Approximation", Prentice Hall (1978). [7] Bravo, J. L.; Fair, J. R.; Rocha, J. A.; Hydrocarb. Proc. 65, 45, (1986). [8] Sequeira, M. M., "Simulação de Colunas de ...
MODELLING AND SIMULATION OF STRUCTURED PACKING COLUMN DISTILLATION Ana Maria Barreiros, Gabriela Bernardo-Gil Dep. de Eng. Química - IST - Av. Rovisco Pais, 1096 Lisboa Manuel Menezes de Sequeira, João Miranda Lemos INESC - Rua Alves Redol 9, 1000 Lisboa
Abstract The modelling and simulation of distillation columns is mainly applied to plate columns and less to random packing columns. In order to increase the mass transfer efficiency, and simultaneously to decrease the pressure drop, structured packings are being more and more used, although full models that include all the problems associated with these packing can not be found in the literature. A complete model for a distillation column using the Sulzer CY structured packing was developed. This packing, according to the manufacturer, allies the advantage of a low HETP (Height Equivalent to Theoretical Plate) with a low pressure drop, making it very adequate for units operations that need a high number of transfer units. The model developed consists of a system of partial differential equations, whose resolution can be based on the orthogonal collocation method which converts the initial system into system of ordinary differential equation, which in turn can be solved by a third order semi-implicit Runge-Kutta method. The validation of the model developed was made in a semi-pilot plant using the system alpha-pinene + beta-pinene at 80 kPa. The number of theoretical plates was computed by the Bravo, Rocha and Fair model [1]. Introduction Modelling and simulation of distillation columns mainly of plate columns and less of random packing columns are referred in literature [2, 3, 4, 5]. In order to increase the mass transfer efficiency, and simultaneously decrease the pressure drop, Stedman developed structured packing, but the credit for modern geometries must go to Sulzer Brothers in Switzerland. The advantages of structured packing have led to an increasing use in industry but, though there has been a continuous development of dynamical model of distillation columns, mainly fast and approximate, for use in process control tasks, the literature lacks complete models of packed distillation columns.
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Development of the model The model consists of: • A set of partial differential equations (obtained from mass and energy balances in an infinitesimal element of packing); • A set of algebraic relations (used to predict the physical properties, density and viscosity, and some parameters which are very important in characterizing the column operation, interfacial area between liquid and vapor, mass transfer coefficients, holdups and dispersion coefficient; • A set of differential equation (obtained from boundary conditions) • The equilibrium relation between the vapor and the liquid phases. Each section of the packing is considered to hold tree phases: the dynamic liquid and vapor phases and a third phase of stagnant liquid which can interact solely with the dynamic liquid. In the derivation of the model the following assumption were made: - Axial dispersion is accounted for using the axial dispersion coefficient; - Radial dispersion is accounted for using the radial dispersion coefficient; - The holdup in condenser and reboiler are constant; - Vapor-liquid mass transfer is governed by the two film theory; - The vapor is ideal and the liquid is non-ideal, thus the equilibrium can be represented by one activity coefficient predictive equation; - Tower pressure drop is neglected. - Constant holdup is assumed in the condenser and the reboiler mass balances. Axial and radial dispertion are considered negligible. Mass Balances 1) Vapor Balance Partial balance
Global balance
2) Liquid Balance Partial balance
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Global balance
3) Stagnant Liquid Balance Global balance
Global balance
Where: - Rate of accumulation of material in the vapor phase. Bulk flow transport of vapor phase Axial dispersion in vapor phase • Radial dispersion in vapor phase Heat loss due to vapor condensation - Mass transfer through the vapor-liquid interface • Mass transfer through the stagnant liquid - dynamic liquid interface Energy Balances 1) Vapor Balance
2) Liquid Balance
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Condenser and reboiler balances 1) Condenser balances (total condenser is considered)
2) Reboiler balances
Boundary Condition The column has two discontinuities: a) Condenser / packing b) Packing / reboiler a) - Condenser / packing ; z = N;
b) - Packing / Reboiler; z= 0;
Simplified Model Simplified forms of the generalized model can be obtained by assuming that: - Physical properties are constant; - The radial dispersion coefficient is small in comparison with axial dispersion coefficient; - Liquid and vapor flows rates are constant; - Saturated liquid and vapor strearns can be used (thus no heat balances are needed); - There is no heat loss from the tower. Due to these simplifications the model changes to: Vapor balance
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Liquid balance
The condenser and reboiler mass balances, and the boundary conditions are the same used in the non-simplified model. The solution of this resulting set of partial differential equations is difficult to obtain analytically, except in very simple cases. However, numerical solution is possible by using discretizing space and time. Discretizing the space variable is achieved using the orthogonal collocation method [6]. This method attempts to minimize the residual in the different equations at selected points in the column - collocation points - by choosing the points to be the zeros of an orthogonal polynomial. Integration in the time domain was accomplished using a third order semi-implict Runge-Kutta method. The number of theoretical plates was computed by Bravo, Rocha and Fair model [1], and the liquid holdup in each plates was computed dividing the total liquid holdup by the number of theoretical plates. The total liquid holdup was calculated through the Bravo, Fair and Rocha model [7]. Simulation The simulation was done using a program developed by Sequeira [8]. The conditions are presented in table 1.
