·"Critique of Chemical Process Control Theory," AIChE J., 19(2), 209 (1973).

The purpose of the following three introductory chapters is:

1. To define what we mean by chemical process control2. To describe the needs and the incentives for controlling a chemi­

cal process3. To analyze the characteristics of a control system and to formu­

late the problems that must be solved during its design4. To provide the rationale for studying the material that follows in

subsequent chapters

To achieve the foregoing objectives, we will use a series of exam­ples taken from the chemical industry. These examples are usuallysimplified and serve only to demonstrate the various qualitative pointsmade.

A. S. Foss"

The needs are intimately related to the problems, and the problems, asusual, wear a sometimes effective camouflage.

IThe Control ofa Chemical Process:Its Characteristics

and AssociatedProblems

Let us examine these needs using various examples.

Suppressing the influence of external disturbancesEnsuring the stability of a chemical processOptimizing the performance of a chemical process

All the requirements listed above dictate the need for continuousmonitoring of the operation of a chemical plant and external interven­tion (control) to guarantee the satisfaction of the operational objectives.This is accomplished through a rational arrangement of equipment(measuring devices, valves, controllers, computers) and human interven­tion (plant designers, plant operators), which together constitute thecontrol system.

There are three general classes of needs that a control system is calledon to satisfy:

A chemical plant is an .ar.ran~ement of pro~~~~;:e:sni~~a~~~~~~:;,heat exchangers, pumps, .dhlstl11atlOntChOelrUffil'nnsa'systemati~ and rational

k ) . tegrated WIt one ano .tan s, etc. , 1D, 11 b' tive is to convert certain raw matenals~:;~:rf~~~~::)t si~~er~esrr~~cproducts using available sources of

energy, ~nt~e most e~onoml~a~~~~i plant must satisfy several require-Dunng Its opera~lOn,a.c e eneral technical, economic,

~e:~o~:r~~~~~io~~s i~e:~~n~:~s~~~et~~ :ver;ctt;~g::: f~~:~:~~~:influ-ences (disturbances). Among such requuemen s

. . 'mary. The safe operation of a chemical process IS a pn1. Safety. f h 11being of the people in the plant and forrequirement or t ewe - . 1 t Th sits continued contribution to the econo:~~e~~;:t~::~; ~he;-the operatingo~re:~~~~~~~::sr~:r:~~h~n allowable limits. For

E~~~if::ef~~~:~:~:nc~~~~~:~:;~::~:t~:~iFSt~ressure below this value. As another example, we.s ou _

~void the development of explosive mixtures dunng the operation of a plant.

I h ld produce the desired2. Production specifications: A pant s ou F mple we mayamounts and quality of the final products. or exa ,

require the production of 2 million pounds of ethylene per day, of99.5%purity. Therefore, a control system is needed to ensure thatthe production level (2 million pounds per day) and the purityspecifications (99.5%ethylene) are satisfied.

3. Environmental regulations: Various federal and state laws mayspecify that the temperatures, concentrations of chemicals, andflow rates of the effluents from a plant be within certain limits.Such regulations exist, for example, on the amounts of S02 that aplant can eject to the atmosphere, and on the quality of waterreturned to a river or a lake.

4. Operationalconstraints: The various types of equipments used ina chemical plant have constraints inherent to their operation. Suchconstraints should be satisfied throughout the operation of a plant.For example, pumps must maintain a certain net positive suctionhead; tanks should not overflow or go dry; distillation columnsshould not be flooded; the temperature in a catalytic reactor shouldnot exceed an upper limit since the catalyst will be destroyed.Control systems are needed to satisfy all these operational con­straints.

5. Economics: The operation of a plant must conform with themarket conditions, that is, the availability of raw materials and thedemand of the final products. Furthermore, it should be as eco­nomical as possible in its utilization of raw materials, energy,capi­tal, and human labor. Thus it is required that the operating condi­tions are controlled at given optimum levels of minimumoperating cost, maximum profit, and so on.

1Incentives for ChemicalProcess Control

3Incentives for Chemical Process ControlChap.

impact of the changing disturbances and keep T and V at the desiredvalues.

