Dynamics and Control of Fluidized Catalytic Crackers. 4. The Impact of

Ind. Eng. Chem. Res. 1997, 36, 747-759

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Dynamics and Control of Fluidized Catalytic Crackers. 4. The Impact of Design on Partial Control Arnon Arbel, Irven H. Rinard, and Reuel Shinnar* Department of Chemical Engineering, City College of New York, 138 Street at Convent Avenue, New York, New York 10031

In this paper the impact design has on the control of a fluidized catalytic cracker (FCC) is explored. The available control options depend strongly on the availability of manipulated variables as well as on downstream equipment. Also of importance is the range in which each variable can be manipulated. An important distinction is made between the total number of manipulated variables and the effective degrees of freedom for control, especially of the product specification vector Yp. Control both in complete CO combustion when there is no CO boiler available and in partial combustion when a boiler is present is analyzed. The fast manipulated variables of air flowrate, catalyst circulation rate, feed preheat, and catalyst cooler heat removal rate are all considered. It is shown that the sufficiency of a partial control structure changes when the operating conditions change and that it strongly depends on the control objectives. Also examined is the impact of catalyst activity. 1. Introduction The design of chemical plants is often based on a specific steady-state flow sheet and specific mass and heat balances at one operating point. In addition, the design of the control system is usually done by a separate group once the basic design is finished. However, the ability of the control system to maintain product specifications in the face of disturbances and to respond to changes of these specifications as the need arises strongly depends on the design of the plant. It is therefore important to introduce control-related considerations into the initial design. This is by no means a new idea; the impact of design on control has been the subject of many papers and symposia (see, for instance, Zafiriou, 1994; Perkins, 1992). The focus of this paper is on how the design affects the availability of manipulated variables in the face of the requirements of partial control. Design effects the performance of the plant in several ways: (1) The choice of the equipment and its actual design determines the dynamic behavior (in particular, time scales of response) and the ability of the plant to operate at different throughputs and operating conditions. For example, packed beds have a higher turn-down ratio than do fluidized beds. On the other hand, fluidized beds allow one to maintain constant catalyst activity in the face of rapid deactivation and to change the catalyst activity during operation. (2) The initial design determines the manipulated variables available for control and the range over which they can be manipulated. Adding them is costly so one needs to understand their impact on control during the design phase in order to justify their cost. (3) While measured variables can often be added easily and inexpensively, in many cases, such as in highpressure equipment, provision for proper measurement has to be provided in the initial design. The impact of design on control has been discussed by many investigators. A by-no-means exhaustive list will include Morari et al. (1982), Meadowcroft et al. * Author to whom all correspondence should be addressed. E-mail: [email protected]. Telephone: (212) 650-6679. Fax: (212) 650-6686. S0888-5885(96)00356-9 CCC: $14.00

(1992), Huq and Morari (1995), Balchen and Mumme (1988), Silverstein and Shinnar (1982), and Fisher et al. (1988). Most of this work deals with the situation where the control is square; i.e., there are enough manipulated variables to control all output variables of interest at desired set points. It is our intention to investigate this impact for the situation of partial control, i.e., where the number of output variables exceeds the manipulated variables available for control. In a previous paper by one of the authors (Avidan and Shinnar, 1990) the historical development of the design of the FCC was discussed from a reaction engineering point of view. This paper also introduced control considerations, but in a general and qualitative way. In the current paper the impact of the design modifications to the FCC will be examined quantitatively. The emphasis will be on the impact of the number and type of manipulated variables available. As discussed in Avidan et al. (1990), a significant number of the FCC design modifications introduced over the years have dealt with the introduction of additional manipulated variables such as the ability to manipulate catalyst circulation, control feed temperature, or independently control regenerator temperature using a catalyst cooler. Most of these modifications required the addition of major equipment, such as a furnace for controlling feed temperature or a catalyst cooler which is really another fluid bed equipped with a heat exchanger and a boiler. The only exception is the ability to control catalyst circulation which involves, in principle, only a slide valve but also requires other design modifications. As shown in Avidan and Shinnar (1990), there are other aspects of the design that impact the obtainable product composition. Among these are the design of the reactor, the design of the regenerator, and the availability of a CO boiler. Of these, only the availability of a CO boiler will be discussed here. With present environmental regulations, the lack of a CO boiler requires one to operate the regenerator in full CO combustion. This has been shown by Arbel et al. (1996) to have significant control ramifications. In addition, the effects of changing catalyst activity and combustion promoters, which in an FCC are also manipulated variables (Arbel et al., 1996), will also be examined. © 1997 American Chemical Society

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This paper is part of a series on partial control (Arbel et al., 1995a,b, 1996) and utilizes the results of these previous papers. In particular, the model used for calculations is that of Arbel et al (1995a), and the choice of the control structure is based on Arbel et al. (1996), which explains our approach to the control of complex nonlinear systems, an approach which we termed partial control. While this paper deals only with the control of fluidized-bed crackers, the goal is to present the methodology in a form that is applicable to a wider range of problems. Detailed reviews of different FCC designs and their justification which also describe the roles of the various manipulated variables are given in Avidan (1992) and Avidan et al. (1990) and will not be repeated here. Additional details are contained in the earlier papers of the current series, namely, Arbel et al. (1995a,b, 1996). 2. Goals of Control in FCC Operation, the Concept of Sufficiency It was shown in Arbel et al. (1996) that one cannot design a control system for a complex reactor solely based on the process model even if this model is an accurate one. The choice of the control loops is strongly affected by the goals of the control. The impact of these goals looms large when designing the control system itself, especially in the choice of the manipulated variables and the range over which these can be varied. These goals and their importance change from process to process. One cannot even generalize them for an FCC as they depend upon local conditions as well as upon the capability of the unit. When defining the specifications, there is an interplay between the desirable and the available. This is not true for all processes, as for many the specifications are determined by the market and the capability of competitors. Let us classify the potential goals of the control in a broader way such that they apply to a broader range of processes: (1) Control Yp, the vector of all product specifications and constraints. Constraints are included in Yp for simplicity, as their impact and mathematical description is analogous to specifications. For partial control Yp is always defined not as a single value but as a range for each element:

Ypj,min < Ypj < Ypj,max

(1)

In some processes product specifications are narrow and absolute in the sense that any product that falls outside the range of the conditions of eq 1 is scrapped. For the FCC this is not true, as it is sufficient if eq 1 can be met on the average. The time has passed when any results from an FCC were economically acceptable. However, some of the constraints in the FCC are hard. For example, wet gas production has to be kept below the capacity of the wet gas compressor to prevent tripping. Only a limited subset of Yp will be discussed here, but the results can be easily generalized to the total set applicable to refinery operations. For some processes Yp is fixed. In others there is a great economic advantage to independently change various components of Yp. For the FCC the value of this capability varies greatly from refinery to refinery. (2) Control production rate. The ability to vary the production rate is an important goal in the design of

Figure 1. Block diagram of the partial control scheme: Gcd, frequent/fast control; Gcd, nonfrequent/slow control.

the unit and its control system. The range over which it can be varied depends strongly on the design. (3) Manage disturbances. There are three main disturbance perturbations to the FCC. The composition of the feed varies, often intentionally. When intentionally varied, it can be considered a slowly manipulated variable. While the complete composition of the feed matters, only the coking rate will be considered as a disturbance because it has the strongest impact. The second perturbation is the change in the state of the catalyst. In principle, it is possible to keep the activity constant by addition of fresh and the removal of spent catalyst. However, since the catalyst is also affected by metal deposition from the feed, some short-term changes in activity are unavoidable. The impact of changes in activity on Yp and operation is quite similar to that of coking rate. Therefore, only intentional changes of catalyst activity will be considered here. The third perturbation is the ambient temperature which affects air compressor capacity. This is only important when operating close to the constraint of maximum air capacity and will not be discussed in the paper. The ability of the control system and a unit to take care of the whole range of desired variability in Yp, production rate, feed variations, and other perturbations while maintaining Yp in an acceptable domain is termed by us as sufficiency (Arbel et al., 1996). As this ability is always limited, care has to be taken to prevent excessive perturbations from entering the system and to keep goals within the reachable limits for each unit. For specification-dominated processes with hard limits on Yp, sufficiency is a rigorous term. In other processes such as the FCC, the capabilities of the control impact strongly on the economics and the minimum sufficiency has to be evaluated from this point of view. 3. Manipulated Variables and Degrees of Freedom 3.1. Manipulated Variables. Arbel et al. (1996) gave a definition of a typical partial control structure, which is graphically shown in Figure 1. A primary dynamic control structure Gcd(Ucd,Ycd) is used to keep the system stable and deal with perturbations. A supervisory control scheme Gs(Ucs,Yp,Ycd,sp) measures Yp and sets the set points for Gcd and other manipulated variables Ucs. How to choose the square structure Gcd(Ucd,Ycd) was discussed in Arbel et al. (1996) and will not be repeated. The supervisory structure does not need to be square, as it has no integral control loops. To avoid interactions between the supervisory control and the primary dynamic control, the time scale between adjustments of Ucs and Ycd,sp made by the supervisory

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 749 Table 1. Variables in the FCC manipulated inputs may be used as fast or slow air rate to the regenerator catalyst circulation rate (slow in Model IV) feed temperature catalyst flow through cooler steam to stripper pressure feed rate

can only be used as slow catalyst activity catalyst properties catalyst additives feed composition

outputs riser top temperature regenerator temperature stack gas temperature temperature rise in the regenerator excess oxygen conversion gasoline yield wet gas yield heavy fuel oil yield light fuel oil yield and properties dry gas yield (C2-) C3-C4 composition olefins octane NOx SO2 CO emission

control has to be much larger than the time scale of response of Gcd (Ucd,Ycd). Therefore, the manipulated variables in Ucs are called slow control variables though this does not reflect on their speed of response. For example, feed temperature or feed rate are often used in the vector Ucs but can just as well be chosen for Ucd. However, some variables such as catalyst activity, catalyst type or feed quality, while important, cannot be chosen for Ucd since these can only be changed relatively slowly. There is another constraint on the use of a variable in Ucd instead of Ucs. The refinery manager may want to keep control over certain decisions such as feed rate. As Ucd is in the hands of the operator, such managerial decision variables should not be included in it. Table 1 gives a list of manipulated inputs and also discusses their possible use for Ucd and Ucs. It also lists those which are of primary concern in this paper, namely, those which are strong functions of the design. These are air rate, catalyst circulation rate, feed temperature, availability of a catalyst cooler, and the existence of a CO boiler. In the design phase decisions have to be made whether to introduce a CO boiler, a catalyst cooler, both, or neither; how much and how rapidly Fcat and Fair can be varied; and whether to provide a preheater to control feed temperature. If catalyst properties are to be used for control, a system for easy and frequent removal and addition of catalyst must be available. 3.2. Effective Degrees of Freedom. One important question in evaluating the sufficiency of a design for meeting a complex specification Yp is to determine the unit’s degrees of freedom for control. This is normally defined as the number of manipulated variables available. Those for the FCC are listed in Table 1. In an FCC, as in many other processes, there are two basic types of manipulated inputs: those that are manipulated mechanically on the unit itself (e.g., valve positions) and those that are related to feed properties and catalyst properties. Depending upon the circumstances, the latter can be either perturbations or intentionally manipulated inputs. For design only the first type is considered. Complicating the problem is the fact that some potential manipulated variables have no real impact on Yp. Sometimes it is clear that a variable should be kept at its limit. For example, in the majority of FCC’s, the stripper should be run at maximum efficiency; i.e., the steam flowrate is set to its upper limit. Therefore, it is not useful for controlling

