Design of Vinyl Acetate Monomer (VAM) Plant Vaporizer Section

In a Vinyl Acetate Monomer (VAM) production process, ethylene (C2H4), oxygen (O2) and acetic acid (CH3COOH) are fed in their gaseous phase to the reactor to form VAM and water as given by Equation 1.1. The process flow diagram (PFD) of the VAM production plant is shown in Figure 1.1, which is obtained from the study of Machida, et.al. (2016) which simulated the process using Visual Modeler software. One of the significant units in the VAM plant is the vaporizer section considering the feed must be fed at their gaseous phase for the reaction to occur.

Fresh ethylene feed (stream 2) is mixed with recycle gas (stream 1) coming from the reactor effluent which mostly contains unreacted ethylene feed. The mixed ethylene feed is then fed to a heater for the stream to reach the required feed temperature (stream 3). On the other hand, acetic acid recycle (stream 5) which contains unreacted acetic acid from the reactor effluent is mixed with fresh acetic feed (stream 6) with both streams at the liquid phase.

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Since the reaction requires the feed to be in the gaseous phase, the mixed aqueous acetic acid feed mixture (stream 7) is fed to a vaporizer. The resulting acetic acid gaseous feed stream (stream 8) is mixed with the heated ethylene vapor stream (stream 4) and fresh oxygen feed (stream 9). The resulting vapor mixture (stream 10) is the feed to the VAM reactor.

This paper aims to provide a detailed design of the vaporizer section. This include heat and mass balance around the section and equipment sizing.

Analysis of the mechanical, safety and environmental aspects of the design will also be performed together with the associated process and instrumentation diagram (P&ID) showing appropriate process control scheme in relation with the performed hazard and operability analysis. Lastly, cost estimation of the design will also be conducted. Temperature and pressure data to be used in the design are obtained from the VAM plant simulation of Machida, et.al. (2016).

From the journal article, only key streams such as fresh feed streams and reactor feed stream are provided with the temperature and pressure data. As such, it is assumed in this analysis that the ethylene and acetic acid feed mixers are operating at isothermal and isobaric conditions resulting to same temperature and pressure between the fresh feed and recycle feed streams for ethylene and acetic acid. Meanwhile, mass flowrates are scaled from the data provided by the literature to consider a plant capacity of 300,000 tonnes per year of VAM. Considering no reactions occuring in the vaporizer section, the mass and molar balance can be easily calculated. To complete the heat balance required for equipment design, necessary fluid properties are obtained below. For vapor streams, the density is obtained by assuming that the gas behaves ideally. The ideal gas equation (Equation 2.1) can be re-arranged in the form of density (ρ) and molar mass (M) (Equation 2.2).

n=PV/RT Equation 2.1

ρ_avg=(M_avg P)/RT Equation 2.2

where n refers to the number of moles, P as the pressure, V as the volume, T as the absolute temperature and R as the ideal gas constant. The average molar mass of a gas mixture can be approximated by Equation 2.3

M_avg=∑(y_i M_i ) Equation 2.3.

where y refers to the molar fraction of component i. Shown below is a sample density calculation for stream 1 (gas recycle) using the density from Table 2.1. For liquid mixtures, the assumption that the solution behaves ideally was also used such that their density can be approximated using Equation 2.4 below, where x refers to the mass fraction of the solution’s compenent. For the density of the pure component, it is also assumed that pressure has negligible effect.

1/ρ_avg =∑x_i/ρ_i Equation 2.4

Sample density calculation for stream 5 (acetic acid recycle) is given below using the density data for liquid components in Table 2.2. For heat capacity calculation of gas mixtures, we also assumed ideal behavior such that it can be approximated using simple mixing rules given in Equation 2.5.

(Cp)_avg=∑〖x_i (Cp)_i ) Equation 2.5

(Cp)_(i,gas) [J/(kmol-K)]=C1+C2[(C3/T)/sinh⁡(C3/T) ]^2+C4[(C5/T)/cosh⁡(C3/T) ]^2 Equation 2.6 For heat capacity of liquids, Equation 2.7 is used by utilization of constants given in Table 2.4 from Perry & Green (2008).

(Cp)_i [J/(kmol-K)]=C1+C2T+C3T^2+C4T^3+C(5T)^4 Equation 2.7 Pure component viscosity data of vapors are also calculated by method of Perry & Green (2008) as given in Equation 2.8 using constants from Table 2.5.

μ [ Pa-s]=(C1T^C2)/(1+C3/T+C4/T^2 ) Equation 2.8 A mixing rule to approximate gas mixture viscosity as given by Equation 2.9 below can be used (Guo, Liu and Tan, 2017).

μ_(avg,g)=(∑(y_i μ_i √(M_i )) )/(∑(y_i √(M_i )) ) Equation 2.9

Meanwhile liquid viscosity data for pure components are approximated using Equation 2.10 with the necessary constants provided by Table 2.6.

μ [ Pa-s]=exp⁡(C1+C2/T+C3 ln⁡(T)+C4T^C5 Equation 2.10

To determine the viscosity of the liquid mixture, the method proposed by Gambill (1959) as given by Equation 2.11 written below in terms of dynamic viscosity can be used.

