(772f) Plantwide Control for Economically Optimal Operation of An Ethyl Benzene Process

                                                                                                                              Ashok S Pathak and Nitin Kaistha

Department of Chemical Engineering

Indian Institute of Technology Kanpur 208016

In this work, plantwide control system design for economically optimal operation of an ethyl benzene process is studied for Luyben’s recently developed base-case design. The process is depicted in Figure 1 and consists of two CSTRs followed by two simple distillation columns with two liquid recycle streams.  Ethyl benzene (EB) is produced by the alkylation of fresh benzene with ethylene (Main Reaction: Bz + C₂ --> EB). The EB can further alkylate with ethylene to form diethyl benzene (DEB) (Side Reaction: EB + C₂ --> DEB). The reactors are therefore operated in excess benzene environment to suppress DEB formation. The effluent from the reaction section is separated to recover the unreacted benzene from the top of the first column, which is recycled back to the first CSTR. The bottoms from the first column is further distilled to recover nearly pure EB product as the distillate and DEB with some EB as the bottoms. The DEB stream is recycled to the second CSTR where DEB transalkylates with benzene to form EB (Transalkylation: DEB + Bz --> 2EB). The DEB is allowed to build in this second recycle stream to a level where the DEB formation by the side reaction and consumption by transalkylation exactly balance each other. The DEB is thus recycled to extinction.

The nine steady state operating degrees of freedom for the process are optimized for the given base-case throughput to maximize the yearly operating revenue. The constrained optimization is equivalent to minimizing energy consumption per kmol product for a fixed product quality. The three active constraint variables, one throughput specification and two product quality specifications leave 3 unconstrained dofs. The ethylene feed ratio to the reactor, the EB impurity in the benzene recycle stream and in the DEB recycle stream are chosen to specify these unconstrained dofs. For a ±20% throughput change around the base-case, the difference in the rigorously optimized yearly revenue and the revenue holding these three variables constant (at their base-case optimum values) is found to be very small (<0.5%). Process operation holding these three variables constant is thus deemed as economically optimal for a large change in throughput around the base-case.

Constrained optimization is also performed with the throughput itself as an optimization variable to maximize the product rate (maximum throughput) corresponding to the maximum achievable yearly process revenue. At the optimum solution, the six active constraints and two product purity specifications leave one unconstrained degree of freedom. The throughput shows a maximum with respect to this unconstrained degree of freedom, namely, the EB mol fraction in column 2 bottoms. The EB mol fraction versus throughput curve is however quite flat so that process operation at constant column 2 bottoms EB mol fraction is deemed acceptable for process operation close to maximum throughput.

A plantwide control scheme is devised to mitigate snowballing in the DEB recycle stream and transients in the active constraints at the maximum throughput steady state solution. Rigorous dynamic simulations are then performed to quantify the back-off in the active constraints and consequent economic loss for a worst-case feed composition disturbance. A quantitative comparison of the economic loss due to back-off using the synthesized control system with a conventional one which fixes the throughput manipulator at the ethylene fresh feed shows that the former results in significant economic benefit to the tune of 5%. The energy savings for process operation at the base-case throughput is also found to be ~ 3% higher. The study clearly demonstrates a “top-down bottom-up” plantwide control system design approach as being the most appropriate for economically optimal process operation.

References

1.      Luyben, W. L. Design and control of the ethyl benzene process. AIChE J. 2011, 57: 655-670.

2.      Luyben, W. L. Snowball effects in reactor/separator processes with recycle. Ind. Eng. Chem. Res. 1994, 33, 299-305.