Rocio Solar-González¹

¹ Chemical Engineer. M.Sc., in Chemical Engineering, Universidad Autonóma Metropolitana, Mexico. Ph.D., in Chemical Engineering, Universidad Autónoma Metropolitana, Mexico. Member, Division of Graduate Studies, Universidad del Istmo, Mexico. olgr@sandunga.unistmo.edu.mx

ABSTRACT

This paper explores a parallel control structure for improving the behaviour of a chemical plant having recycling and multiple feed streams; a ternary system is taken as an example,having an A+B→C second-order irreversible reaction. Material recycling dynamics can induce the so-called snowball effect in the presence of disturbance in the feed stream. The snowball effect can be prevented by distributing load through the parallel control scheme. A control structure was thus proposed where product composition was regulated by means of simultaneous feedback manipulation of final column vapour boilup rate and reactor temperature. An extension was made for one reactor, one distillation column and recycle stream configuration. Nonlinear simulations showed that effective composition control could be obtained with moderate vapour boilup control efforts.

Keywords: parallel, control, ternary system, column, reactor.

Received: may 21th 2009

Accepted: jun 11th 2010

Introduction

A chemical plant includes independent operating units such as reactors, distillation columns, heat exchangers and so on. There is a distinct difference between these units' steady state and dynamic behaviour when they are used in an interconnected system,especially when recycling is used in a particular chemical plant. Although recycling reduces costs, it has some disadvantages from the control point of view. Luyben (1994) has shown that changes in concentration and feed flow rate may result in the snowball phenomenon for processes involving recycling. The snowball effect implies that a slight change in inlet feed flow rate causes a significant change in recycling flow rate. This effect may act as positive feedback and cause the whole system to become unstable. The balanced control idea was thus suggested by Wu and Yu(2003) and Hung et al., (2006) for preventing the snowball effect. Balanced control means distributing the effect of load throughout different parts of the process; this improves control structure ability regarding load rejection and rejecting disturbance exceeding larger magnitude thresholds (Alizadeh et al., 2006).

The process considered by Tyreus and Luyben (1993) having an A+B→C second-order reaction has thus been taken as an example. Two reactants A and B were fed, separately, to a isothermally-operated continuous stirred-tank reactor. Reaction rate was expressed as:

where ^R_C was the reaction rate of product C , k was the specific reaction rate,z_A and z _B were the mole fractions for reactants A and B in the reactor and V _R was reactor holdup. As pointed out by Tyreus and Luyben (1993), the "moles" were not conserved in this system because the reaction was not equimolar.

Reactor effluent was assumed to be a saturated liquid containing a ternary mixture of A , B and C , because some A and B remained unreacted. A was the light component in the ternary mixture, B was the heavy component and product C was an intermediate boiler. This produced a process flowsheet having two columns and two recycle streams, as sketched in Figure 1 . Component volatilities were assumed to be α_A=4,α_B=1 and α_C=2. It was assumed that component B (the heaviest) was recycled fromthe bottom of the first column (in stream B₁ ) back to the reactor. Component A (the lightest) was recycled from the top of the second column (in stream D₂ ) back to the reactor.Figure 1 gives the nomenclature used in this work.

The overall reaction rate depended on the product of the two concentrations ^z ₁ and ^z₂ ; if one composition became decreased, then the other had to become increased to maintain the same productivity. Such interplay between the two compositions could produce large changes in the required recycle flow rates.

This work thus proposes that extensive variables (e.g. flowrates) be used to balance work evenly amongst process units as process inlet streams change. This is similar to Georgakis's approach (1986) where intensive variables were kept constant in different operating conditions.

The control work was distributed by looking for suitable controlled output and manipulated input one-to-one pairing. On the other hand, reactor temperature is kept constant by manipulating the jacket coolant flow rate in ternary systems having two recycle streams control schemes reported in the literature (see, for instance,Cheng and Yu, (2003). However, reactor temperature is an intensive variable which may be varied (via feedback manipulations) to induce significant composition changes having relatively small steady-state control efforts. Reactor temperature can be considered as being an additional degree of freedom which can be exploited (within a safe operating range) to enhance controlled process performance. Luyben (1994) has stated that the reactor does not need to be kept at a constant temperature.