In Figure 1.2we see such a control action to keep T = T,when T, orF, changes.A thermocouple measures the temperature T of the liquid inthe tank. Then T is compared with the desired value Ts, yielding adeviation E = T,- T. The value of the deviation E is sent to a controlmechanism which decides what must be done in order for the tempera­ture T to return back to the desired value T; If E > 0, which implies thatT < Ts, the controller opens the steam valve so that more heat can besupplied. On the contrary, the controller closes the steam valve whenE < ° or T > T; It is clear that when T = T, (i.e., E = O), the controllerdoes nothing. This control system, which measures the variable of directimportance (T in this case) after a disturbance had its effect on it, iscalled the feedback control system. The desired value T, is called the setpoint and is supplied externally by the person in charge of production.

A similar configuration can be used if we want to keep the volume V,or equivalently the liquid level h, at its set point h, when F, changes. Inthis case we measure the level of the liquid in the tank and we open orclose the valve that affects the effluent flow rate F, or inlet flow rate F,(see Figure 1.3). It is clear that the control systems shown in Figure 1.3arealso feedback control systems. All feedback systems shown in Figures 1.2and 1.3 act post facto (after the fact), that is, after the effect of thedisturbances has been felt by the process.

Returning to the tank heater example, we realize that we can use adifferent control arrangement to maintain T = T,when T, changes. Mea­sure the temperature of the inlet stream T, and open or close the steamvalve to provide more or less steam. Such a control configuration iscalled feedforward control and is shown in Figure 1.4.We notice that thefeedforward control does not wait until the effect of the disturbances hasbeen felt by the system, but acts appropriately before the external disturb­ance affects the system, anticipating what its effect will be. The charac­teristics of the feedback and feedforward control systems will be studiedin detail in subsequent chapters.

Figure 1.2 Feedback temperature control for a tank heater.

F, T

Tj, Fj = constant

5Incentives tor Chemical ProcessControlChap. 1

Figure 1.1 Stirred tank heater.

Steam

1.1 Suppress the Influenceof ExternalDisturbances

Su ressing the influence of external disturbanc.es on a process i.sthem~~ common objective of a controller in a chemlc~l plant. Such distur­b es which denote the effect that the surroundings (external world)h:~~ o~ a reactor, separator, heat exchanger, compressor, and so on, areusually out of the reach of the human o~erator. Consequently, we needto introduce a control mechanism that will make the p~oper changes onthe process to cancel the negative impa~t that such disturbances mayhave on the desired operation of a chemical plant.

Example 1.1:Controlling the Operation ofa Sti~-!~~,ran~HeaterConsider the tank heater system shown in Figure Ll, ~ liquid en~e~s

the tank with a flow rate F, (fe/min) and a temperature T, ( F), where It~Sheated with steam (having a flow rate Fst lb/min), Let F and T be t .eflow rate and temperature of the stream leaving the tank. The tank ISconsidered to be well stirred, which impli~s t~at. the temperature of theeffluent is equal to the temperature .ofthe liquid In the tank.

The operational objectives of this heater are:1.To keep the effluent temperature T at a desired valu~ T,2. To keep the volume of the liquid in the tank at a desired value Vs

The operation of the heater is disturbed by external factors such. aschanges in the feed flow rate and temperature (Fj and rs. If nothl:gchanged then after attaining T = r, and V = Vs, ~e could leave t ~

t m alone without any supervision and control. It ISclear, though, tha~~~secannot be true since t, and Fj are subject to frequent c~anges.Consequently, some form of control action is needed to alleYlate the

\ Iv I( j

Part IControl ot a Chemical Process: Characteristics and Associated Problems4

Figure 1.6 Alternative responses of unstable systems.

y

Figure 1.5 Response of a stable system.

x

Consider the behavior of the variable x shown in Figure 1.5.Notice thatat time t = to the constant value of x is disturbed by some externalfactors, but that as time progresses the value of x returns to its initialvalue and stays there. If x is a process variable such as temperature,pressure, concentration, or flow rate, we say that the process is stable orself-regulating and needs no external intervention for its stabilization.It is clear that no control mechanism is needed to force x to return toits initial value.

