Mathematical Model and System Identification to Optimize Inputs Conditions for Plant Design of Cyclohexane

Transcription

1 Mathematical Model and System Identification to Optimize Inputs Conditions for Plant Design of Cyclohexane Article Info Received: 10 February 2012 Accepted:22 February 2012 Published online: 1st March 2012 Nor Suraya 1, Ahmmed Saadi Ibrahem 1* Universiti Teknologi MARA (UiTM) Chemical Engineering Department University40000Shah AlamMlayasia ISSN: Design for Scientific Renaissance All rights reserved ABSTRACT In this work, system identification method is used to capture the reactor characteristics of production rate of cyclohexane based on mathematical model by using hysis software. The identification method is used to measure the percentage effect on the production rate of cyclohexane by measuring the effect of input factors of temperature of reaction, hydrogen concentration, and benzene concentration. Temperature of reaction has big effects on the output of the system and. Also, hydrogen concentration has big effects on the output of the system. Benzene concentration has big effect on the output of the system but less than the reaction temperature and hydrogen concentration. All these results depend on model of hysis software and these results are very important in industrial plants. Keywords: Modeling, design, optimization, system identification, reaction 1. Introduction Cyclohexane is a very important precursor for the production of nylon as it is the main raw material for adipic acid and caprolactam as both adipic acid and caprolactam are the intermediates for producing nylon. Figure 1 shows the mechanism of cyclohexane production via hydrogenation of benzene. Benzene will react with hydrogen with the mol ratio of 1:3 to form 1 mol of cyclohexane.

2 Fig. 1 Hydrogenation of benzene to cyclohexane Cyclohexane is said to be a clear liquid with pungent petroleum odor or sweet odor like chloroform. Generally, it is not dissolved in water but soluble to certain organic liquids. Besides that, cyclohexane is a noncorrosive organic compound, flammable and slightly less toxic than its raw material, benzene (McKetta, 1982). Global production and consumption of cyclohexane in 2010 were found out approximately to be 4.6 million metric tonnes. The global capacity utilization of cyclohexane averaged 72% in 2010, which is a significant increase from 67% in Consumption of cyclohexane in 2010 is estimated to have increased by almost 10% from It is expected to have average growth of 3.6% per year from 2010 to 2015, and then 2.3% per year from 2015 to 2020 (sriconsulting, 2011). According to the global production of cyclohexane, it is said that 63% of the cyclohexane demand comes from caprolactam in the manufacturing of nylon 6 while the rest is consumed by adipic acid for manucfacturing nylon 6,6 (27%), cyclohexanone (6%) and other applications (4%) (ICIS, 2011). There are two types of commercial processes (Gildert, 2001), multistage reactor vapourphase process and liquid and vapourphase reactor process. Nonetheless, the existence of catalyst deactivator such as carbon monoxide and sulphur may disturb the hydrogenation process in reactor. Based on Ullmann s Encyclopedia of Industrial Chemistry, the optimum operating condition for the process is must not exceed 573 K because above this temperature, the equilibrium begins to shift in favor of benzene. Therefore, high purity of cyclohexane cannot achieve. In this research, the main focused is on the production of cyclohexane via hydrogenation of benzene using multistage of reactor of vapourliquid. Fresh feed benzene and hydrogen will fed to the reactor where the reaction will be take place. Then, the reactor effluent being cooled down before being further separated in the separator. The bottom of the separator will produce the desired product, cyclohexane while the top of separator containing unreacted benzene and hydrogen are recycling back with the fresh feed. Recently, more researches has been developed using only single reactor or using combination of a liquid and vapour phase reactor (B. Haut et al., 2002). It is very helping in terms of reducing the capital cost and increase energy consumption of the process. Other than that, through these latest developments, the production of cyclohexane can be set to the optimum level with better yield and purity (McKetta, 1982). To carry out the mathematical model, few assumptions have been made. The assumptions are classified as below: 2