μ_(avg,l)=(ρ_avg (∑((x_i μ_i)/ρ_i )^(1/3) ))^3 Equation 2.11.Pure component thermal conductivity of vapors are calculated by method of Perry & Green (2008) as given in Equation 2.10 using constants from Table 2.7.

k [W/(m-K)]=(C1T^C2)/(1+C3/T+C4/T^2 ) Equation 2.10 To determine the thermal conductivity of the gas mixture, the method suggested by Brokaw (1961) can be used which state that the gas mixture’s thermal conductivity is the mean of the thermal conductivities of the structures formed by alternating plane layers, arranged parallel (k_sm) and perpendicular ((k)_rm) to the heat flux direction. The thermal conductivity of the gas mixture can be calculated using Equations 2.11 to 2.13.Meanwhile, liquid thermal conductivity of pure componets are obtained through Equation 2.14 using constants from Table 2.8. To calculate the thermal conductivity of the solution, a correlation by Filippov (1955) for binary liquid solutions can be applied as given by Equation 2.15.

k_(avg,l)=x_1 k_1+x_2 k_2-0.72x_1 x_2 |k_2-k_1 | There are three points of the heat balances in the system based on Figure 1.2: (1) heating the mixed ethylene feed, (2) heating and vaporizing the mixed acetic acid feed and (3) mixing of acetic acid, ethylene and oxygen feed. The streams with complete pressure and temperature data are streams 1-3, 5-7 and 9-10. By performing degrees of freedom analysis in the system considering the streams with known pressure and temperature, we need to have another stream with known temperature and pressure to complete the heat balance around the mixer for the total vapor feed.

For the heated ethylene feed (stream 4), we need to have either temperature or pressure data since the stream should be a superheated vapor. We can assume that the resulting vaporized stream of acetic acid (stream 8) is a saturated vapor to be able to calculate its pressure once the temperature is already known or vice-versa by application of Raoult’s law to zero-out the degrees of freedom around the heat balance. However, for this to work, we also need to assume that the vaporizer operation is either isothermal or isobaric to zero out also the variables needed by the Raoult’s law calculation. This is less realistic because isobaric operation might be difficult to achieve due to inherent pressure drop within the equipment.

On the other hand, if inlet and outlet mixed acetic acid stream has the temperature but different phase only, the resulting pressure at 300C will be very low considering normal boiling points for water and acetic acid are higher at 1000C and 1180C, respectively (NIST, 2020). This will result to unrealistically very high pressure drop along the vaporizer.

Thus, to obtain zero degrees of freedom around the total vapor feed for the mixer, the most realistic assumption that we can have is that the heated acetic acid feed (stream 8) and the heated ethylene feed (stream 4) have the same temperature entering the mixer. As such, we can calculate their temperature by heat balance around the mixer assuming that its operation is adiabatic. Upon knowing their temperature, we can then calculate their pressure and be able to calculate the necessary heating load of the ethylene feed heater and acetic acid feed vaporizer. Assuming no heat loss, the heat balance around the mixer is given by Equation 2.16.

∆H=Q=0 Equation 2.16

Therefore, as we have earlier assumed ideal model of the gas and considering only sensible heating is occuring around the system, we can rewrite Equation 2.16 as Equation 2.18 by application of Equation 2.17 for enthalpy change at constant pressure heat capacity below.

∆H=∑∫_(T_initial)^(T_final)((n_i Cp)_i dT)Equation 2.17

∑∫_(T_initial)^(T_final)((n_i Cp)_i dT)=0 Equation 2.18.

Since we know the final temperature, which is the temperature of stream 10, and temperature of the feed oxygen (stream 9), we can then calculate the temperature of stream 4 and 8. Numerical solution/program is needed to solve the final temperature for Equation 2.17. Matlab code for the calculation is given in the appendix section. The resulting stream 4/8’s temperature is at 423 K. The change in temperature with respect to stream 10 (421 K) is quite minimal only considering minimal fresh O2 feed mixed. Since temperature of stream 4 is already known, equations 2.5 and 2.6 can be applied to determine the average heat capacity of the stream. The resulting heat capacity of stream 3 is 35.18 J/mol-K while stream 4 is 38.10 J/mol-K. The heat balance can be written using Equation 2.17 below.

Q=∆H=9363.84 kmol/hr x (1 hr)/(3600 s) x (1000 mol)/(1 kmol) x(38.10 J/(mol-K) x423 K-35.18 J/(mol-K) x303.15K)x (1 kW)/(1000 J/s) Equation 2.19.

Q=14180 kW

Thus, the necessary heating load of the ethylene pre-heater is 14180 kW. Since there is a phase change involved in the system, the heat requirement is given as:

Q=∫_(30C,vap)^(149.9C,vap)nCpdT+∆H_(vap,30C) Equation 2.20

Similar to the application of Equation 2.19, the sensible heating requirement is calculated as:

∆H_sens=1,584.12 kmol/hr x (1 hr)/(3600 s) x (1000 mol)/(1 kmol) x(55.78 J/(mol-K) x423 K-43.84 J/(mol-K) x303.15K)x (1 kW)/(1000 J/s)=4543 kW

From literature data (DDBST, 2020), heat of vaporization of acetic acid at 300C is 23433.6 J/mol while water is 43779.9 J/mol. Consequently, the total heat of vaporization needed is:

∆H_vap=1584.12 kmol/hr (1 hr)/(3600 s) x (1000 mol)/(1 kmol) (23433.6 J/mol x 0.932+43779.9 J/mol x0.068)x (1 kW)/(1000 J/s)

∆H_vap=10920.4 kW

Therefore, total heat load needed by the vaporizer is 15,463 kW.

Conclusion

This paper provides a comprehensive approach to designing the vaporizer section of a VAM production plant. Through detailed calculations and analysis, the study emphasizes the importance of the vaporizer section in ensuring efficient feedstock conversion and reactor feed preparation. The proposed design considerations and cost estimation offer valuable insights for the development of an effective and economically viable vaporizer section in VAM production facilities.