In contrast to the behavior described above, the variable y shown inFigure 1.6 does not return to its initial value after it is disturbed byexternal influences. Processes whose variables follow the pattern indi­cated by y in Figure 1.6 (curves A, B, C) are called unstable processesand require external control for the stabilization of their behavior. Theexplosion of a hydrocarbon fuel with air is such an unstable system.Riding a bicycle is an attempt to stabilize an unstable system and weattain that by pedaling, steering, and leaning our body right or left.

1.2 Ensure the Stability of a Process

The suppresion of the impact that disturbances have on the operatingbehavior of processing units is one of the main reasons for the use ofcontrol in the chemical industry.

7Chap. Incentives for Chemical ProcessControl

Figure 1.4 Feedforward temperature control for stirred tank heater.

IL _

(b)

Figure 1.3 Alternative liquid-level control schemes.

F, ~ constant

+ Set point

Fj h,

T, ~ constant

__ ~ Controller I-- - - -~€

(a)

f I+ Set point

h,

Level measuringdevice

Part IControl of a Chemical process: CharacteristicSand Associated problems

6

:ii~~;eo~~hDyn~~;~response of a CSTR: (a) and (b) indicate the insta­stabilityOftehrmh e steady state, while (c) and (b) demonstrate the

e ot er two.

(d)(c)

oo

~ ----------------

III

-'1--- --- - -- _I

~ -t--------------

~ -----------------

(b)(a)

oTime to

I-i--------------

{uently to increased rates of reaction. Increased rates of reaction produceI:~~e; a:o:nts of heat released by the exothermic reaction, which in turn. 1'. 0 ig er temperatures, and so on. Therefore we see that an increasem i takes the ~eactor temperature away from steady state P2 and that the:e;:je~~tu;e 7111.eventually reach the value of steady state PJ (Figure~ould tl~1 aifi If T; were to decrease, the temperature of the reactorwere 0 a et? rom P2 and end up at PI (Figure 1.9b).By contrast, if weth pera ~ngat steady state PJ or PI and we perturbed the operation ofst:r~e~7or, ~.WOUldreturn naturally back to point PJ or PI from which it

Se se.e igure 1.9c,d).(Note: The reader should verify this assertion)t dometimes we would like to operate the CSTR at the middle unstabie:t;: ~ state, for the following reasons: (I) the low-temperature steadyande(2)lt~au~:shvery low yields because the temperature TI is very low,

c. e . ~g -temperature steady state P J may be very high causingunsare conditions de t . h '. th ' s roying t e catalyst for a catalytic reactor, degrad-mg e product B, and so on.In such cases we need a t II' ... con ro er that will ensure the stability of the

~p:~~~~~~%~~~m~ddlesteady ~t.ate.(Question: The reader should suggestt bl anism to stabilize the operation of the reactor at the

uns a e steady state P Thineed for st bili . 2· IS example demonstrates very vividly the. th a I izmg the operation of a system using some type of control}~ometPhredsen~edOfe~ternal disturbances that tend to take the system away

e esire point.)

9Incentives for Chemical Process ControlChap. 1

Figure1.8 The three steady states of a CSTR.

Temperature

Heat/time

Example 1.2:Controlling the Operation 0/ an Unstable ReactorConsider a continuous stirred tank reactor (CSTR) in which an irre­

versible exothermic raction A ....B takes place. The heat of reaction isremoved by a coolant medium that flows through a jacket around thereactor (Figure 1.7). As is known from the analysis of a CSTR system, thecurve that describes the amount of heat released by the exothermic reac­tion is a sigmoidal function of the temperature T in the reactor (curve Ain Figure 1.8).On the other hand, the heat removed by the coolant is alinear function of the temperature T (line B in Figure 1.8).Consequently,when the CSTR is at steady state (i.e., nothing is changing), the heatproduced by the reaction should be equal to the heat removed by thecoolant. This requirement yields the steady states PI. P2, and PJ at theintersection of curves A and B of Figure 1.8. Steady states P I and P J arecalled stable, whereas P2 is unstable. To understand the concept of stabil­ity, let us consider steady state P2•

Assume that we are able to start the reactor at the temperature T2 andthe concentration CA2 that corresponds to this temperature. Consider thatthe temperature of the feed T; increases. This will cause an increase in thetemperature of the reacting mixture, say Ts: At T2 the heat released by thereaction (Q'z) is more than the heat removed by the coolant, Q2 (seeFigure 1.8),thus leading to higher temperatures in the reactor and conse-

Figure1.7 CSTRwith coolingjacket.

