Modelling and Optimisation of an Industrial Batch Process for the Production of Dioctyl Phthalate

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volved in the corresponding industrial process. We then proceed to describe the key features of the dynamic model developed for this process, and its im-

plementation and validation. The main issues in-

volved in determining optimal process designs and operating strategies are then analysed, and our approach to solving this dynamic optimisation problem is presented, together with some of the results obtained. Finally, some more general conclusions on the lessons learned from this work are presented.

PSE '97-ESCAPE-7 Joint Conference

P R O C E S S D E S C R I P T I O N Chemistry

Dioctyl phthalate (DOP) is formed by the diesterification of phthalic anhydride (PA) and 2- ethylhexanol (2EH). The two main reactions taking place are as follows:

Monoester formation This results in the formation of (mono) octyl phthalate (MOP):

PA + 2EH -+ MOP (A)

This reaction is irreversible and very fast.

Diester formation

MOP + 2EH ~ DOP + H20 (B)

This reversible reaction can proceed via both a catalytic route involving a homogeneous catalyst and a non-catalytic path, and is conse- quently characterised by rather complex kinetics.

In practice, in order to increase the rate of the DOP formation by reaction (B), an excess amount of 2EH is used. The achievable conversion is limited by equilibrium considerations. However, by removing the water formed during the diesterification reaction, it is, in fact, possible to achieve almost complete conversion of the limiting reactant. This idea forms the basis of the industrial process described below.

Equipment and Operating Procedures The plant is designed around a kettle reactor, suit- able for the production of different plasticisers. A simplified schematic of the process is shown in figure 1.

The operation of the plant involves a sequence of steps. The most important of these are as follows:

Feeding: The preheated fresh 2EH together with the PA and homogeneous liquid catalyst are fed to the reactor. The fresh 2EH may be partially replaced by 2EH recovered from the previous batch cycle (see below) which is also charged to the reactor via the preheater.

Esteriflcation: The contents of the reactor are con- tinuously stirred and heated with steam sup- plied to the jacket of the reactor. This causes

2EH Saturat~ with H 2 0

l ... }

PA

S~gad Steam

W a ~

R ~ w ~ d 2 ~ 1

2EH

Figure 1: Flowsheet of DOP Reactor an evaporation of most of the water formed by the esterification, together with some of the alcohol (i.e., the two most volatile components).

This overhead vapour is totally condensed and allowed to separate into two liquid phases in the overhead reflux drum. The aqueous phase is removed from the system while the alcohol rich phase is recycled back to the reactor. A separator unit placed between the reactor and the condenser (see figure 1) is used to improve the effectiveness of 2EH/water separation.

Stripping: At the end of the esterification stage, the reactor contains primarily a mixture of DOP with excess 2EH. The latter is removed in the overhead vapour by further heating. In contrast to the step above, the alcohol rich phase recovered in this manner from the reflux drum is not recycled to the reactor but is instead stored in a separate 2EH recovery tank for use in subsequent batches (see Feeding step above).

Chemical Additions: Any unreacted MOP and catalyst still left in the reactor are neutralised and decomposed respectively through the addition of further chemicals and hot water.

D e h y d r a t i o n a n d V a c u u m Stripping: The DOP product in the reactor is brought up to the desired final product purity by removing the remaining water and 2EH by steam stripping the reactor contents under vacuum.

During this period, steam is simultaneously sparged directly into the reactor and fed to the reactor jacket.

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P R O C E S S M O D E L L I N G • The key features of the models used for the main units in the process are as follows:

R e a c t o r This is modeled as a perfectly mixed jack- eted stirred t a n k reactor that may contain both vapour and liquid phases. The model assumes t h a t all reactions are homogeneous and occur in the liquid phase and t h a t the liquid and vapour phases are in thermodynamic equilibrium.

The model also allows phases to appear and disappear, taking into account the three potential operating regimes (all liquid, mixed liquid- vapour and all vapour) and the transitions between them.

S e p a r a t o r This is modeled as an adiabatic flash drum. As in the case of the reactor, the model allows for phase appearance and disappearance.