3 1. Determine the flow rates of all stream component using material balances. 2. Determine the specific enthalpies of each component. 3. Solve the energy balance according to the desired one. 4. Assume no pressure drops during the calculation of enthalpy change from its reference point in the units operations. 5. Assume all liquid is uncompressible. 6. Assume no heat loss around the unit operation and along the piping system. 7. Assume there is no kinetic or potential energy loss in the system. Methodology In this design project, after choosing the flow sheet of the process, the next step is to calculate the mass balance. Mass balance is performed manually and verified using simulated calculation, ASPEN HYSIS. The general mass balance is shown in Equation 1. Input + Generation Output Consumption = Accumulation (1) where Input = total mass enters through system boundary Generation = total massproduced within the system = 0 Output = total mass leaves though system boundary Consumption = total mass consumed within the system = 0 Accumulation = total mass build up within the system = 0 Some assumptions are made to simplify the manual mass balance calculation. 1. Operating days for the plant is 330 days, 24 hours a day. 2. No leakage in pipe line and vessel in the system. 3. The entire components in the system behave as ideal gas and ideal solution. 4. No other impurities besides methane and nitrogen. The basis is set to 100kmol/hr for benzene feed and 330kmol/hr for the hydrogen feed. The recycled stream does not being considered when calculating the mass balance at first. After that, the composition and the mass flow of the recycle stream can be obtained and the calculation is continued for the recycle stream. Lastly, the value will be scaled up to achieve the desired mass flow rate of kg/hr. The required production rate of cyclohexane is 100,000 metric tonne per year. Thus the amount of cyclohexane to be produced per hour is: 3

4 Therefore, the target flow rate to be achieved at the end of the process is 150 kmol/hr. Figure 2 shows the mixer s input and the output streams (stream 14). Benzene balance: Figure 2: Mass balance in mixer Molar flow rate: Mass flow rate: Hydrogen balance: 4

5 Molar flow rate: Mass flow rate: Methane balance: Molar flow rate: Mass flow rate: Nitrogen balance: Molar flow rate: Mass flow rate: Total molar flow rate balance: n 1 +n 3 +n 15 =n 4 5

6 Total mass flow rate balance: After performing the calculation on the mass balance using the equation, the collected data is transferred into table for ease of reading. Table 1 and Table 2 show the mass flow rate and the component composition in mixer. Table 1 Summary of the mass balance at mixer Component Stream 1 Stream 3 Stream 4 Mass Flow (kg/hr) Mass Flow (kg/hr) Mass Flow (kg/hr) Benzene Hydrogen Methane Nitrogen Cyclohexane Total

7 Table 2 Summary of composition at mass balance Component Stream 1 Stream 3 Stream 4 Composition (mol fraction) Composition (mol fraction) Composition (mol fraction) Benzene Hydrogen Methane Nitrogen Cyclohexane Total The calculation is continued using the same method done for mixer for others equipment. The summary of calculations is shown in the Tables 3 to 8 as shown below. Table 3 Summary of the mass balance at reactor Component Stream 6 Stream 7 Mass Flow (kg/hr) Benzene 7811 Hydrogen Mass Flow (kg/hr) Methane Nitrogen Cyclohexane Total Table 4 Summary of composition in reactor Component Stream 6 Stream 7 Composition (mol fraction) Benzene Hydrogen Methane Nitrogen Cyclohexane Composition (mol fraction) Total 1 1 7

8 Table 5 Summary of the mass balance at separator Component Stream 9 Stream 10 Stream 11 Mass Flow (kg/hr) Mass Flow (kg/hr) Mass Flow (kg/hr) Benzene Hydrogen x Methane Nitrogen Cyclohexane Total Compare Table 6 Summary of composition in the separator Component Stream 9 Stream 10 Stream 11 Composition (mol fraction) Composition (mol fraction) Composition (mol fraction) Benzene Hydrogen x Methane Nitrogen x Cyclohexane Total Table 7 Summary of the mass balance at tee Component Stream 11 Stream 12 Stream 13 Mass Flow (kg/hr) Mass Flow (kg/hr) Mass Flow (kg/hr) Benzene Hydrogen Methane Nitrogen Cyclohexane Total

9 Table 8 Summary of composition in the tee Component Stream 12 Stream 13 Stream 14 Composition (mol fraction) Composition (mol fraction) Composition (mol fraction) Benzene Hydrogen Methane Nitrogen Cyclohexane Total After obtaining the new value for the value for the fresh benzene feed and hydrogen is inserted into the Aspen HYSIS software to compare with the calculated value. Value of recycled stream can be obtained. There was a difference on the input mass flow rate based on manual calculation and hysis software. Thus, value for recycled stream can be obtained. Error that exists between manual calculation and simulation is; The basis of 100 kmol/hr of fresh benzene feed produces kmol/hr of cyclohexane from HYSIS. The scale up factor is: Table 9 show the summary of mass balance after scale up with recycle stream. 9