Coolant

Part IControl of a Chemical Process: Characteristics and Associated Problems8

This example indicates that the control of the steam flow rate is notused to e~sure the stability of the reactor or to eliminate the effect ofexternal disturbances on the reactor, but to optimize its economic per­formance.

Figure 1.11 Optimal profile of the steam flow rate for the batch reactorof Example 1.3.

Q Steam now rate

ti?Ie,.will affect the temperature in the batch reactor and the temperaturewill, I,ntU,rn,affect the rates of the desired and undesired reactions. Theques~lO.nIShow we sho~ld vary Q(t) with time so that the profit <1> ismaximized. Let us examme some special policies with respect to Q(t).

1. If <;!(t) is given the largest possible value for the entire reactionpenod te, the te~perature of the reacting mixture will take thel~rgest.value that ISpossible. Initially, when cA is large, wewill havehigh Yieldsof B but we will also pay more for the steam. As time~oes on and the concentration of B increases, the yield of C alsoincreases. Consequently, toward the end of the reaction period thetemperature must decrease, necessitating a decrease in the steamflow rate.

2. If the s,teamfl~w rate.is kept at its lowest value [i.e., Q(t) = 0] forthe entire reaction penod ts, wewill have no steam cost but wewillalso have no production of B. '

'!Ie see clearly f~omthese two e~treme cases that Q(t) will vary betweenIts lowest an~ ~Ighest values dunng the reaction period ts- How it shouldvar~ t? m~xlmlze the profit is not trivial and requires the solution of theoptirruzatron problem posed above.

In Figure .1.1.1 we see a general tr~~d that the steam flow rate mustfoB.owt~ optimize the profit <1>. Therefore a control system is neededwhlc~ will (lJ compute the ?est steam flow rate for every time during thereaction penod and (2) adjust the valve (inserted in the steam line) sothat the steam flow rate takes its best value [as computed in (1)]. Suchproblems are known as optimal control problems.

11Incentives tor Chemical ProcessControlChap. 1

Figure,1.IO Batch reactor with two consecutive reactions.

+ cost of steam} dt +cost of purchasing A (1.1)

where t R is the period of reaction.The only variable that we can change freely in order to maximize theprofit is the steam flow rate Q. The steam flow rate, which can vary with

r-maximize <1> = Jo {[rev~nuefrom the sales of product Bj-.~-' \ ~~,'" ~.,

Both reactions are assumed to be endothermic with first-order kinetics.The heat required for the reactions is supplied by steam which flowsthrough the jacket around the reactor (Figure 1.10). The desired product isB; C is an undesired waste. The economic objective for the operation ofthe batch reactor is to maximize the profit <1> over a period of time tR: thatis,

Example 1.3: Optimizing the Performance of a Batch ReactorConsider a batch reactor where the following two consecutive reac­

tions take place:

Safety and the satisfaction of production specifications are the twoprincipal operational objectives for a chemical plant. Once these areachieved, the next goal is how to make the operation of the plant moreprofitable. Given the fact that the conditions which affect the operationof the plant do not remain the same, it is clear that we would like to beable to change the operation of the plant (flow rates, pressures, concen­trations, temperatures) in such a way that an economic objective(profit) is always maximized. This task is undertaken by the automaticcontrollers of the plant and its human operators.

Let us now see an example from the chemical processing industrywhere the controller is used to optimize the economic performance of asingle unit.

1.3 Optimize the Performanceof a ChemicalProcess

Part IControl ot a Chemical Process Characteristics and Associated Problems10