An interesting problem concerns studying how to manipulate reactor temperature to alleviate the feedback control structures' control effort based just on extensive variables. This work focuses on this problem by exploring an alternative control structure for controlling ternary systems having two recycle streams. A parallel control structure has been used for distributing control effort between the reactor and the second distillation column. The idea was to simultaneously manipulate reactor temperature and vapour boilup rate in the second distillation column to regulate process product composition. Input stream composition disturbance thus became reduced by means of relatively small changes in reactor temperature.

Rigorous nonlinear simulations have shown that effective composition control can be obtained with moderate vapour boilup control efforts in the event of composition disturbances in feed composition streams.

Ternary system control

Control for a system having a reactor, two distillation columns and two recycle streams was studied. One of the most important problems was to select a control structure (i.e. input/output pairing) to guarantee satisfactory stabilisation (e.g. smooth setpoint tracking) and regulation properties (e.g. rejecting disturbances having "small" control effort). As mentioned in the introduction, control structures reported so far have been based on a one-to-one pairing scheme. That is, manipulated input is used for regulating a regulated output. This work has departed from the non-redundant control structure proposed by Cheng and Yu (2003), where reactor holdup ( V_R ) is assumed to be constant, to propose a redundant (i.e. rectangular) control structure to improve control performance. Such control structure had the following features:

-The production rate was set by the fresh feed of A (F_0A );

-Reactor holdup was kept constant by controlling reactor effluent flow rate ( F );

-The recycle ratio of the first column (B₁/F_OA ) was fixed;

-The bottom composition of the first column (^X_B1,B ) was controlled by changing boilup ratio (V₁/B₁ ) in the first distillation column;

-The bottom level of the first column was controlled by manipulating the fresh feed of reactant B ( ^F_OB);

-The reflux ratio of the first column (R₁/D₁ ) was fixed;

-Product composition (X_B2C ) was held by manipulating the boilup ratio of the second column (V₂/B₂ ); and

-The second column's reflux ratio (R₂/D₂ ) was fixed.

It should be noted that only extensive variables (e.g. flowrates) were used as manipulated inputs. In particular, reactor temperature was kept constant. The rationale behind Cheng and Yu's control structure was to obtain a balanced control effort throughout the process flowsheet while satisfying the product quality (X_B2C ) requirement. The plant was designed in line with that suggested by Elliot and Luyben (1996), where constant density and molecular weight, equimolar overflow, theoretical trays, total condensers and partial reboilers were assumed. Tray holdups and liquid hydraulic time constants were calculated using the Francis weir formula, assuming a 1-ⁱⁿ weir height. All feed streams were assumed to be saturated liquid. The reflux drums and column bases were sized to provide 5^min of holdup resulting from the respective steady-state flow rates into each. The values obtained by using this design were used as nominal values and have been reported for Tyreus and Luyben (1993). Measurement delays for flow, temperature and composition were taken as being ^0.1.1 and 6^min, respectively.

The control loop consisted of a PI compensator based on stepresponse(first-order plus time-delay) models which were then tuned following the IMC tuning guidelines reported by Skogestad (2003), prescribed closed-loop time constants being taken as max{0.75τ_o ,θ }, where ^τ₀ was the open-loop time-constant and ^θ was loop delay. It was noticed that although product compo-sition became regulated, the response had an oscillatory pattern which could have been due to the fact that regulating x_B2;Cwas only based on second distillation column vapour boilup rate manipulations. The product quality control loop was thus unable to provide a quick response to fresh feed disturbances, thereby affecting the whole process with subsequent work imbalance in different pieces of process equipment. Introducing a sort of feedforward compensation was a possible way of remedying this situation, to provide advanced control action in the event of fresh feed disturbances. A second alternative was to re-balance the processing work in the different pieces of equipment to reduce the effects of fresh feed disturbance in product quality dynamics. The next section shows that control can be improved by incorporating the reactor temperature as a secondary manipulated variable to regulate product composition in collaboration with the boilup ratio of the second column,V₂/B₂ .