Yp. In the following discussion we will consider four manipulated variables, namely, Fair, Fcat, Fcool, and Tfeed. Also, some designs might have additional manipulated inputs available, such as split feed to the reactor or product recycle. Split feed allows one to introduce feed at various points along the riser reactor; introducing feeds of different compositions at different points allows some additional control of Yp. For the sake of simplicity, they will not be discussed, but the approach demonstrated here applies to them as well. Next is the question of what are the dominant variables in the unit itself that impact Yp and unit operation (for an explanation of dominance, see Arbel et al., 1996). We call this number the effective or useful degrees of freedom for control. If the number of manipulated variables that can be used to control these dominant variables is equal or larger than the number of dominant variables, we have for practical purposes exact control of the unit itself. This situation has been discussed, for example, by Meadowcroft et al. (1992) and Morari et al. (1982) but is not the concern of this paper. Exact control of the unit does not mean we have exact control of Yp. As Yp has a larger dimension than the number of dominant variables, we have partial control of Yp despite having exact control of all the dominant variables in the unit. However, very often (and in most FCC units) there are fewer manipulated variables than the dominant variables which we wish to control. We therefore have not only partial control of Yp but also partial control of the unit itself. It should be pointed out that the number of dominant variables is not equal to the number of state variables. Not all state variables are dominant, and the definition of a state variable also depends on how the model is defined. In our model all fast processes are described by quasi-steady-state relations and thus do not enter the equations as state variables. If, for example, the riser is dynamically modeled as a series of stirred tanks, Tris is a state variable (temperature of the last tank), whereas in our case it is an output, but it is dominant, as it represents reactor temperature. This problem is not limited to the FCC but is a central problem in the design of any nonlinear complex system. Let us illustrate it by a simple example. Consider a liquid-phase stirred-tank reactor with a homogeneous catalyst and a complex reaction rate model (ri ) Kije-E/RTCj). Suppose there are 10 components that are either products, reactants, or inerts in addition to the catalyst. This system has 12 state variables: temperature, the 10 component compositions Cj, and the catalyst concentration. We may have up to 10 specifications on Yp. However, we can only control three variables independently: residence time (through either feed rate or liquid level), reactor temperature, and catalyst concentration. We might have several ways to control reactor temperature (feed temperature, cooling rate, residence time, catalyst activity, etc.), but this does not change the effective degrees of freedom. Even though we have many more output variables than manipulated variables, adding more manipulated variables may be useful for constraint management but does not add additional degrees of freedom for control. If we put two reactors in series, each with separate temperature controls, we get only 1 more degree of freedom through control of the temperature of the second reactor but the number of state variables doubles. Adding a separate catalyst addition to the second


reactor gives another independent degree of control freedom. Independent control of the liquid levels in the two tanks and hence their residence times provides another effective degree of freedom. Now let us return to our prime example, the FCC. We noted that we want to concentrate on four manipulated variables in the unit: Fair, Fcat, Tfeed, and Fcool (flowrate through the catalyst cooler). We neglect three other potential inputs: pressure and catalyst holdup, each of which has only a small impact over the range that can be varied, and stripper steam rate, which is normally kept at the rate needed to get efficient stripping. These are somewhat arbitrary decisions but are typical of what one faces in dealing with complex systems. One has to justify these based on the characteristics of the specific system being studied. From the four manipulated variables, only two can be fixed in most designs in a feed forward way: Fair and Tfeed. Fcat and Fcool are determined by a feedback control loop controlling slide valves and in most units cannot be measured or adjusted independently. They can only be adjusted by a feedback control circuit measuring Tris for Fcat and Trgn for Fcool. [In theory, any other variable could be substituted as discussed by Arbel et al. (1996).] Now, are there more than four dominant variables on the unit itself that one would want to adjust? Let us look at the important or dominant variables related to the unit itself in our model which are Trgn, Tris, Tmix, Crgc, Cspent, catalyst holdup (or cat to oil ratio in the riser), and gas residence time. We neglect Twall in the regenerator, the impact of which is small, and in our specific design gas residence time, which in most reactors has a strong impact independent of catalyst holdup (or contact time, see Avidan, 1992). The impact of gas residence time in an FCC is also quite large, but, within the range of change that is available in a given design, the impact is negligible. If it would be significant, we would have to add feed rate as an independent fifth control variable. This leaves us with five important variables. One can show from the model (or from simple considerations based on heat and mass balances and laboratory kinetic experiments) that only four of these variables are independent, such that adding more manipulated variables would not increase our effective degrees of freedom. Thus, adding a preheater for air would change the constraints on the heat balance but not add another effective degree of freedom. There are important additional control capabilities. One results from the fact that in a refinery the composition of the feed to the FCC can be adjusted. The second results from the fact that the design of the fluid bed reactor allows independent, albeit slow, control of catalyst activity and composition. This is a special advantage of fluid bed reactors. Strangely enough it is often underutilized or neglected in modern control schemes for FCC’s. There is one important aspect of the design that should be mentioned briefly. In any process that has multiple steady states one has to ask the question, can we introduce a control system or design modification that eliminates the multiplicity problem? In that case we would not have to worry about nonlinear stability due to perturbations. This was discussed in more detail in a previous paper (Arbel et al., 1995b). The only way to do this is to design the unit to be nonadiabatic with large additions and removal of heat. While this is technically feasible for the FCC, it is not economically sensible since it is possible with good control to operate

Figure 2. Practical degrees of freedom in the reactor.

