Design simulation and economic optimization of a benzene-toluene-xylene system distillation process upon the energy cost

. Distillation is the most extensively used in separation process of the chemical industry. Relationships between non-linear variables, multivariable interactions, dynamic system properties, and other irregularities render the study of design simulation and process optimization an interesting challenge for process engineers. The objective of the process optimization is to produce the most economical to conduct the system. This paper discusses the process engineering strategy started from the determination method of the degree of freedom, design variables, process tools, economic parameters, and the optimization process. The distillation variable optimized in this study was limited to reflux ratio. The optimum variable was construed from the reflux ratio producing the lowest total annual cost (TAC). Furthermore, it was analyzed the energy cost as optimization parameter in the total annual cost (TAC) calculation method to obtain minimum reflux ratio in distillation unit.


Background
Distillation plays a substantial contribution towards a chemical factory. Distillation is a very common method of separation employed in the chemical industry and presents complex process in its modelling and control [1,2]. The distillation columns are employed in many separation process of the chemical industry [3], whereby control is needed to obtain products with a specified purity at minimum cost. This is by all means very difficult to achieve due to the presence of process irregularities, multivariable interactions, dynamic system properties and microscopic disturbances in the distillation column [4]. More specifically, the continuous distillation exhibits very dynamic properties during a process. A distillation process is based upon the vapour-liquid equilibrium. Distillation can be used to separate chemical components that settle at different concentrations at the two different phases. Using the principles of mass transfer and heat transfer, processes in the distillation column can be simulated/modelled. Dwekar et al (1989) studied multivariable optimization in a distillation column, and produced formulas for single-fraction distillation and multi-fraction batch distillation under constant operating conditions and reflux ratio [5]. Ren et al (2010) presented a model of the stages in the distillation column to optimize the reflux ratio by resolving the nonlinear objective function of the design [6]. Optimization of the propane-propylene system distillation has been figured out by Mauhar et al (2004) applying simulation software of Aspen Plus [7]. An approach that produces pressure value and reflux ratio to minimize energy duty of the reboiler and produce product assigning to the standard.
The operating conditions of a petroleum refinery column have been optimized by using a tool to minimize energy consumption [8]. This simulation result at a later stage was successfully applied to the pilot plant unit [8]. Earlier optimizations of two distillation columns have been carried out using reflux ratio variable in a petroleum refinery facility [9].
Economic design calculations are very important in an industrial design. Optimization processes of distillation columns have been carried out in previous literatures to compute a minimum Total Annual Cost. In this simulation, optimization of a three components distillation process has been carried out by using a variation of the reflux ratio to designate the lowest annual operating costs. In general, the stages of this simulation are include the illustration of processes, analysis of degree of freedom and design variables, compilation of calculation algorithms, modelling, and simulations using MATLAB, Ms. Excel, and Polymath software to discern the optimum reflux ratio value.

Case Study
Distillation columns constructed in a series are used to separate components contained in the feed comprised of 30% benzene, 55% toluene and 15% xylene. The first column distillate is expected to generate 94.4% benzene, 4.54% toluene, and 1.06% xylene. The second column is designed to recover 92% of the toluene from the incoming feed, through which analysis showed a composition of 94.6% toluene. Additionally, the bottom of the second column is expected to recover 92.6% xylene making up 77.6% of the whole composition. Feed enters under saturated liquid conditions at a pressure of 1 atm. The detail of process is displayed in Figure 1.

Aims
This paper goals are referred to identify the degree of freedom and design variables of the system, to generate a system design model, to analyse reflux ratio with the lowest total operating cost/TAC 2 Discussion

Analysis of Degree of Freedom of the System
Analysis of degree of freedom is needed to determine the characteristics of a system and the number of design variables needed to settle the flow of information into a defined variable system. The method of determining the degree of freedom of the system refers to the book Strategy of process engineering [11]. In the present discussion, the analysis of degree of freedom is carried out in three different approaches with the aim of ensuring the accuracy of the analysis of degree of freedom performed. Analysis of the degree of freedom of the system can be done through the following three methods: (1) Calculation from the relationship between the number of variables minus the available free equation (2) Calculation from a holistic review of the system (3) Calculation from the relationship between the local degree of freedom of each sub-system and the existing local degree of freedom

Analysis of degree of freedom with method (1)
Calculation of the degree of freedom with this method requires the overall number of variables and the number of variables in the system [11]. The information flow of each variable in this distillation system can be seen in Figure 2. Variables information can be seen in Table 1 and the equations expressing the relationship between variables in the system can be seen in Table 2.
The degree of freedom of this system calculated based on all variables and related equations is 1.

Analysis of degree of freedom with method (2)
This calculation method is done by reviewing the overall system through the mass flow of components in and out of the system. The specific information on the variables and related equations of this method can be seen in Table 3.
The degree of freedom of this system is calculated using 1 variable and all related equations.
Number   (3) The degree of freedom in this method is calculated from the relationship of the local degree of freedom of each sub-system and the existing local degree of freedom. The variables information flow in subsystem 1 can be seen in Figure 3 and subsystem 2 in Figure 4. Applied equations: Applied equations: The degree of freedom of the system calculated in this method is 1. The result is the same as the value obtained in methods (1) and (2), and thus the analysis of degrees of freedom in this case is conclusively valid.