R e f l u x d r u m This model describes two liquid phases present in equilibrium in the mix- ing/settling compartment of the reflux drum, taking account of the hydrodynamics of the flow of the organic phase over the weir. The height of the interface between the organic and aqueous phases is maintained between strict limits by a controller regulating the flow of the aqueous phase from the tank.

The overall process model also characterises the flows between the above units in terms of appropriate flow/pressure drop relations.

An activity coefficient based model was used for computing the vapour and liquid equilibrium. The pure component physical properties (vapour and liquid enthalpy and density) are computed as correlated functions of temperature. Mixture properties were computed assuming ideal mixture behaviour.

The reaction rate model for the formation of DOP has been derived through laboratory experiments and describes both the catalytic and the non- catalytic routes in this reaction.

M O D E L I M P L E M E N T A T I O N

The key characteristics of the model are as follows:

• C o m p l e x i t y : The physical and chemical mechanisms that govern the time dependent behaviour of the complete DOP reaction system are quite complex. The equations describing the performance of the system have been derived from first principles in terms of the con- servation laws, physical constraints and equilibrium relations which describe the performance of each equipment item, taking account of its detailed geometry. The resulting model contains approximately 2000 ordinary differential and algebraic equations.

D i s c o n t i n u o u s p h y s i c s : The DOP system exhibits both continuous and significant discrete aspects. For instance, the overhead separator is initially completely dry, containing

only a vapour phase. As the reaction pro-

ceeds, the water and some of the excess 2EH are vapourised and then totally condensed and fed to the reflux drum. While the latter is fill- ing up, no actual reflux stream exists. However, once the level of the liquid in the reflux drum exceeds the level of the weir, a 2EH-rich organic liquid phase starts being fed back to the separator. This then leads to the appearance of a liquid phase in the latter.

• C o m p l e x o p e r a t i n g p r o c e d u r e : The DOP system is a dynamic system driven by a sequence of external manipulations representing a number of processing steps, some of which were described above.

The above process model was implemented in the

gPROMS

process modelling tool (Barton and Pan- telides, 1994; Oh and Pantelides, 1996) developed at Imperial College. Unlike earlier modelling software which was aimed at primarily continuous processes,

gPROMS

is specifically designed for the modelling, simulation and optimisation of processes with both discrete and continuous characteristics. This allows the detailed modelling of both the physicochemical behaviour of the system and its operating procedures.

The package also provides effective mechanisms for handling complexity in both of these aspects of process modelling.

P R O C E S S M O D E L V A L I D A T I O N A N D S I M U L A T I O N

Typical dynamic simulation results obtained using the model described above are illustrated in figures 2 and 3*. Figure 2 shows the variation of the mole frac- tions of DOP and 2EH in the reactor throughout a single batch cycle. As the reaction proceeds, the mole fraction of DOP increases reaching a limiting value by the end of the esterification stage (around the mid- dle of the figure). At the same time, the 2EH mole fraction decreases reaching again a limiting value determined primarily by the excess amount of 2EH that has been fed to the reactor. During the subsequent stripping, chemical additions and vacuum stripping phases, the molefraction of 2EH is further decreased.

This generally leads to an increase in the DOP mole fraction although a sharp temporary decrease is ob- served over a short period of time due to the addition of other components to the reactor. Eventually, the DOP mole fraction reaches the final product purity specification.

Figure 3 shows the corresponding pressure and temperature profiles in the reactor. It is worth not-

*The numbering of the axes in these and other results plots in this paper has been removed for commercial confidentiality reasons.

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S1242

ing the sharp changes in pressure signifying the be- ginning of the various processing stages. At the same time, the temperature varies between lower and upper bounds dictated by product quality considerations.

E V A L U A T I O N OF D E S I G N A L T E R N A T I V E S

Having validated the simulation model with the mea- sured plant data, it was then possible to perform a number of operational and design studies using the

same gPROMS model and to quantify potential im-

provements.

The studies included a number of operating sce- narios (heating profiles, feed policies etc.) as well as

design modifications (e.g. improved separator design

and introduction of a prereaction unit). However, because of the complexity of the process, it is clear that a more systematic way of searching the rather

=~= "- large space of possible operating and design decisions is required. This is discussed below.