10 Table 9 Summary of mass balance after scale up with recycle stream Stream Molar flow rate (kmol/hr) Mass flow rate (kg/hr) Mole fraction Benzene Hydrogen Methane Nitrogen Cyclohexane In a process, it is very important to determine the overall energy balances that come in and out of the process or else, the heat requirement for the process. To perform energy balances, the method is almost the same as performing the mass balances. Typical problem that can be solved by energy balances such as power required by the pump to pump the desired fresh benzene flow rate, kmol/hr and rate of energy that must be transferred from reactor to keep the contents maintain at constant temperature. Energy balances within the process is the basic for plant design. All the manual calculation is calculated using a spreadsheet computer program, Microsoft Excel This spreadsheet software ensures the compatible and easy way for fast editing of calculation and formula. The First Law of Thermodynamic is referred to energy that cannot be created or destroyed. It is used extensively in the discussion of heat engines. The standard unit for all these quantities would be the joule although they are sometimes expressed in calories or BTU. Typically the first law is writing as; 10

11 (2) In other word, (3) Equations that will be utilized to calculate the enthalpy and heat in energy balance are as follow; 1. General Equations (4) Based on the assumptions stated above, Hence, equation 4 can be reduced to (5) 2. Equation for Reactive Process (6) 3. Equation for Process with Phase Changes (7) 4. Equation for Nonreactive Process (8) 5. Equation for Heat Capacity, C p (9) 11

12 Hence for sensible heat, 6. Total Heat for the Energy Balance (for nonreactive process): (10) All of the information relating to the calculation of the energy balance must be clearly shown in the flow chart. State all of the enthalpy of each stream component together with the unknown temperatures and pressures. Steps: 1. Determine the flow rates of all stream component using material balances. 2. Determine the specific enthalpies of each component. 3. Solve the energy balance according to the desired one. However, there are few considerations that must be considered into account: 1. Assume no pressure drops during the calculation of enthalpy change from its reference point in the units operations. 2. Assume all liquid is uncompressible. 3. Assume no heat loss around the unit operation and along the piping system. 4. Assume there is no kinetic or potential energy loss in the system. For energy balance, example of calculation will be done on the reactor. 12

13 Inlet enthalpy: : Benzene : Hydrogen : Methane : Nitrogen : Cyclohexane 13

14 Outlet enthalpy: : Benzene : Hydrogen : Methane : Nitrogen 14

15 : Cyclohexane Total energy balance The total heat for the energy balance in the reactor is: The individual energy balance for each type of units in the system is calculated by using the Equation 2 to Equation

16 In this paper, modern system is introduced, system identification of the process by manipulating the variable on the system with purpose of defining of the output effect and the interaction between them (Ahmmed S. Ibrehem, 2011). The first step to do the system identification is to model the process using hysis software. But, before the process can be modeled out, mass and energy balance is done in order to design the cyclohexane system. Figure 2 below shows the process flow diagram of the production of cyclohexane. Fig. 2 Process flow diagram of cyclohexane production As have been highlighted in the first paragraph, this paper is done purposely to study on the effect of the reactor output conditions by manipulating reactor variables; benzene feed flow rate and the hydrogen feed concentration using system identification method. System identification involves building a dynamical model from an input/output data without using any law and the properties of the non linear system. The variables are chosen based on the most astonishing effect that may affect the process performances. Depending on work by Ahmmed S. Ibrehem (2011), the most active input parameters that give effect on the system can be verified. Hence new identification method to specify the percentage effect of the cyclohexane production can be known. Figure 3 below shows the variables that take part in the system identification of the production of cyclohexane. 16

17 Fig. 3 Variables in the production of cyclohexane The main objective of system identification method is to calculate the average slope, θ. The average slope represents the overall effect of the parameters on the measured output. θ 1 represent the effect of reactor temperature, θ 2 represent the effect of benzene feed flow rate and θ 3 represent the effect of hydrogen concentration on the system. By following Ahmmed S. Ibrehem, preliminary partitioning of estimating groups can be identified as follows: (θ) 20 0 : Give large effects on the system 20 0 >(θ) >15 0 : Give middle effects on the system 15 0 (θ) 10 0 : Give weak effects on the system 10 0 <(θ):cannot be establish Equations below are the equation that used to calculate the optimum value of. 17

