Real-Time Optimization of an Industrial-Scale Vapor Recompression

Article pubs.acs.org/IECR

Real-Time Optimization of an Industrial-Scale Vapor Recompression Distillation Process. Model Validation and Analysis Diego. F. Mendoza,† Lina M. Palacio,† José E. A. Graciano,† Carlos A. M. Riascos,†,‡ Ardson S. Vianna, Jr.,† and G. A. Carrillo Le Roux*,† †

Departamento de Engenharia Química, Escola Politécnica, Universidade de São Paulo, Avenida Prof. Luciano Gualberto, trav. 3, 380, São Paulo, Brazil ‡ Departamento de Ingeniería Química y Ambiental, Universidad Nacional de Colombia, Avenida Carrera 30, 45-03, Bogotá, Colombia ABSTRACT: The modeling, analysis, and simulation validation of an industrial-scale depropenizer column (Refinaria de Capuava, Mauá, São Paulo) owned by Petrobras S.A. are carried out using equation-oriented and sequential modular approaches. The model implemented in the equation-oriented environment proved to be suitable for real-time optimization (RTO) applications due to its robustness, fast convergence, and ability to represent the real process. The analysis of the model allows better understanding of the process and establishment of boundaries to process specifications and the parameters updated in the RTO cycle; furthermore, it is shown that feed composition and column pressure drop are critical aspects in the model to represent the actual process.

1. INTRODUCTION In the chemical process industry real-time optimization (RTO) is a crucial tool to increase process profitability in a scenario where feedstock composition and market price variations demand rapid adaptation of the process conditions. The benefits derived from the implementation of an RTO strategy in a process plant depend on1 the value of increased processing capacity, differences among product prices, specific energy consumption, number of independent variables and constraints, and the ability to accurately model process responses. To date, there are around 300 RTO applications,2 spanning a wide variety of chemical and petrochemical processes.3−9 The present work focuses on generating a model suitable to the RTO of an industrial-scale depropenizer column (Refinaria de Capuava, Mauá, São Paulo) owned by Petrobras S.A. This is a highly integrated energy-intensive vapor recompression process involving close-boiling mixtures, with high reflux ratios and more than 100 stages. The main steps of a classical RTO scheme are10,11 steady state detection, parameter estimation, and optimization. Online plant data are analyzed in the first step (including data reconciliation and gross error detection) to determine, by some criterion, if the process is (reasonably) steady. In the second step, the steady state data are used to update some (relevant) parameters of the model such that it can represent the actual plant conditions as closely as possible. In the third step, the fitted (adjusted) model is used to find a new optimal operation point, which becomes the new set point for the control system; then a new RTO cycle starts. The success of an RTO strategy largely depends on the mathematical model of the process and its solution. The model must be flexible to adjust the real behavior within a wide interval of process conditions12 and accurate enough to guarantee that the calculated optimum is close to the real one.13,14 The solution strategy must be able to handle large © XXXX American Chemical Society

plant disturbances in a fast and robust way to guarantee a new optimal point at every RTO cycle. These requirements make mechanistic models and equation-oriented (EO) simulation environments especially suitable for RTO applications.15−17 Vapor recompression assisted distillation (VRD) is a heat integration technique, widely used in the chemical industry to economically separate close-boiling mixtures.18,19 The main feature of VRD is that the energy of the overhead vapor, with added external mechanical energy provided by a compressor, is employed to boil up the mixture in the reboiler. The pursuit of decreasing energy and capital costs has led to highly integrated VRD designs such as the one implemented at Refinaria de Capuava (Figure 1). Although the mathematical modeling of the equipment involved in a VRD process is well-known, the highly interlinked structure, added to process nonlinearities and the number of equations used to describe this superfractionator (around 5000) make this simulation particularly difficult to converge, especially in sequential modular (SM) simulators,20,21 and partially explains why simplified and pseudo stream approaches have been previously proposed to simulate and optimize this process.22,23 These simplifications, together with neglecting the presence of minor components ( 0.7. The isentropic efficiency is a model parameter to be updated in each RTO cycle using the outlet temperature of the compressor, stream 10. The actual isentropic efficiency, calculated from the steady state plant data available, is close to 0.87, which is within the expected efficiency interval (ηCP > 0.7). An important aspect to keep in mind, regarding efficiency, is that compressors are designed to operate efficiently within a (narrow) flow interval; this constraint must be taken into account during the optimization step in the RTO cycle. 5.2.6. Bottom Flow Rate. The bottom flow rate, stream 3, has a function analogous to the reflux ratio in the column performance; i.e., it determines the distillate purity, the energy consumption, and the recovery of the desired product. The behavior obtained (Figure 7) clearly shows the trade-off between energy input and fractional recovery. A profitable operation is characterized by a trade-off between energy consumption and the recovery of the desired product. The most favorable bottom flow rate in the simulations is close to 250 kmol/h, a value which cannot be considered as the optimum flow because it was not obtained from an optimization procedure; it only indicates that there are optimum process conditions for this process. 5.2.7. Outlet Temperature in Heat Exchangers and Reboiler. Heat exchangers HX1 and HX2 and reboiler RB regulate the amount of recycled vapor to the compressor. Vapor recirculation is necessary because the energy required in RB is larger than the one that could be supplied by the compression of stream 2 alone and to avoid compressor instability (surge). A desirable operational condition is recycling the smaller amount of vapor required for a stable operation. The process conditions used for the base case show that the 87.8% of the recycled vapor is used in the reboiler; the rest is sent to HX1. Better operation conditions can be achieved by optimizing the heat exchange distribution in RB, HX1, and HX2. 5.3. Comparison with Experimental Data. The adjusted temperature profile shows that the model developed is able to MV fit real plant data using efficiency (EMV r , Es ) and pressure drop (ΔP jr, ΔPjs ) parameters. These parameters cannot be considered the true values for pressure drop or mass transfer efficiencies, but only adjusting parameters which lump the