Table 1. Simulation conditions Theoretical plates = 41 L
S1 S2 S3 S4
(mole/min.)
0,170 0,170 0,170 0,170
Holdup (mole)
0,0029 0,0029 0,0029 0,0029
Initial concentration of the most volatile component in the reboiler
18 40 70 95
Figure 1 shows the simulated evolution of the concentration in the top plate for various values of initial concentration of the most volatile compound in the reboiler, while keeping constant the flows rate. The UNIQUAC and the UNIFAC equations were used to model the non-ideality in liquid phase. Figure 2 represents the evolution of temperature in the plates forthe S1 conditions, using the UNIFAC model.
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Figure 1. Simulated evolution of the concentration in the top plate for various values of initial concentration of the most volatile compound in the reboiler, while keeping constant the flows rate _ S1 UNIFAC; _ S2 UNIFAC; : S3 UNIFAC; — S4 UNIFAC; + S1 UNIQUAC; * S2 UNIQUAC; ° S3 UNIQUAC; x S4 UNIQUAC.
Figure 2. Evolution of temperature in me plates for the S1 conditions using the UNIFAC model. 326
Validation and conclusion The validation of the model was made in a semi-pilot plant using the system alpha-pinene + beta-pinene at 80 KPa. The column used is 2m high, has a diameter of 3 cm and was filled with Sulzer CY packing. The results show mat only a qualitative comparison is possible. In fact, a quantitative comparison is not possible because: - The program used in the simulation did not consider the column hearing period; - The most volatile element is present only in the reboiler; - To calculate the liquid holdup in the column, average physical property estimates were done; - The number of theoretical plates is the average of the calculated values for each of the different purities obtained in the experimental work, and the variation of the theoretical plates with flow was considered negligible; - It was not possible to follow the concentration profile with time from empty column. It was only possible to follow the concentration profiles after the steady state had been achieved and a change in the flow rate was introduced. When experimental and calculated values are qualitatively compared, one verifies, in both cases, that: - The steady state was achieved quickly; - The separation increases when the flow rate is increased; - The steady state was achieved more quickly when the initial concentration of the most volatile component in the reboiler is increased. Analysing the figure 1, it can be concluded that UNIQUAC and UNIFAC models lead to almost the same results.
Nomenclature a - vapor-liquid interfacial area, cm cm C - Total molar concentration, mol cm D - Dispersion coefficient, cm s -1 h - Holdup cm cmH - Enthalpy cal molk - Global vapor - liquid mass transfer coefficient, mol s-1 L - Liquid flow rate, mol s-1 Q - Heat loss per unit of column height cal s -1 cm-1 t - Time, s T - Temperature, K U - Global Heat Transfer Coefficient, cal s - K V - Vapor flow rate, mol s -1 2
3
-3
2
3
3
1
v
p
1
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1
x - Mole fraction in liquid phase y - Mole fraction in vapor phase z - Distance from top of packing, cm Subscripts v - vapor l - liquid i - component s - stagnad Acknowledgments The authors are grateful to JNICT, INESC and PEDIP for financial supportReferences
[1] Bravo, J. L., Rocha, J. A. and Fair, J. R., Hydrocarbon Processing, 64(1), 91, 1985. [2] Prett, D. M., Ph.D. Thesis, University of Maryland, (1976) [3] Sahromi, M. Fellah, et al., Chem. Engi. J. 25, 125, (1982) [4] Aly, J. et al.; Entropie 136, 47, (1987) [5] Srivastava, R. K., Joseph, B. Comp. Chem. Eng. 8, 43, (1984) [6] Villandsen, J. V. and Michelsen, M. L., "Solution of differential equation by Polynomial Approximation", Prentice Hall (1978) [7] Bravo, J. L.; Fair, J. R.; Rocha, J. A.; Hydrocarb. Proc. 65, 45, (1986) [8] Sequeira, M. M., "Simulação de Colunas de Destilação", INESC (1991)
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