18 Result and discussion In system identification method, the relation between reactor temperatures, benzene feed flow rate and hydrogen concentration can be seen after performing the calculation (Ahmmed S. Ibrehem, 2011). The variables are being manipulated by changing the step size. For an example, using a step change of 10, the optimum temperature for the process is at 500 K. hence, the effect of the output must be measured in between K. The relationship between the reactor temperature and output profile is shown in Table 1. The θ average between the reactor temperature and output profile is at the optimum condition. It shows that the percent effect of the reactor temperature give large effect towards the system, 64.73%. As being stated in Table 2, the k average is 2.81 and the θ average is for the relationship between benzene feed flow rate and the output profile at the optimum condition of kmol/hr. It shows that benzene feed flow rate has the largest effect on the system, % compared to reactor temperature. Based on Table 3, the k average is 1.27 with the θ average is This means that hydrogen concentrations do give effect to the system by 57.58%. detailed calculation can be seen in Table 1,2 and 3. 18

19 Table 1 Calculation of the percent different between reactor temperatures against output profile. Temperature, x Product Concentration, y a, ((Xi b, ((yiyni)/yni) Xni)/Xni) slope (b/a) Kavg slope avg,θ % effect, (θ avg x 100)/

20 Table 2 Calculation of the percent different between benzene feed flow rate against output profile. Flow rate,x Product Concentration,y a, ((Xi Xni)/Xni) b, ((yiyni)/yni) slope (b/a) K avg θ avg % effect, (θ avg x 100)/

21 Table 3 Calculation of the percent different between hydrogen concentrations against output profile. Hydrogen Product a, ((Xi b, ((yiyni)/yni) slope (b/a) concentration,x Concentration,y Xni)/Xni) Kavg θ avg % effect, (θ avg x 100)/ Therefore, from the above calculation, the θ avg for the variables are: Using Equations 11, 12 and 13, the optimum and can be identified. Then, using equation 14 and 15, we can simplified the equation into; 21

22 The calculation is completed using MATHLAB software. Table below shows the result for the percent effect between inside the system and the outputs interactions. Table 5: Percent effect for the inside the system and interaction between the inputs variables Action Percentage effects in the system (%) Percentage interaction effects (%) Reactor temperature Benzene feed flow rate Hydrogen concentration Conclusion From Table 5, the most active input is benzene feed flow rate compared to hydrogen concentration. It affected 51.83% in the system for the production of cyclohexane with 18.56% for the interaction effect between the two factors. Despite of that, still hydrogen concentration do give huge effect to the system. The percentage effect in the system is 38.18% while the interaction effect between the two factors is 13.65%. Based on the result gained, both of the variables; benzene feed flow rate and hydrogen concentration affect the overall active process. They may affect the active side of the catalyst surface reaction by deciding which variables do give the largest effect on the system. These findings are absolutely very important in the industries for increasing the rate of cyclohexane production. 22

23 References McKetta, J.J. (1982). Encyclopedia of Chemical Processing and Design. New York and Basel. Marker Dekker Inc. Wolfgang, G (1986). Ullmann s Encyclopedia of Industrial Chemistry. Fifth, Completely Revised Edition Volume A8. Weinheim, New York. VCH. Gildert, (2001). Hydrogenation of Benzene to Cyclohexane. (U.S. Patent 6, 187, 980). Ahmmed, S. Ibrehem (2011). System Identification for Experimental Study for Polymerization Catalyst Reaction in Fluidized bed. Bulletin of Chemical Reaction Engineering & Catalysis, Article in Press. Ahmmed, S.Ibrehem, & Hikamt SI. (2009). New Dynamic Analysis and System Identification of Biodiesel Production Process From Palm Oil. Bulletin of Chemical Reaction Engineering & Catalysis 4(2), Haut, B., Halloin, V. and Ben Amor, H. (2002). Development and analysis of multifunctional reactor for equilibrium reactions: benzene hydrogenation and methanol synthesis, Chemical Engineering and Processing 43(2004)