imperfect knowledge about phase equilibrium, mass transfer, flow patterns, and heat losses occurring in the real process. However, it is worth noting that the parameter values obtained make sense with the distillation operation since greater pressure drop and efficiency is expected for the trays as the liquid flow increases, which is the case of the stripping section. The increase in liquid flow on the trays increases the flow resistance to the rising vapor (higher pressure drop) and the contact time between the liquid and vapor phases (higher efficiencies). The experimental temperature reported for the last tray is higher than that predicted by the model; a possible explanation for this behavior is the presence of unreported (uncharacterized) heavy component(s) in the feed. Routine feed composition analysis at Refinaria de Capuava is performed for a few components besides propylene and propane; the compositions of other components in the mixture are inferred from historical data of a more exhaustive (infrequent) analysis. A proof of the importance of a good characterization of the feed composition is that a slight modification in the mole fraction of one of the minor components (isobutene) notoriously improves the model fit (see Figure 12 and case 3 in Table 3). This result suggests that, for maximizing the benefits of the RTO implementation at Refinaria de Capuava, a better characterization of the feed composition than the one provided by routine analysis is required. Although the model can properly fit to steady state plant data, there is the need to address the identifiability problem; i.e., it must be ensured that the model structure and the quality and quantity of experimental data available allow the determination of the updated parameters because otherwise the adjusted model could be unreliable for optimization purposes. More elaborate parameter estimation routines than the one used at this stage of the work (unweighted least squares) are required to properly address the estimability problem to guarantee a model with good prediction capacity. Studies on practical identifiability have been undertaken in our group and show that there are some biased parameter estimation methods that could properly handle the identifiability problem.

6. CONCLUSIONS AND OUTLOOK The highly interlinked vapor recompression distillation process of an industrial depropenizer was modeled and simulated in sequential modular and equation-oriented environments. The comparison between these two approaches showed that both are able to simulate the processes in a large range of process conditions. It was possible to simulate the process without using the pseudo stream approach in both environments, differently from what a recent publication suggests.22 However, an equation-oriented environment will be used to execute the optimization step in future works due its superior characteristics (speed, robustness, flexibility in process specifications, and availability of analytical first order derivatives) as compared to the sequential modular approach. The analysis of the model is a valuable tool to gain general understanding and to assess the robustness of the model; some important conclusions drawn from this analysis are the following: (i) Minor components (between 0.001 and 1 mol %) have significant effects on product composition and temperature profile. They should not be disregarded if composition changes in the feed are expected; this also calls attention to the importance of good characterization of the feed stream in RTO. I

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summation (eq A7), and total flow (eq A8) equations, and the thermal and mechanical equilibria of the streams leaving the stage (eqs A9 and A10). F, V, and L denote the molar flow rates of the feed, “V” and “L” represent the internal liquid and vapor streams, x and y are the mole fractions of the liquid and vapor phases, hV and hL are the vapor and liquid molar enthalpies, and Pj and ΔPj are the total pressure and pressure drop in tray j, respectively. The expansion valves are modeled as an adiabatic process in which the outlet stream is in vapor−liquid equilibrium. The 2C + 5 equations involved in the modeling of the expansion are shown in Table 6; these equations come from the component

(ii) Pressure drop is an important feature to take into account in the model, mainly because of its effect on phase equilibrium, especially on saturation (dew and boiling) temperatures. MV (iii) Parameters EMV r , Es , ΔPjr, ΔPjs, and ηCP can be estimated from the available plant data, to obtain a good representation of the actual process. (iv) Outlet temperatures in heat exchangers and reboiler as well as the reflux ratio (or bottom flow rate) are important decision variables in the optimization process, because they have a direct effect on product composition and recovery as well as on the energy demand of the process. The least-squares method used to adjust the model (parameter estimation) is not suitable to handle gross errors and the parameter identifiability problem. The next step in this project is to implement parameter estimation routines, with a robust objective function as the redescending estimator in which it is possible to perform data reconciliation, gross error detection, and parameter estimation in one step.47,48 The initialization strategy using the results of a simplified simulation in Aspen Plus (without recycling streams) is useful to solve the flow sheet in EMSO. However, it is desirable to generate an initialization routine independent of Aspen or any other process simulator; this can be done by exploiting the compatibility of EMSO with programming languages such as C, C++, and FORTRAN. The idea is to create an application in C++ capable of solving a flow sheet with simplified thermodynamics that generates a file fully compatible with the naming convention and structure of EMSO.