Parallel control methodology

Designing a feedback controller for the simultaneous manipulation of reactor temperature T_R and vapour boilup rate V₂ led to formulating a non-square ^2x1 input/output model as follows:

y(s)= G(s)u(s) (1)

where G(s) denoted the process plant model, y(s) the measurements and u(s) the manipulated input. Thus:

Where y(s)=Δx_B2,_C(s) was the regulated output,u₁(s)=ΔV₂(s) and u₂(s)=ΔT_R were the manipulated input. A strategy for additional control 2 u had to be specified in this non-square case. One alternative was t use a sort of regularisation technique to square the rectangular control system. In line with Monroy et al.'s ideas(2004) it was thus proposed to split the input/output model to introduce parameter β, as follows:

y₁(s)=βG₁(s)u₁(s)

Where y(s)=y₁(s)+y₂(s), and y₁=βy(s) and y₂=(1-β)y(s) were virtual outputs, and βЄ[0,1]was the segmentation.

If the control objective was y(s)→y_sp(s)y_sp(s) was a setpoint signal, then the control objective of the segmented control system (2) was thus:

y₁(s)→y_sp,1(s) y y₂(s)→y_sp,2(s) (3)

Hence, if both control objectives given by Eq. (3) were achieved, then y(s) → y_sp(s) was guaranteed.

It should be noted that since Eq. (2) was an uncoupled control system,and the transfer functions G₁(s) and G₂(s) were stable, then the control objective could be achieved with two decentralised PI compensators (also having been tuned as in the non-redundant control configuration).

It should also be noted that when β = 0 , the reactor temperature was maintained at its nominal value T_R^- and all dynamical and stationary control efforts were executed by the second column distillation controller. This corresponded to the conventional control scheme described in the preceding section. When 0<β<1 both controllers made a non-trivial contribution to regulating bottom flow composition ^XB₂,c. The proposed parallel control scheme thus had the structures of a balanced controller for 0<β<1. As β was increased, more processing work was executed by the reactor, leaving less control effort (i.e. less vapour usage) in the second distillation column.

As in the square case, pertinent values for the parallel controller design were obtained from input/output step response near the nominal operating point and assuming stable first-order models. An 8%feed fresh composition disturbance was assumed where fresh feed stream composition was F_OA. Referring to Figure 2, the conventional control scheme (i.e. β= 0 ) showed slight oscillation in the recycle streams. Composition of product ^C in the bottom of column 2 first converged to 0.9803 and then to 0.9897 , reaching the set point after 30h . It should be noted that the composition of component A in the reactor decreased from 0.1299 to nearly 0.1225 after 20h an component B composition rose from 0.2538 to 0.2620 after 20h.

When the product composition of component C was controlled by means of the reactor temperature (i.e. β= 1), then the following observations could be made. Component A reactor composition slowly converged to a 0.116 value and component B rose from 0.2538 to 0.2675 in 80h . It should be noted that all B₁and D₂ flows had a smooth dynamic pattern. However, the reactor temperature moved from 150F to 148.5F during the first 5h and then began to increase smoothly to a value of 152.5F in 80h . Component C composition in the second column's bottom product presented an overshoot during the first 2h and then converged to the set point through an undershoot to reach a set point around 100h .

This showed that using the reactor temperature as a manipulated variable for controlling component C composition in the bottom product of column 2 provided a slow but stable control pattern for the whole plant. Figure 2 shows that using proposed parallel control with β= 0.5 combined the desired features of the conventional control scheme and the reactor temperature control scheme thereby providing a well-behaved control scheme.