an FCC adiabatically. For other reactors which may be more difficult to control, this problem needs to be evaluated during the design. Let us now discuss the impact of these control variables on the performance of the FCC starting with the reactor (see Figure 2). For a fixed feed the only variables that affect Yp in the reactor are catalyst flowrate Fcat (which is normalized to feed rate), Tmix at the bottom of the riser, and the state of the catalyst. Tmix is a unique function of regeneration temperature Trgn and feed temperature and thermal properties. For fixed catalyst properties the catalyst state is a function of Crgc only. Pressure can be adjusted in all units but has a small effect (higher pressures being detrimental) and will not be included in this discussion. Also excluded are other options such as steam or LPG addition at the bottom of the riser. In that sense we have only four effective degrees of freedom for control. The reader might wonder why we did not include feed rate which controls residence time. In most cases one tries to avoid the use of feed rate as a manipulated variable to control Yp. One prefers to leave this control item for the overall control of the plant. Further, in the FCC the impact of manipulating the feed rate on Yp is rather small because of a unique property of the riser. Within the range that feed rate can be manipulated, feed rate has only a very small impact on Yp when keeping all other variables constant. This is due to the rapid decline of activity as the catalyst cokes. Thus, decreasing the feed rate by 30% while keeping all other inlet variables constant will change conversion by less than 1.5%. Feed rate is only used as a manipulated variable to meet constraints on air rate or the wet gas compressor, factors which are outside the present discussion. In our nomenclature Fcat is normalized to feed rate, and we assume feed rate is reasonably close to its design value. For fixed feed and catalyst properties the behavior of the reactor is totally determined by defining Fcat, Tmix, and Crgc. We normally control the reactor by setting Tris, Trgn, and Tfeed. Fcat is determined by the heat balance. The heat balance itself is also determined by the heats of reaction and therefore the extent of the reactions. Therefore, Fcat also depends on activity and Crgc. While in some units one can, in principle set all four variables (Tris, Trgn, Tfeed, Crgc) independently, there are only three dominant variables in the reactor itself (Tmix, Fcat, Crgc). In evaluating the impact of design on control, it is important to understand that adding

Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 751

Figure 4. Impact of increase in coking rate on Trgn in complete and partial combustion when using the structure [Fair, Fcat, Tris, Trgn]. Complete combustion indicated by two points of O2,sg. Tris ) 100 °F; Tfeed ) 400 °F.

Figure 3. Practical degrees of freedom in the regenerator.

additional manipulated variables does not necessarily increase the effective degrees of freedom for adjusting Yp. There is a substantial difference between the three variables Tmix, Fcat, and Crgc. Both Crgc and Fcat affect all reactions in an identical manner. The only item relating to the reactor itself that appears in the individual terms is the temperature in the activation energy E/RT term. In an isothermal reactor changing Fcat and Crgc will result in a single trajectory in component space. The values of Fcat and Crgc will determine how long along the trajectory the reaction proceeds. Changing reactor the temperature will change the position of the trajectory in component space. Therefore, on a range of reactor temperatures a surface becomes available. The FCC riser is, however, not isothermal. Due to the endothermicity of the reactions, the top temperature is lower than Tmix. The difference depends on Fcat and on the extents of reaction. This introduces a different temperature profile for each combination of Fcat and Crgc and a slightly different trajectory. Therefore, theoretically one should be able to access a volume in component space. This clearly indicates the need to use steady-state catalyst properties as a control variable if we have to control Yp more accurately. Modern catalyst technology gives some freedom in changing the relative magnitudes of individual rates of reaction; considerable research has been undertaken to increase this potential. Alternatively, one can control feed composition, but only within limits. For many processes it is the latter which is critical. Let us now look at the regenerator (Figure 3). The design itself has significant impact on temperature uniformity, time scale of response, bypass of catalyst or air, etc. Their impact is primarily on Crgc and ∆T across the cyclone; Trgn is much less sensitive. The only variables that can be manipulated are air rate, pressure, catalyst holdup, and catalyst circulation through the cooler. Again let us eliminate pressure, since it can be rapidly adjusted but has only a small impact over the range it can be adjusted. We will also not concern ourselves with catalyst holdup. If it is sufficient, it will have only a small impact on Trgn or Crgc. It is an important control variable in Ucs in older units with no slide valves, as it allows control of Fcat by changing the pressure balance. So, we are left with two effective degrees of freedom, namely, air rate and catalyst flow through the cooler. The CO boiler does not supply a

manipulated variable but affects the operation, as without it one has to use air rate to control the excess oxygen to ensure the unit stays in total CO combustion. The regenerator has two main outputs that affect the reactor, Trgn and Crgc. However, without a catalyst cooler one can only control one of the two independently. Furthermore, in partial combustion without a catalyst cooler, one can control Trgn by air rate (Figure 4). Crgc will be determined by the interaction with the reactor. This is a crucial feature of partial combustion. As will be shown later, control of Trgn allows stable operation of the unit over a wide range of feedstocks and coking rates since Crgc adjusts to keep the unit heat balanced. In partial combustion it is important to control Trgn, as it will not only impact directly on Tmix but also control the CO2/CO ratio which is important for the heat balance. To control both Trgn and Crgc, one needs to operate the regenerator in partial combustion with a catalyst cooler. In complete combustion Crgc is negligible and Trgn is not controllable (Figure 4), a severe problem as Trgn impacts on the reactor and is also the critical parameter determining the rate of catalyst deactivation. Air rate has almost no impact on Trgn as long as it is sufficient to provide the minimum excess oxygen. The only way to control Trgn independently of the reactor is by a catalyst cooler. With a cooler Trgn can be controlled over a wide range (1250-1430 °F). Crgc cannot be independently controlled, but by maintaining a reasonable value of excess oxygen, it can get low enough that it is practically zero. With present FCC catalysts it is preferable to keep Crgc low, but adjusting it independently has limited value. We can get the effect of a higher Crgc by lowering catalyst activity. This is not true for catalytic reactors in general. For some catalysts a high value of Crgc can lead to higher selectively. The fact that Crgc is always low in complete CO combustion has a severe penalty for control despite the fact that this is very good for the reactor. In the absence of a catalyst cooler, the unit loses its resiliency and inherent ability to adjust to different coking levels in the feed. In partial combustion where Trgn is controlled, Crgc adjusts itself by the heat balance to keep coke generation in the reactor constant (provided the base activity of the catalyst is in the right range). One can therefore deal with very highly coking feeds at the expense of conversion. In complete combustion this ability is lost, and the main way to stay heat balanced is by removing heat via a catalyst cooler. Without a catalyst cooler a unit without a CO boiler cannot handle highly coking feeds. The main advantage of having both a CO boiler and a catalyst cooler in partial combustion is that air rate is reduced for the same conversion without them. In this paper we are interested in the ability to keep Yp