\

Figure 2: Reactor compositions 2EH, DOP

it_ -

0

Figure 3: Reactor Temperature and Pressure The simulation results shown above aimed to re- produce the current operating policy at one existing plant. The agreement between model predictions and actual plant measurements is excellent both qualita- tively and quantitatively. In this context, it is worth emphasising that the values of all thermodynamic and kinetic parameters used in the model were derived from appropriate laboratory experiments. No parameter fitting using the plant data was performed.

O P T I M A L P R O C E S S O P E R A T I O N A N D D E S I G N

The DOP process involves several important degrees of freedom, such as the rates of addition of the main reactants, catalyst and heat to the reactor, as well as the recycle policy for recovered 2EH. It is also subject to several constraints, including:

Physical constraints: These are due to the limited

provision of resources (e.g. steam availabil-

ity) and operational restrictions on the various equipment items (e.g. minimum pressure, max-

imum reactor capacity etc.).

Product quality constraints: These exhibit them- selves directly as constraints on the final composition of the material left in the reactor at the end of the batch, and also indirectly as constraints on the operating conditions during the batch. For instance, the reactor temperature must never exceed a certain limit relating purely to the quality of the final product.

Overall, it is clear that the determination of a design and/or optimal operating policy is a non-trivial task, especially in view of the complex interactions between the reaction kinetics and vapour-liquid and liquid-liquid equilibria in the system. Our approach has been to formulate this as a dynamic optimisation problem incorporating an economic objective function, the time-dependent decision variables and all important constraints. This was then solved using

the dynamic optimisation facilities in gPROMS.

Objective Function

The objective function to be minimised is the total cost per unit mass of DOP produced. For the design of new DOP plants, the objective function comprises two main components:

1. The operating costs associated with making a

batch of DOP, including:

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• Costs of raw materials (2EH, PA and catalyst).

• Cost of utilities (mainly steam of various qualities).

• Cost of chemicals used for MOP neutrali- sation and catalyst deactivation.

2. The fixed capital costs associated with the plant equipment, including the costs of the reactor shell and its heating coil, and the costs of the condenser and the separator.

Of course, in the case of optimising the operating procedure for an existing plant, the objective function includes only the operating costs listed above.

Decision Variables

The solution of the dynamic optimisation problem involves the determination of the total duration r of the operation and its individual processing steps, as well as the variation of the following five time-dependent control variables over the time horizon t E [0, r]:

• The rate of addition of PA feed to the reactor.

• The rate of addition of fresh 2EH feed to the reactor.

• The rate of addition of recovered 2EH feed to the reactor.

• The rate of supply of steam to the reactor heating coil.

• The pressure profile in the reactor.

In addition, the optimiser will need to determine optimal values for the following time-invariant parameters:

• The amount of catalyst to be fed to the reactor t .

• The volume of the reactor (design case only).

Constraints

Our current optimisation formulation includes the following constraints:

• Constraints on the minimum and maximum permissible temperatures within the reactor at all times during the batch cycle.

• A constraint on the maximum permissible temperature within the reactor at the end of the batch cycle.

• Constraints on the minimum and maximum al- lowable volume of liquid in the reactor at all times during the batch cycle.

?The addition of catalyst takes place as a single discrete injection of material rather than as a continuous flow over a period of time.

• A constraint on the minimum mean production rate of DOP (defined as the amount of DOP produced per batch divided by the total batch processing time). This is derived from the lower bound on the desired annual production of DOP.

• A constraint that ensures that the total amount of recovered 2EH fed into the reactor does not exceed the total amount recovered during a batch.

O P T I M I S A T I O N M E T H O D O L O G Y The problem described above involves the optimisation of a complex dynamic system subject to a variety of constraints, and this is to be achieved by manipu- lating several time-varying quantities as well as some time-invariant ones. The solution of this problem has been carried out using the dynamic optimisation facilities in gPROMS.

