(516d) Simultaneous Process and Recipe Design of an Acrylic Fiber Production System

Polymerization
has been historically an area where process systems engineering tools have been
widely applied by combining polymer science, chemistry, and technology, with
process engineering principles [1]. A significant amount of work has been
devoted to the modeling and simulation of polymerization reaction systems,
which are characterized by complex interactions between productivity indicators
(conversion, batch time, profit, etc.) and polymer properties (polydispersity, molecular weight distribution, etc.). As a
result, the design, operation and control of such polymerization processes
constitute challenging problems, where the choice of the trajectories of the
reactor temperature and monomer feed rate is targeting at an optimum trade-off
between productivity and polymer quality [1,2].
However, other downstream tasks, in addition to the polymerization reaction,
also contribute to the optimization of production objectives, either economic
or environmental, as shown in the solution of the scheduling problem for
polymerization manufacturing facilities [3].

In this
context, the aim of this work is to direct attention towards simultaneous
process and recipe design of industrial-sized polymerization processes,
understood as the selection and interconnection of process stages and the
specification of their operating strategy. A model-based optimization approach
is used to optimize simultaneously the process and the corresponding recipe to
produce a polymer in single-product batch campaigns as part of the design of a
polymerization plant. This way, a trade-off between process and recipe design
can be achieved  to improve production targets
while maintaining polymer quality. Decisions related to the design and synthesis
of the process include the selection of the type and number of process stages
(also referred as tasks) and operations, the technological specification of
processing units, the location of storage units, the recirculation of
intermediate flows, the configuration of process stages in single, series or
parallel operation, and the synchronization of tasks. Decisions referring to
the operational design include the reference trajectories of the control
variables, the batch  times, material transfer
synchronization between tasks, and batching decisions. Besides, equipment
investment, processing costs, raw material costs, waste treatment costs, and
economic impact of product quality are considered in the optimization objective
function.

In model-based optimization
approaches for process synthesis, all processing alternatives are first
represented in a superstructure, which is later formulated into a mathematical
program to be finally optimized [4]. Particularly, the modeling approach used
in this work relies in the combination of mixed-logic modeling [5], previously
applied to continuous process synthesis, and the use of multistage models [6]
to represent the performance of each batch task. The approach is similar to the
disjunctive multistage modeling by Oldenburg and Marquardt [7], developed in
the context of individual batch unit optimization, and now extended to
represent concurrent process stages and their synchronization.

The main steps are
following described: The available information for each processing stage is
first identified, such as appropriated technologies or practical control
variables. Then, a superstructure is constructed, which gathers together all
potential synthesis alternatives. For that, state-equipment network (SEN)
representation is used, assuming a direct relation between task and equipment.
Logic variables and disjunctive equations are following defined to
mathematically represent the qualitative information of such alternatives.
Further available knowledge of the process that relates the various processing
options can be incorporated into the model through logic propositions, which
also limit the dimension of the combinatorial problem. Finally, multistage
models are provided to represent each potential processing task, where material
input and output stages are identified to allow the synchronization with other
tasks. Dynamic, steady-state, or linearly approximated models can be used,
according to the impact of each process stage on the decision criterion.

The
acrylic fiber process is presented as an example of the proposed modeling
approach to solve the process  and  recipe
design problem simultaneously. The production target is a fiber composed of 85%
in weight of acrylonitrile (AN), and 15% of vinyl
acetate (VA) in spun format. Hence, primary copolymer production and secondary
spun production stages are required. For that, the principal features of the
manufacturing process are incorporated into the superstructure and the
optimization model from related state-of-the-art literature. The principal
information featuring the process is composed of:

·      
the main stages in acrylic fiber
production [3],

·      
the use of suspension and solution
copolymerization technologies [8],

·      
the possibility of avoiding solvent separation
after the solution copolymerization reaction [9,10],

·      
the operational information and dynamic
models of copolymerization [11] and separation [7] processes,

·      
and the possibility of recovering and
reusing the water used to wash the final product [8].

As a
result, the following process stages or tasks are subject to inclusion in the
process model: (1) copolymerization reaction, (2) recovery of unreacted monomer, solvent and suspension medium after
reaction, (3) washing and filtration, (4) repulping,
(5) filtering, (6) wet spinning, (7) second washing and filtration, and (8)
second recovery of solvent after spinning. For each process stage, several
subtasks and configurations are allowed, which determine the required equipment
pieces and their synchronization. All in all, eleven alternative disjunctions
are considered for plant and process synthesis in the example, like the
selection of solution or suspension copolymerization technology, organic or
aqueous solvent in solution polymerization, separation
of solvent or direct transference of solved copolymer to repulping,
etc. Each of these options leads to a particular cost profile in the objective
function. For example, the use of organic solvent drastically increases the
waste treatment costs. The process superstructure is presented in Figure 1,
where all synthesis alternatives are included, as well as the Booleans
indicating if such alternative is selected (true value) or not (false value).

