, are always imprecise because some information is incomplete or unavailable over the scheduling horizon. In order to avoid unrealistic modeling and improper decisions, the use of fuzzy mathematical programming can be recommended. Fuzzy mathematical programming, first introduced by Bellman and Zadeh (1970), is developed to treat the uncertainty in optimization problems. Inuiguchi et al. (1994) classified this method into two categories in view of the kinds of the treated uncertainties: fuzzy flexible programming (FFP) and fuzzy possibilistic programming (FPP). In the FFP methods, fuzzy constraints and fuzzy goals, which represent the flexibility in the constraints and fuzziness in the objective, are introduced into ordinary mathematical programming models. On the other hand, in the FPP methods, uncertainty parameters in mathematical programming models are considered as fuzzy numbers associated with possibility distributions on their values. FPP has been applied with considerable acceptance since it was first presented. Zadeh (1978) used fuzzy sets as a basis to derive the theory of possibility in his pioneering work. After his initial study, possibility theory has played a vital role in resolving practical decision-making problems. Lai and Hwang (1992) proposed an auxiliary multiple objective linear programming model to solve the possibilistic programming problem. An investment problem was solved to illustrate that this strategy could simultaneously maximize the most possible value of the imprecise profit, minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit. Sun et al. (2000) formulated the optimal natural gas pipeline operation problem in which customer demand was a fuzzy variable specified by its possibility distribution. Sadeghi and Hosseini (2006) used fuzzy coefficients to deal with the investment cost uncertainty in energy supply planning problem. Özgen et al. (2008) developed a two phase possibilistic programming method for multi-objective supplier evaluation and order allocation problems. Liang, 2007a and Liang, 2007b presented an interactive possibilistic linear programming approach for solving the aggregate production planning problem and distribution planning problem respectively. Industrial cases demonstrated that the interactive method in the solution procedure will help to yield a set of efficient compromise solutions with high satisfaction degree. Other studies on the FPP method include Muela et al. (2007), Wang and Shu (2007), Vasant et al. (2008) and Torabi and Hassini (2008). Although FPP models have been widely applied to modeling, few research works have been reported on the performance evaluations, namely sensitivity analysis, of these models. Hsieh and Wu (2000) proposed a possibilistic linear programming model for aggregate planning problem with imprecise natures, and simulated the imprecise natures to evaluate their effect to production plans. Tang et al. (2003) also used the simulation method to analyze the performance and effect of the fuzzy coefficients to the aggregate planning problem. These researches both used the simulation method to give the sensitivity analysis. However, the evaluation procedure which involved substantive numerical experiments has to be re-executed in order to obtain the right result once the parameters in the model are changed. From the above discussion, this study will employ the FPP method to establish a possibilistic model for optimal fuel gas scheduling in refinery involving imprecise supply, demands and cost. Furthermore, sensitivity analysis of the possibilistic model will also be given in this paper, and it is implemented by the method of marginal value analysis, which will facilitate the evaluation procedure. The rest of the paper is organized as follows: Section 2 describes the fuel gas scheduling problem. Section 3 presents the mathematical formulation of the scheduling problem in detail, where imprecise natures are considered. This is followed by the sensitivity analysis of the fuzzy possibilistic model. Conclusions are finally drawn in Section 5.

The purpose of the paper is to propose a fuzzy possibilistic model for optimal fuel gas system scheduling in refinery complex and a flexible sensitivity analysis method for the imprecise parameters in this fuzzy possibilistic model. In this work, imprecise natures in the system, such as prediction of production rate of fuel gas, prediction of energy demand of the equipments and the cost coefficient in the objective function, are defined as fuzzy numbers which are characterized by triangular possibility distributions. The fuzzy possibilistic model is defuzzified by the definition of necessity measure and the α-level method. In order to illustrate the effects of the imprecise natures intuitively, this work implements sensitivity analysis of various imprecise parameters by using the marginal value analysis method. Compared with the simulation based method, marginal value analysis based sensitivity analysis is much more flexible so that no substantive numerical experiments will be needed during the analysis procedure. Some suggestions are also made by the analysis to assist the engineering operation in real refinery. The proposed analysis method can also be used in other scheduling model. Further research needs to be conducted liking into producing fuzzy possibilistic model by imprecise parameters with nonlinear possibility distribution. Also, developing corresponding sensitivity analysis method is another important future project.