The solution method used by gPROMS for this type of problem is based on the control vector param- eterisation approach as recently described by Vassil- iadis et al. (1994a, 1994b). This involves representing each of the five time-varying control variables in terms of a finite number of parameters. For instance, a certain control variable may be varied in a piecewise constant fashion over a given number of intervals spanning the batch processing time. The constant value of the control in each interval and the duration of the latter form a finite set of parameters to be determined by the optimisation. The time-invariant decision variables are also added to this set of parameters.

The current optimisation of the DOP process in- corporates a detailed description of the plant operation over the feeding and esterification stages of the operating procedure, and an aggregate description for the remaining stages. A piecewise constant time variation is assumed for all control variables except for the reactor pressure which is defined to be a piecewise lin- ear and continuous function of time. The time horizon of interest is divided into 4 intervals of variable duration for the purposes of defining these piecewise functions. The length of each time interval, as well as that of the total time horizon, is determined as part of the solution of the optimisation problem.

O P T I M I S A T I O N R E S U L T S

Typical optimisation results are shown in figures 4 to 5. Figure 4 shows the optimal feed addition policy.

The optimal solution starts by feeding the PA simultaneously with the recovered 2EH; the latter is then replaced by a fresh 2EH feed.

Figure 5 presents the temperature profile resulting from the optimal control manipulations. The optimiser maintains the temperature within the bounds specified by the product purity constraints at all times, keeping it close to the upper bound at the start of the esterification phase.

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S1244 PSE '97-ESCAPE-7 Joint Conference In addition to control profiles of the type illus-

trated here, the optimisation determines simultaneously the values of the optimal reactor volume, the optimal amount of catalyst to be added to the reactor, and the optimal batch duration.

.... t.~." It2m

. . . l

---:---!

~ t Q 4 • 464b • • & ~ O Q

Figure 4: Optimal Feed Addition Policy

C O N C L U D I N G R E M A R K S

The study reported in this paper, carried out jointly by Mitsubishi Chemicals and Imperial College, has led to substantial improvements in the throughput and profitability of the DOP process. It has also opened the way for strategic comparisons among different plant configurations and even geographical lo- cations to be placed on a rational and meaningful basis by comparing the optimal design and operating policies of all such alternatives.

The importance of using accurate dynamic models for this study cannot be overemphasised. This is especially true given the tight economics of the process and the tight operating constraints under which it operates. For instance, the difference in the unit DOP production cost achievable by competing optimal designs was often found to be of the order of only a few percentage points, which, nevertheless, represents a large improvement in process profitability. The predictive capability of the model must be within this range of accuracy.

The study presented here also provides some evi- dence of the capability of currently available software tools such as gPROMS to deal with complex industrial batch processes. Of particular note is the in- creasing ability to solve dynamic optimisation problems involving fairly large models with many interact- ing decisions and constraints. This significant devel- opment over what was practically feasible only a few

Figure 5: Optimal Temperature Profile

years ago is already finding a wide range of applica- tion for improved process design and operation. How- ever, it must again be emphasised that the availabil- ity of validated process models that can accurately predict the plant behaviour is an essential prerequi- site for these benefits to be reaiised. There is little sense in applying a sophisticated mathematical tool to a process that is poorly understood and characterised.

R E F E R E N C E S

P.I. Barton and C.C. Pantelides. Modeling of Com- bined Discrete/Continuous Processes. AIChEJ., 40:966-979, 1996.

M. Oh and C.C Pantelides. A Modelling and Simu- lation Language for Combined Lumped and Dis- tributed Parameter Systems. Comp. chem. En- gng., 20:611-633, 1996.

V.S. Vassiliadis, R.W.H. Sargent and C.C. Pan- telides. Solution of a Class of Multistage Dy- namic Optimisation Problems. 1. Problems with- out Path Constraints. Ind. Eng. Chem. Res., 33:2111-2122, 1994.

V.S. Vassiliadis, R.W.H. Sargent and C.C. Pan- telides. Solution of a Class of Multistage Dynamic Optimisation Problems. 2. Problems with Path Constraints. Ind. Eng. Chem. Res., 33:2123-2133, 1994.