Sensitivity of distillation column design to data against which thermodynamic models are correlated

Cara E. Schwarz*

Department of Process Engineering, Stellenbosch University, Banghoekweg, Stellenbosch, 7600, South Africa

* cschwarz@sun.ac.za, +27 21 8084485

Introduction

The conventional process for distillation column design entails quantifying the separation based on the equilibrium thermodynamics of the system followed by accounting for the degree to which equilibrium is not achieved and the efficiency of the column internals equipment. The first step of this process is dictated by the phase behavior of the underlying systems and is the focus of this study.

During the design process of a distillation column a thermodynamic model is selected to describe the phase behavior of the system. The model is usually fitted to previously measured data and is selected depending on the system, and the type and degree of non-idealities present. Both the phase behavior data as well as the models have inherent inaccuracies. Usually the majority of the inaccuracies of the models are accounted for through fitting the model to the data and safety factors built into the column design. However, uncertainty in the phase behavior data used to fit the model parameters perturbates to the column design and can exacerbate the uncertainty therein [1] and therefore requires quantification.

Studies have been conducted to determine the effect of the experimental uncertainty of phase behavior [1–4] and physical property [5] data on the design of distillation columns. These studies have provided an indication of the safety factors that are required due to the uncertainty in the phase behavior measurements. Other studies have focused on the uncertainty in the model parameters and determined the influence of perturbation of the model parameters on the distillation column design [6–9].

To the best of the author’s knowledge, to date no study has compared the design of distillation columns based on different sets of experimental phase behavior data available. Typically, during the design process, engineers select what they believe is a suitable set of data and base their design thereon. However, for many systems many data sets exists at the same or similar conditions and subtle differences between the data sets will propagate to differences in the distillation column design/separation prediction. The purpose of this study is to consider different data sets and determine what effect of the data set used to fit model parameters on the distillation column design/separation prediction.

Aim and scope

The aim of this study is to investigate how sensitive a distillation column design/separation prediction is to the data set which is used to correlate the thermodynamic model parameters.

To achieve this aim, the ethanol + water system was considered and modeled with the well-known Non-Random-Two-Liquid (NRTL) activity coefficient model (ACM) of Renon and Prausnitz [10]. Both the fitting of the model parameters as well as the simulation of the distillation column was conducted in Aspen Plus ® V11.0. The ethanol + water system was selected as the system has been well measured with over 220 systems in the NIST ThermoData Engine (TDE) in Aspen Plus® V11.0. This system also has significant industrial application as ethanol obtained through the fermentation of biomass is used as a biofuel. The NRTL ACM was selected as it is known to be a suitable model to represent alcohol + water system. Aspen Plus® was selected as it represents a typical process simulator in which such a design task may be fulfilled.

Approach and methodology

Different phase equilibria data sets were obtained from NIST TDE in Aspen Plus V11.0. Each data set was evaluated to determine its inclusion in the study based in the following requirements:

1. All data points should be at a pressure of no higher than 5 bar. The NRTL model as used in this work assumes that the vapour phase is ideal and is thus only applicable to low pressures. While the 5 bar limit is arbitrary, it allows for a balance of many data sets and adherence to the limitations of the thermodynamic model.
2. All data points should contain values of pressure, temperature, liquid composition and vapour composition. Where one of more of these parameters are not included the data set is omitted.
3. Only data sets with 5 or more mixture data points are included in the study.
4. All data sets should pass the Redlich-Kister area test for thermodynamic consistency, as implemented in Aspen Plus®.

The expression for the activity coefficient of component i in a mixture, γ_i, of the NRTL model as used in this study has a functionality as given in equation [1] and the model parameters are defined in Equation [2] to [6]:

Where

For a binary system 5 parameters are required: a_ij, a_ji, b_ij, b_ji and c_ij. The default parameters available in Aspen Plus® were used as the initial values for the fittings. In this study only a_ij and a_ji were fitted. The default values of b_ij, b_ji and c_ij were retained. The temperature dependence of τ_ij is captured in the values of b_ij and b_ji. However, for isothermal data sets, no temperature dependence is available in the data and therefore the fitting of b_ij and b_ji is not possible. Further, the recommended value c_ij = c_ji = 0.3 for alcohol water systems will be retained. Finally, as the number of data points are limited, only fitting a_ij and a_ji assists in ensuring that sufficient data are available to achieve the required fit.

A base case separation process was designed in Aspen Plus® V11.0. A simulation was set-up using the RADFRAC unit operation with 5 stages in the column, the feed on stage 4, a total condenser and a kettle reboiler. The condenser pressure was set at 1.0 bar and the stage pressure drop at 0.005 bar/stage. The column was fed with a 0.1 kmol.s^-1 saturated liquid feed at 1.05 bar containing 0.15 mole fraction ethanol. The column was specified with a reflux rate of 0.135 kmol.s^-1 and a bottoms withdrawal rate of 0.8 kmol.s^-1. The separation process was setup to mimic, as closely as possible, the ‘hard-shell’ of a distillation column. Further, the number of stages and the feed stage were selected to ensure that pinching close to the ethanol + water azeotrope and pure water did not occur and that differences in the simulations are well observed while at the same time ensuring the simulation is robust and will converge for all cases. The simulation was run for the different sets of model parameters to determine their effect on the simulation outputs.

Results and Conclusion

In order provide context to the simulation results, the variation in the model parameters and their phase behavior prediction were first considered as well as possible inter-correlation of the and parameters. Thereafter simulations were run using the various sets of fitted parameters and the effect of the different parameters compared to the base case through consideration of the variation in the distillate and bottoms composition and the reboiler and condenser duties. This study showed the degree of variation that can be expected based on data set used for the correlation of the experimental data and provided an outcome as to the degree of a safety factor that is required in the design process.

This study was, however, limited in its application and scope, prompting future work. The column was setup to amplify the differences in the phase behavior and would not represent a column typically used in an industrial process. Therefore, various different setups should be considered as the degree of variation may differ. Further, the study was conducted on a system in the phase envelope range where a large difference exists between the composition of the vapour and the liquid phases. Although similar qualitative trends are expected for other systems, the magnitude of the outcomes will differ depending on the phase behavior and thus warrant investigation of other systems. Finally, the current study did not consider the effect of the hydrodynamics on the separation that can be achieved. Ultimately, compositions and flow rates affect the hydrodynamics and therefore also warrant investigation.

References

[1] Hajipour et al., Fluid Phase Equilibria. 364 (2014) 15–30.

[2] Burger & Schwarz, Fluid Phase Equilibria. 458 (2018) 234–242.

[3] Whiting, J. Chem. Eng. Data. 41 (1996) 935–941.

[4] Whiting et al., Ind. Eng. Chem. Res. 32 (1993) 1367–1371.

[5] Wakeham et al., Fluid Phase Equilibria. 185 (2001) 1–12.

[6] Mathias & Kister, J. Chem. Eng. Data. 62 (2017) 2872–2883.

[7] Mathias, J. Chem. Eng. Data. 61 (2016) 4077–4084.

[8] Mathias, Fluid Phase Equilibria. 408 (2016) 265–272.

[9] Mathias, J. Chem. Eng. Data. 59 (2014) 1006–1015.

[10] Renon & Prausnitz, AIChE J. 14 (1968) 135–144.

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