Table 6. Summary of the Equations for Modeling an Adiabatic Expansion FxiF − Vyi − Lxi = 0

(A11)

(i = 1, ..., C)

FhF − Vh − Lh = 0

(A12)

yi − K ixi = 0

(A13)

V

L

(i = 1, ..., C)

L

V

(A14)

L

V

(A15)

T −T =0

P −P =0 C

1−

∑ yi = 0

(A16)

i=1

(A17)

F−V−L=0

and energy balances (eqs A11 and A12), the phase equilibrium condition (eqs A13−A15), the sum of composition, and the total mole balance. The equations used to model the total reboiler are shown in Table 7. The cold side of the total reboiler, identified by subscript “C”, is the liquid coming from the last tray of the distillation column while the hot side, denoted by subscript “H”, is the overheated vapor coming from the compressor. The cold-side fluid leaves the reboiler as saturated vapor while the hot-side fluid can exit the reboiler as saturated or subcooled liquid. Equations A18−A20 correspond to the material balances (total and by component) and the dewpoint condition. Equations A21−A31 describe the hot side

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APPENDIX: MODEL IMPLEMENTED IN THE EQUATION-ORIENTED ENVIRONMENT This appendix summarizes the equations used to model the flow sheet. They correspond to the distillation column, expansion valves, reboiler, and compressor. The adiabatic distillation column was modeled as a collection of individual trays (numbered from top to bottom). The equations used to model a tray j of the column (Table 5) comprise 3C + 6 equations, viz., the component and energy balances (eqs A1 and A2), efficiency (eqs A3−A5), hydraulic (eq A6),

Table 5. Summary of the Equations for Modeling an Adiabatic Distillation Tray FjVyiF V + F jLxiF jL + Vj + 1yij + 1 + Lj − 1xij − 1 − Vjyij + Ljxij = 0

(i = 1, ..., C)

j

(A1)

FjVh FVV + F jLh FLL + Vj + 1hjV+ 1 + Lj − 1hjL− 1 − VjhjV + LjhjL = 0

(A2)

EjMV (yij* − yij + 1) − (yij − yij + 1) = 0

(A3)

j

j

K ijxij − yij* = 0

(i = 1, ..., C − 1)

(A4)

(i = 1, ..., C)

C

1−

∑ yij* = 0

(A5)

i=1

Pj − 1 + ΔPj − PjV = 0

(A6)

C

1−

∑ yij = 0

(A7)

i=1

FjV + F jL + Vj + 1 + Lj − 1 − Vj + Lj = 0

(A8)

T jL = TjV

(A9)

P jL = PjV

(A10) J

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Table 7. Summary of the Equations for Modeling a Total Reboiler xiinC

yiout C

−

(i = 1, ..., C)

=0

out yiout − K iout C xiC = 0 C

(i = 1, ..., C)

(A19) (A20)

TCL,out − TCV,out = 0

(A21)

PCL,out − PCV,out = 0

(A22)

C

1−

∑ xiout C = 0

(A23)

i=1

(A24)

FHin − FHout = 0 yiinH − xiout H = 0

(i = 1, ..., C)

out yiout − K iout H xi H = 0 H

THL,eq

−

THV,eq

−

PHV,out

PHL,out

(i = 1, ..., C)

(A25) (A26) (A27)

=0

(A28)

=0

C

1−

=0 ∑ yiout H

(A29)

i=1

THout − THL,eq + ΔTHsub = 0

(A30)

FCinh FL,in + FHinh FV,in − FCouth FV,out − FHouth FL,out =0 C H C H

(A31)

of the reboiler and include the material balances, the boiling-point condition which allows the calculation of the outlet temperature using a subcooling degree, ΔTsub H , and the energy balance around the reboiler. The equation set derived for the reboiler can be applied to the other heatexchange devices of the flow sheet. The compressor was modeled using isentropic efficiency, η CP, to find the actual outlet temperature of the compressor; the equations involved in the compressor modeling (Table 8) are material balances (eqs A32 and A33), the Table 8. Summary of the Equations for Modeling an Isentropic Compressor (A32)

F in − F in = 0 yiin P

−

out

yiout

=0

(i = 1, ..., C)

− P − ΔPCP = 0

in

s −s

out

out

ηCP(h

(A35)

=0 in

(A33) (A34)

in

isen

− h ) − (h

in

−h )=0

(A36)

pressure change through the compressor (eq A34), the isentropic condition (eq A35), and the isentropic efficiency expression (eq A36).

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(A18)

FCin − FCout = 0

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 30 91 11 70. Fax: 38 13 23 80. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Petrobras S.A. for financial support (Project 0050.0068488.11.9). K

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