within bounds. We are not dealing with cost minimization. In existing units one often is concerned in maximizing production rates or dealing with constraints on the available manipulated variables. This is, for example, the special goal of DMC controllers (Cutler and Ramaker, 1980). For design one would want to design the unit to meet the specs and the expected variations in feedstock quality and range. To summarize, we have two groups of manipulated variables: one group includes feedstock properties and catalyst properties, both of which can only be used in Ucs, and the second group is variables that directly affect unit operations such as air rate, catalyst circulation rate, feed temperature, catalyst coolers, feed rate, and air temperature, all of which can be used in Ucd or Ucs. 4. Criteria for Performance Evaluation We gave in the beginning a definition of sufficiency which strongly depends on specifications and demands put on the process by the market. For our purpose here we will evaluate the performance of different designs by two separate criteria: (1) the ability of the units to handle large changes in coking rate including addition of feeds with Conradsen carbon or noncatalytic coke, and (2) the ability of the unit to vary independently different elements of Yp. 4.1. Partial Control of the Unit Itself. Minimum Requirements. It was shown in the previous section that, to have complete control of the unit itself, four loops are needed. A number of modern FCC’s have this capability, but it is still partial control in the sense that there are more specifications on Yp than there are manipulated variables. However, a large number of units do not have catalyst coolers, and some old units have very limited independent control of catalyst circulation rate. In the 1960s when one of the authors started his experience (25 years after the first FCC began operation), very few units had feed preheaters. It is therefore of interest to check what is the minimum number of control loops that allows one to stabilize the system from perturbations in feed and catalyst properties and to determine what is gained in the ability to control Yp by adding more loops. This is the focus of the next section. While again the discussions are specific to the FCC, the methodology and approach should be applicable to many other systems. As controller designs for complex nonlinear systems require some minimum information about the properties of the system, we foresee little possiblity of a generalized algorithmic formulation but rather a systematic design approach which follows the steps outlined in each section of this paper (not necessarily in the same order). It should be of general interest that an FCC, a very complex nonlinear system with multiple states, inputs, and multiplicities, can be controlled and stabilized quite reasonably by a single loop if that loop is properly chosen. However, the ability to control Yp will be very limited. We could determine only one loop that does this reasonably well. The loop [Fair - Trgn]. The reason for this is that stability of an adiabatic reactor is determined by the heat balance, which, in turn, is determined by the combustion in the regenerator. The ability to prevent the loss of the hot stable steady state and stabilize the unit should this stable steady state become unstable depends on several conditions. These are that there is a CO boiler (or no constraint on CO emission),

that the catalyst is active enough, and that the other fixed inputs are designed to be in the proper range for the operation of the unit. Another crucial condition is a property of the FCC cracking catalysts currently in use, namely, that coking activity is a function of Creg. Not all catalysts have this property, but that one can design a complex system such that it is controllable with a single loop or very few loops has wide implications for control of complex nonlinear systems. While it is easy to understand why Fair is such an important variable, why is the choice of Trgn as the manipulated variable crucial? First of all, in a system with three steady states for a given Fair, fixing Fair is not enough. We need a measured variable to determine the state of the system. Several measured variables could achieve this. There is, however, another crucial problem related to model information and properties. If we want to operate at the upper stable steady state, we need to meet three conditions: (1) We have to be able to guess with reasonable model information what range of values of that manipulated variable leads to a stable upper steady state. (2) Once we choose the set point for this variable, the reactor should have a reasonable chance to stay at that upper stable state for a wide range of input perturbations. (3) The measured variable should have a reasonable steady-state gain with respect to the manipulated variable. No other single variable using Fair as the manipulated variable and no other loop meets these three criteria (see Arbel et al., 1995b, 1996). For multiple loops, the same problems apply. In fact, they become much more difficult as was discussed in the previous paper (Arbel et al., 1996). It was shown that the problems of crashing and instabilities in the FCC due to feedstock perturbations were mainly due to the wrong choice of measured variables. In what follows, the specific loops underlying our analysis will be specified, even if doing so is, at times, redundant. Although for steady-state purposes it is only necessary to specify the inputs and measured outputs, we will quote the conventional pairings for convenience. In the next section the impact of adding loops is discussed in a quantitative way, with the focus on the ability to handle a wide range of feedstocks and to control elements of Yp independently. 4.2. Control against Changes in Coking Rate. 4.2.1. Fair Only. Let us start with the simplest case, that of one manipulated variable. For this the obvious choice is the most dominant of the inputs, namely, Fair. In some sense this is not a realistic case, as all units have to have control of the feed rate, which at constant catalyst flow allows control of cat/oil. However, in the past many units operating in partial combustion did so with this single loop. Figure 5 shows Tris and conversion for this case in partial combustion, with Trgn chosen as the measured variable. Controlling Trgn with Fair does a reasonable job of control over a wide range of coking rates provided the value of Fcat is chosen properly. The unit remains stable, and Tris changes only moderately and can be kept in line by changing Trgn. In partial combustion Trgn can be varied from 1150 to 1270 °F and Tris from 900 to 1015 °F, about the same range. Conversion drops for higher coking rates and becomes even lower if Trgn is reduced to keep Tris below the permitted maximum value, but this also allows some control of conversion within the


Figure 5. Partial combustion: handling of coke by a single control loop [Fair - Trgn]. Cat/oil ) 9.2; Tfeed ) 400 °F; A ) 1.