Determination of Design Variables and System Calculation Algorithm
The analysis of degree of freedom of the system obtained a value of 1, meaning that the number of design variables in this system is 1. Determination of the design variable employs the structural array method cited from the book Strategy of process engineering [11]. The variable elimination method is illustrated in Figure 5. Through the structural array elimination, the non-eliminated variable found is N1. Therefore, the design variable involved in this case is N1 denoting the feed molar flow rate that enters the distillation column. In this system there is no recycling flow parameter.
The non-eliminated variable is N1, placing the feed molar flow rate as the design variable of this distillation column design. The system calculation algorithm that expresses the process of defining each state variable in this particular case can be seen in Figure 6.

Mass Flow and Composition
The design of the system outsets from the calculation of unknown values using the design equations compiled in section 2.1. The calculation of the value of unknown variables employs the Polymath software with Non-linear equations solver. The equation models are listed in Figure 7. Calculation results are presented in Figure 8.  The results in Figure 8 can be assigned onto the distillation process scheme to facilitate the design of the column series. The resulting scheme can be seen in Figure 9.

Distillation Column Design
All data relating to the mass flow and composition in this distillation sequence system are generated. In this section, a simulation of reflux ratio in relations to profitability parameters is made since the relationships between reflux ratio and certain parameters tend to be nonlinear and in opposition to one another. Accordingly, to acquire the reflux ratio conditions that result in the highest profitability, it is necessary to simulate and optimize the process. a) Method The distillation column design in this case study incorporates the Mc-Cabe-Thiele model. Several assumptions were used in the design of this column: 1. The flow rate between vapour and liquid along the column is constant (constant molar overflow) as is the relative volatility 2. Latent heat evaporation is assumed to be the same at all times and all compositions in each tray 3. The distillation system does not experience foaming 4. Total condenser and partial reboiler are applied 5. The first and second distillation columns have the same operating conditions and types The design procedure is simulated using Ms. Excel and MATLAB with the following steps: 1. Employment of all data on the multicomponent system vapour-liquid equilibrium curves; 2. Collection of thermodynamic data of benzene, toluene, and xylene; 3. Calculation of the flow rate in and out of the column; 4. Calculation of the value of the minimum reflux ratio and the minimum number of trays; 5. Calculation of the loads of the reboiler and condenser; 6. Calculation of the maximum and minimum values of vapour and liquid flow in a column; 7. Iteration to get a balanced composition; 8 11. Determining the relationship between different reflux ratio of tray, feed tray location, tray diameter, column height, condenser load, reboiler load, condenser area and reboiler area. b) Design outcome Through a calculation simulation the influence of the reflux ratio on the distillation column design parameters is obtained. Sample results from the simulation relating the number of plates can be seen in Figure 10 and the overall results of the design and simulation of the distillation column by using MATLAB can be seen in Table 4.   Figure 11 shows the correlations between the reflux ratio to the number of plates and the location of the feed plate. The number of plates decreases along with an increase in the reflux ratio. The decrease in the number of plates reached a constant value when the given reflux ratio exceeds 3. This is due to the large amount of condensate returning to the column, thereby reducing the number of plates needed for separation [9,12]. The relationship of reflux ratio and number of plates is shown in Figure 12, where increase in reflux ratio results in the decrease of column height caused by the decrease in the number of plates in the column. In contrast, an increase in the reflux ratio causes an increase in the distillation column diameter. This corresponds to the rate of steam affecting the diameter of the column. The rising steam flow rate will affect the column diameter to increase [13]. Meanwhile, based on the study conducted by Irawan and Nata [14], steam flow rate will increase as the number of column plates decreases.  Figure 13 presents that an increase in the reflux ratio and a decrease in the number of plates in the distillation column causes an increase in condenser load that plays role in condensing the distillate yield. Similar result also applies to the reboiler, where the reboiler load used to evaporate the materials at the bottom of the column also increases. The increased reflux ratio causes an increase in the steam flow rate within the column thereby increasing the loads on the condenser and reboiler [13]. However, if the reboiler and condenser loads are set at a minimum, the number of plates needed for separation will be infinite.

Basic of economic calculation
The basis for calculating economic value applied refers to the book chapter Distillation economic optimization [15]. Distillation column economic calculation bases are shown in Table 5. The results of economic calculations of the distillation column are shown in Table  6.   Figure 14 displays the relationship between the reflux ratio and the capital cost incurred. The capital cost for the distillation column tends to decrease with the increase in the reflux ratio. This is due to the decrease in the number of plates in the distillation column as the reflux ratio increases. Different result applies to the price of the heat exchanger which increases in cost when the reflux ratio is increased. This outcome is a result of an increase in condenser and reboiler loads when the reflux ratio is increased, whilst the total capital cost profile follows the conditions of the sum of the heat exchanger and column cost. More in-depth analysis can be done with the total annual cost (TAC) calculation method. TAC is a combination of annual energy costs and capital costs involved in constructing Total Capital cost Heat Exchanger cost Column cost equipment. As can be seen in Figure 15, an increase in reflux ratio increases the energy cost of the distillation column. The energy costs encompass the operational costs of condensers and reboilers. Accordingly, the increase in energy costs is due to the addition of reboiler and condenser loads when the reflux ratio is increased. Moreover, TAC curve in Figure 16 presents that at reflux ratio 1.2, a minimum value is achieved.  Decrease in TAC value only occurs at reflux ratio 1.2, beyond which increase in value occurs until a constant value is reached at reflux ratio of 3. At reflux ratio 1.2, the TAC calculated is $ 850,000, the lowest among the values implied for other reflux ratio variation observed. On this value, it can be concluded that the optimum reflux ratio resulting the highest economic value with the reflux ratio 1.2.

Recommendation
The simulation applied in the present study still uses several design assumptions. Forthcoming simulations should be conducted with less design assumptions to generate results near to the actual operating results.