The above simulations have thus shown that a parallel control scheme based on a single habituating parameter β; was able to provide a distributed control effort between reactor operation (via chemical transformations) and second distillation column operation (via physical separations). The larger the value of β ,the greater the reactor's processing work. Once the single control loops have been tuned, then β; is the only parameter which should be tuned to obtain suitable distribution of processing work. Systematic selection of tuning parameter β should be based on additional criteria involving economic and safety considerations.

Extension ternary system with one recycle stream

Ternary systems having two distillation columns and two recycle streams have been investigated thus far. Process configuration resulted from boiling point distribution (i.e. product C was the intermediate key). There are certainly cases where product C may be the lightest or heaviest component. Let us consider again the second-order elementary reaction where the product was both the heavy key and light key. There was only one distillation column in the recycle structure since relative volatility for both reactants was adjacent to each other, as shown in Figure 3.

When the product was the heavy key, light reactants were recycled back to the column from the top of the first (and only) column; a similar situation applied to the case of the light key.

Following a similar procedure to that described in the previous section, departing from the non-redundant control structure proposed by Cheng and Yu (2003), the control structure had the following features:

-The production rate was set by fresh feed flow B(F_OA);

-The reactor holdup was controlled by reactor effluent flow rat (F) ;

-Total recycle flow (D_TOT=F_OB+D) was rationed to F_OB;

-The bottom level of the column was controlled by manipulating product flow rate (B).;

-The column reflux ratio (R / D) was fixed;

-The column's reflux drum level was controlled by manipulating the fresh feed of reactant A(F_OA ) and

-Product composition (X_B,C ), was held by manipulating colum boilup ratio (V / B) .

Closed-loop responses for production-rate increase clearly indicated that the control structure was indeed operable for biased reactant distribution at low conversion. Classical PI compensators tuned with internal model control tuning guidelines were implemented in the loops; Figure 4. shows the performance of a conventional control configuration. It should be noted that if composition z_A or z_B became decreased, then the other had to become increased to maintain the same productivity. Such interplay between both compositions could produce large changes in the required recycle flow rates.

Following the results from a two-column reactor, input/output pairing for control was selected as follows: using vapour boilup rate V to regulate bottom composition X_B1,C and using jacket temperature T_j , to regulate reactor temperature at set point T_SP∈I_T. Figure 4 shows the response for a +20% step change in fresh feed composition. The regulation objective was achieved without excessive changes in reactor temperature.

It should also be noted that, as more processing work was done by the reactor, the response became more sluggish, mainly because of the reactor temperature's indirect effect on bottom flow composition. The. Figure 4 show the values for flow rates D₁and V₁ for different values of β . As expected, as more processing work was done by the reactor, column flow sensitivity to changes in fresh feed became significantly reduced. The simulation results showed that the parallel control scheme was able to automatically distribute the positive impact of processing in the reactor and the separation column.

Conclusions

This paper has considered controlling a ternary system having recycle and multiple feeds. The proposed control scheme was designed by means of parallel control methodologies for systematiccally distributing control effort amongst the different process units. The main disturbances were feed flow rate and composition. The objective was to simultaneously manipulate the vapour boilup rate in the distillation column and the reactor temperature, expecting that processing work become distributed in both pieces of equipment.The performance of these control structures were compared to a control scheme proposed in the literature. The simulation results indicated that the proposed control structure had a faster dynamic response.

Notation

B_i reboiler bottom flow rate in column ⁱ th column

D_i distillate flow rate from ⁱ th column

F_OA fresh feed flow rate for component A

F_OB fresh feed flow rate for component B

F flow rate out of the reactor

K specific reaction rate

Ri reflux flow rate from i th column

T_R reactor temperature

V_i vapour boilup in column ⁱ

V_R reactor holdup in moles

X_B,kj bottom composition in ^k th column (mole fraction of component ^j )

X_D,kj distillate composition in k th column (mole fraction of component ^j )

Z_j reactor composition of component ^j (mole fraction)