limits on the temperatures. For very low coking rates the upper steady state becomes linearly unstable, and at still lower coking rates, it loses its steady state. This simple single control loop can also stabilize the linearly unstable steady state (see Figure 11 of Arbel et al., 1996). Interestingly, catalyst activity, provided it is high enough, has a more limited impact than would be expected over most of the range. Crgc adjusts itself to compensate for the increased activity just as it does for increased coking rate. However, increasing Trgn and catalyst activity stabilize the unit at the lower coking rates. Catalyst properties that have a larger impact on conversion are improved selectivity and lower coking rate at the same activity. The fact that such a complex unit can be operated with a single control loop is very interesting from a systems point of view. It is also of interest that only one specific loop of all the possible ones does it satisfactorily. However, the ability to control Yp is very limited. For instance, gasoline yield (Figure 12) can only be varied from 48.5 to 49.6% as Trgn is varied from 1180 to 1290 °F. We therefore need to accept very modest specifications. For the FCC units built before World War II, this was the case. Any unit that cracked gas oil to gasoline with a modest conversion (catalysts were much less active and less selective) made money. Older FCC units had no CO boiler but still operated in partial combustion. This is no longer permitted. Promoters make it feasible to operate at full combustion, but this requires operating with excess oxygen. This, in turn, makes the unit no longer controllable with a single loop. It was noted before that in full combustion air rate has no impact on Trgn, which in this case is solely a function of catalyst and feed properties. In fact, above a minimum value excess air affects only CO and NOx emissions but has no impact on any of the dominant process variables. As Tris is also uncontrollable, this means that there is no control of the dominant variables. This can be seen from Figure 6, where Tris, Trgn, and conversion are plotted versus coking rate when O2,sg is controlled with Fair. Also given are the impact of catalyst activities and the set point for excess O2. In full combustion the permissible range of Tris remains the same, 900-1015 °F. For Trgn it changes to 12501430 °F, which is a wider range than permitted for the riser. Note from Figure 6 that for fixed Fcat and catalyst activity there are narrow limits of coking rates for which Tris remains in acceptable limits. This range can be moved by designing at a different Fcat or using a different catalyst activity, but the range remains too

Figure 6. Complete combustion: handling of coke by a single control loop [Fair - O2,sg]. Cat/oil ) 5.2; Tfeed ) 400 °F; A ) 1.

Figure 7. Partial combustion: handling of coke by two control loops [(Fair - Trgn), (Fcat - Tris)]. Tfeed ) 400 °F; A ) 1.

narrow for practical operation. Also note that changes in excess O2 have almost no effect. This is not a useful control scheme for full CO combustion, and at least one additional variable is needed to control Tris in order to increase the range of coking rates over which the unit can be operated. This is important as the FCC is often exposed to rather large fluctuations in coking rate. 4.2.2. Adding Fcat to the Control. If Fcat can be manipulated, an additional control loop is available. Following Arbel et al. (1996), Tris should be chosen as the measured variable. For partial control this changes the accessible range of coking rates very little, as it was wide before (compare Figures 5 and 7). What it gives is better control of Yp (which is discussed later). Figure 7 shows some interesting interactions between the two loops. If Tris is uncontrolled (Figure 5), decreasing Trgn strongly reduces conversion. At fixed Tris the effect is in the opposite direction. Conversion increases, but the impact is much smaller. Increasing catalyst activity has a definite but limited impact on conversion. Increasing catalyst selectivity (a catalyst with a higher ratio of cracking to coking) has a larger effect. Therefore, the control [(Fair - Trgn), (Fcat - Tris)] offers considerable flexibility for handling different feedstocks, but with two limitations. One is very low coking feedstocks for which the unit can become unstable; the other is very heavy feedstocks with high coking rates or CCR, for which conversion drops to unacceptably low values. How to deal with these cases is considered in the next sections. For control in complete combustion, adding the capability to control catalyst circulation improves the situation dramatically. Once Tris is controlled the


Figure 8. Complete combustion: handling of coke by two control loops [(Fair - O2,sg), (Fcat - Tris)]. Tfeed ) 400 °F; A ) 1.

constraint shifts to Trgn, which has to be kept below 1430 °F to prevent rapid catalyst deactivation. The range of coking rates over which the unit can be controlled is now much larger (Figure 8) but still much narrower than that for partial combustion. When Tris is fixed, the increased Trgn due to high coking range reduces Fcat, thereby partially mitigating this effect. One can further increase the range by reducing Tris, which reduces conversion even further. In practice it is preferable to extend this range to higher coking rates by reducing catalyst activity. The conversion is reduced due to the fact that operating at higher reactor temperatures improves the selectivity. Thus, one gets a higher conversion for the same coke make. However, controlling Trgn by catalyst activity means relying on Ucs. The only fast way to reduce Trgn is to reduce Tris. After the catalyst activity has been sufficiently lowered, Tris can then be raised again. In full combustion use of catalyst activity as a control variable is essential, as even smaller changes have a big impact. In partial combustion, one needs much larger changes to get significant results. 4.2.3. Adding Tfeed to the Control. At present most units have a feed preheater. The impact of Tfeed is shown in Figures 5-8 for the different cases. In older units Tfeed is sometimes used instead of Fcat to control Tris. While Tfeed is very useful for control of Yp, controlling Tfeed is not useful for dealing with the impact of higher coking rates in either partial or full combustion. One interesting feature in full combustion is that at constant Fcat, Tfeed has a strong impact on Tris and Trgn (Figure 6), but when Tris is kept constant, changing Tfeed has almost no impact on Trgn (Figure 8). For low coking rates, such as severely hydrotreated feed, having Fair, Fcat, and Tfeed available as manipulated variables allows more stable operation and better flexibility. For such feeds operating in full combustion is often preferable, as the higher heat release is an advantage. A CO combustion promoter helps to process these light feeds in partial combustion by allowing one to adjust the heat balance by increasing the CO2/CO ratio as desired. 4.2.4. Adding a Catalyst Cooler. It was noted that in full CO combustion there is only limited control of Trgn. This is a severe problem at high coking rates. One way to overcome this is to add a catalyst cooler that allows independent control of Trgn in full combustion (provided Trgn without control is higher than 1300 °F). Addition of such a cooler removes some of the constraints on use of high coking rates and allows the use of feeds with significant CCR. Here the constraint is

Figure 9. Complete combustion: handling of coke by two control loops [(Fair - O2,sg), (Fcat - Tris)] and activity and by three control loops [(Fair - O2,sg), (Fcat - Tris), (Fcool - Trgn)] and activity. Tfeed ) 400 °F; A ) 1.