Figure
1: Superstructure of the acrylic fiber process. The equipment pieces are: R11
and R12 (solution and suspension polymerization reactors), C12, C22, C81 and
C82 (distillation columns), F3, F5, F71 and F72 (washing and filtering units),
R4 (repulping unit), S6 (spinnerette),
and T2, T3, T81 and T82 (buffer tanks).

Regarding
processing conditions, the process stages whose control variables have a
critical impact on cost function are: task 1(copolymerization reaction), task 2
(recovery of unreacted monomer, solvent and
suspension medium after reaction), and task 8 (recovery of the solvent after
spinning and washing the final spun). For example, a large separation and reuse
of solvent may partially mitigate its corresponding waste treatment cost, or
the achievement of low conversions in the polymerization reaction may have an
effect on higher processing costs in the subsequent distillation column. Hence,
dynamic models are used to describe the tasks of these process stages, and
their control variable trajectories and batch times are optimized.
Particularly, monomer feed rate and temperature are the main dynamic variables
used for reaction control, whereas distillation processes are basically
controlled through the dynamic adjustment of their respective reflux ratios.
Quality restrictions are formulated for polydispersity
and composition in order to keep the product properties in the reactor within a
predefined quality range. In other process stages, which are not critically
contributing to the objective function, steady-state assumptions or other
approximations can be done in their corresponding tasks.

By
modeling and optimizing the process and recipe design simultaneously, a
potential improvement in the objective function should be met, with respect to
the use of fixed process models and recipes. This result is expected due to the
holistic evaluation of the decision criteria. In particular, the trade-offs
between the various process stages within the complete process is considered in
the optimization, as well as the interactions between synthesis and operational
design degrees of freedom. Additionally, the optimization model permits the
evaluation and comparison of processing alternatives according to multiple
points of view, like processing, economic or sustainable production policies.

Acknowledgements

This work has been
developed   during the research project EHMAN (DPI2009-09386), funded
by the Ministerio de Ciencia
e Innovación of Spain and the European Commission
(ERD Funds). Additional financial support of the Aachen group from the EU FP 7
project F³ Factory (grant agreement no: 228867) and of the MegaCarbon
project (NRW-EU Ziel 2-Programm 2007 ? 2013, EFRE) is
gratefully acknowledged.

References

[1]    R. Giudici,
2000. Latin American Applied Research, Vol. 30, pp. 351-356

[2]    M. Embiruçu, E.L. Lima, and J.C. Pinto, 1996. Polymer Engineering and Science,
Vol. 36(4), pp. 433-447

[3]    E. Capón-García, A.D. Bojarski, A. Espuña,
and L. Puigjaner, 2011. AIChE Journal, Vol. 57, pp. 2766-2782

[4]    I.E. Grossmann and G. Guillén-Gosálbez, 2010. Computers and Chemical Engineering,
Vol. 34(9), pp. 1365-1376

[5]    R. Raman and I.E. Grossmann, 1994. Computers and Chemical Engineering, Vol.
18(7), pp. 563-578

[6]    V.S. Vassiliadis, R.W.H. Sargent
and C.C. Pantelides, 1994. Industrial and Engineering
Chemistry Research, Vol. 33(9), pp. 2111-2122

[7]    J. Oldenburg, W. Marquardt, D. Heinz, and D.B. Leineweber,
2003. AIChE Journal, Vol. 49(11), pp. 2900-2917

[8]    United States Environmental
Protection Agency, 1995.  http://www.epa.gov/ttn/chief/ap42/ch06/

[9]    M. Gol'dfein and B. Zyubin,
1990. Review
Polymer Science, Vol. 32(11), pp.2145-2166

[10] 
P. Bajaj, K. Sen,
and S.H. and S.H. Bahrami, 1996. Journal of Applied
Polymer Science, Vol. 59(10), pp. 1539-1550

[11] 
D. Butala,
K. Choi, and M. Fan, 1988. Computers and Chemical
Engineering, Vol. 12(11), pp. 1115-1127