that the regenerator and the air compressor have to be big enough. This is shown in Figure 9. At high coking rates conversion still decreases, albeit much less than without a cooler, as Trgn is now constant. Conversion can be increased by lowering Trgn and by increasing catalyst activity. However, there are still strong limits on CCR. These limits are due to the fact that, for heavy coking feeds, conversion decreases too much. It does not decrease as much as for the case of partial combustion without a CO boiler. A catalyst cooler removes the constraints of the heat balance. In partial combustion the unit adjusts itself to the higher coke make by increasing Crgc, thereby adjusting conversion. With a catalyst cooler in full combustion Crgc is always almost zero. However, the coke laid down reduces activity, such that, at very high coke makes, conversion becomes too low even with the availability of a catalyst cooler. The limit depends on the design and on the catalyst chosen. There are other reasons for limiting operation with very heavy feeds, such as metals in the feed, but they are outside the scope of this paper. Now, what is the effect of having both a CO boiler and a catalyst cooler? We now have regained Fair as a dominant manipulated variable and can use it to control Crgc, for example by controlling CO2/CO in the matrix Gcd [(Fair - CO2/CO), (Fcat - Tris), (Fcool - Trgn)]. As was said before Tfeed is not helpful for maintaining reasonable conversion for high coking rates or CCR. This gives us the maximum control that we can have with a fixed feedstock and catalyst. However, the highest conversion always occurs when Crgc f 0. Thus, the added flexibility does not really provide an additional effective degree of freedom for dealing with perturbations in coking rate. We will later show that it has an impact on Yp. What it does is reduce the air rate at constant conversion, as combustion to CO requires only half the oxygen compared to CO2. This is important when retrofitting an existing unit. However, for new units we can ensure the availability of enough air by installing a large enough compressor. This has a very interesting and important implication. For a new unit a catalyst cooler has about the same cost as a CO boiler, maybe even lower. These results clearly imply that for a new unit we are better off to introduce a catalyst cooler as compared to a CO boiler. 4.3. Controlling Yp. One of the goals of partial control is to maintain a large vector Yp within a given space defined by eq 1. For an FCC this dimension of


Figure 10. Complete combustion: catalyst cooler and CCR in feed. Impact on Yp by three control loops [(Fair - O2,sg), (Fcat Tris), (Fcool - Trgn)]. Activity ) 1; coking rate ) 1; CCR ) 2%; promoter - Xpt ) 5; Tfeed ) 400 °F.

Figure 11. Partial combustion: CCR in feed, no catalyst cooler. Impact on Yp by two control loops [(Fair - Trgn), (Fcat - Tris)]. Activity ) 1; coking rate ) 1; CCR ) 2%; promoter - Xpt ) 5; Tfeed ) 400 °F.

the vector Yp can be quite large (Table 1), especially in refineries that have to meet tough environmental specs. On the other hand, very few of the product specifications are very tight or rigid, as all products can be blended. This is not so in industries which are specification dominated. Failure to meet product specifications can have severe economic ramifications. At best, the product is sold but at a lower price; at worst, it must be disposed of. The economic ramifications value of the specifications are, of course, very important for the design of a supervisory control system. For our purposes this is not as crucial as the main goal is to demonstrate the methodology. 4.3.1. Catalyst CoolersFeed with CCR. It was noted before that for highly coking feeds having both a CO boiler and a catalyst cooler gives no advantage over a unit having only a catalyst cooler. The same holds for controlling Yp. As in present catalysts Crgc has equal effect on all cracking reactions, increasing Crgc has exactly the same impact as reducing catalyst activity. While this has an impact on Yp, one can achieve the same result, albeit more slowly, by using a lower activity catalyst or by letting the catalyst deactivate. As catalyst coolers are mainly used for heavy feeds, the first example to show its impact is a feed containing 2% CCR. To illustrate the impact on Yp, let us look at four variables, namely, conversion (defined as total conversion of feed to products boiling below 430 °F), gasoline yield, wet gas yield, and heavy fuel oil (HFO) yield. Other important product properties will be discussed in a qualitative way, as our model is not detailed enough to include them. In Figures 10 and 11 we give a comparison between two cases having three dominant manipulated variables: (1) a unit with a catalyst cooler but no CO boiler (Figure 10), and (2) a unit with a CO boiler but no catalyst cooler (Figure 11). For both cases Fair, Fcat, and Tfeed are assumed to be available as manipulated variables. Let us start with Figure 10, complete CO combustion with a catalyst cooler. Despite the four loops, only three dominant variables can be controlled, as Fair is must be sufficient to maintain excess oxygen in the stack gas within specifications. Note that for a given conversion

gasoline yield can be varied over a significant range. The same applies to wet gas yield. There are two ways to further widen the accessible area. One is by increasing activity and the other is by increasing the feed temperature. Increasing activity allows one to go to higher conversion. At constant riser temperature, increasing the activity increases both conversion and wet gas yield. One can, however, get the same conversion at a lower Tris and therefore a lower wet gas yield (or higher gasoline yield). Increasing Tfeed has the opposite effect; it allows one to lower conversion while keeping the wet gas yield constant. This is important, for example, if one wants to lower the gasoline yield and obtain a higher distillate yield during the winter. Another economic incentive for maintaining a constant wet gas yield is to keep the alkylation unit filled. The volume of the accessible operating space can also be made wider by increasing the range of regenerator temperature from 1300-1400 to 1250-1430 °F, but the trends for the other variables would remain the same. We have not given a plot for the case where both a catalyst cooler and a CO boiler are available. This will allow one to control Crgc independently, for example using Gcd[(Fcool - Trgn), (Fair - CO2/CO), (Fcat - Tris)] and Tfeed as a slow-changing input. As discussed above, the ability to control Crgc means that activity can be directly controlled in the unit. Thus, the case with two activities shown in Figure 10 shows directly the impact of controlling Crgc. It is a large volume obtainable without changing the catalyst (or the catalyst management). In a unit with a catalyst cooler, also having a CO boiler does not improve the ability to process feeds with higher CCR. What it does do is shift part of the air needed to the CO boiler, thereby allowing a greater freedom on Yp without changing catalyst activity. The control of CCR is here inferential; normally it is done by controlling the CO2/CO ratio, which at constant Trgn is a function of Creg. In Figure 11 the same case is shown for a unit in partial combustion with a CO boiler but no catalyst cooler. There is no problem of being able to operate with the higher CCR because of the higher average Crgc. However, the achievable conversion is much lower than in the case with a catalyst cooler. Here activity has a


Figure 12. Partial combustion: impact on Yp by two control loops [(Fair - Trgn), (Fcat - Tris)]. Activity ) 1; coking rate ) 0.6; no CCR; no promoter Tfeed ) 450 °F.

Figure 13. Complete combustion: impact on Yp by three control loops [(Fair - O2,sg), (Fcat - Tris), (Tfeed - slow)]. Activity ) 1; coking rate ) 0.6; no CCR; no promoter; Tfeed ) 450 °F.

much smaller impact due to the constraint of the heat balance. For more active catalyst Crgc increases, partially compensating for the increase in activity. The slightly higher conversion is due to the fact that for a more active catalyst the increase in Crgc decreases the CO2/CO ratio and therefore the heat release per unit of coke burned. This allows a higher coke make at the same reactor temperature. Increasing Tfeed also decreases conversion, which is already so low as to render the ability to use Tfeed as a third variable practically useless. It is given here merely to illustrate the principle. We also note that the widths of the accessible areas have shrunk. At constant catalyst activity and feed temperature one can in the data still discern a clear area, but it is practically a single line. It is clear that, given a choice between a CO boiler and a catalyst cooler, the catalyst cooler has a decisive advantage. 4.3.2. No Catalyst CoolersFeed without CCR. Figures 12 and 13 show similar results for a feed without CCR processed in a unit with and without a CO boiler. In both cases a catalyst cooler is not

Figure 14. Complete and partial combustion: impact on Yp impact on HFO. Activity ) 1; coking rate ) 0.6; no CCR; no promoter; Tfeed ) 450 °F.

available. This shows the impact of eliminating the CO boiler without substituting a catalyst cooler. Figure 12 (partial combustion) shows that the achievable conversion is high (>83%). The reachable volume, while not as large as that in Figure 10, is larger than that in Figure 11. Figure 12 also shows the reachable region for the single loop [Fair, Trgn], which is a line on Yp. In Figure 13 (complete combustion) the achievable width of the area (variability of wet gas or gasoline) at constant conversion is wider than that in Figure 12, but the maximum conversion is lower (78%). Changing catalyst activity has almost no impact on the reachable space. For constant Tris and Tfeed, Trgn is lower for lower activity, which increases Fcat. The increase in Fcat compensates for the lower activity. The activity, above a certain level, mainly affects the constraint on Trgn but does not impact Yp. This was shown in Figure 8, when, at constant Tris and Tfeed, decreasing the catalyst activity had very little impact on conversion but lowered Trgn, which is crucial if one wants to handle a more highly coking feed. The reason is because even the reduced catalyst activity is high relative to older catalysts. Thus, in complete combustion without a catalyst cooler, controlling activity is crucial for handling higher coking feeds but not for controlling Yp. While not in our model, correlations (Grace Davison, 1993) show that keeping Tris high results in a more olefinic wet gas and a higher octane for the gasoline. The ability to impact wet gas and other variables while keeping Tris constant is therefore of importance when these items are critical components of Yp. Furthermore, additives based on HZSM5 can increase wet gas and olefin content and octane at constant conversion. It is also important to realize that some items of Yp cannot be changed at constant conversion. These are components of Yp that are controlled by a similar activation energy. One such component is bottom conversion of heavy fuel oil yield (HFO) given in Figure 14 for the cases in Figures 12 and 13. We note that what is for other variables either a volume or a surface is now, for practical purposes, a single line regardless of what manipulated variables are used. As HFO is the lowest value product, it is desirable to decrease it as


much as possible, but one cannot do this without affecting the other components of Yp. The only way to change it is to find a catalyst that has different relative rate constants for conversion of light and heavy gas oil or to recycle it. It is very important in partial control to find out what items in Yp can be controlled partially independently and which are totally correlated, such as HFO yield and conversion. There is another constraint in the accessible Yp that is not apparent from Figures 12 and 13 but was discussed in the section dealing with coking rates. In Figures 12 and 13 all set points result in a stable operation. If in Figure 13 the catalyst activity would have been reduced to the lower activity given in Figure 12 (reduction by a factor of 2), part of the set points given in the plot would have become linearly unstable. Further reduction would result in a part of the set points not representing a heat-balanced upper steady state. The same also holds for Figure 13. Thus, both in partial combustion and in full combustion, there is a lower limit for activity which is different for each but in both cases depends upon the coking tendency of the feedstock and the coke selectivity of the catalyst. In partial combustion there is no upper limit to catalyst activity. In full combustion with no catalyst cooler there is a limit due to the temperature constraint on the regenerator. Understanding the impact on stability is an important part of evaluating the impact of design on control. For present FCC catalysts and design this is not a severe problem but has to be included in the methodology. A previous paper (Arbel et al., 1995b) shows how to predict the region of permissible settings. 5. Available Range of Manipulation for Manipulated Variables The other aspect of the impact manipulated variables have is the range over which they can be changed. This is again a strong function of design. In many FCC’s we face a different problem. No new refineries have been built in the last 20 years and demand has increased. Advances in catalyst characteristics make it possible to process different feeds, usually heavier, than those processed at the time when the unit was designed. They also allow higher throughputs. This, together with advanced control techniques, makes it possible to more fully utilize FCC’s and to operate against constraints. So, even units that were designed with the proper range of input manipulation are today hard-pressed with little space for control. This is not just true for the FCC but for many other processes. Previously units were designed with much more fat. If demand increased it was relatively easy to debottleneck them and increase capacity. Today most companies insist on a tight initial design to minimize investment costs. However, this is a problem outside our range of interest. In a proper design one does not introduce preventable constraints from the outset. Taking this to be the case, we assume that all goals are properly taken care of in the design. The range over which one should be able to vary manipulated variables is a strong function of the goals of the control and must be included in the consideration of sufficiency. One needs to forecast the nature and magnitude of changes in feedstocks, production rates, and specifications. Once one has established the number and nature of manipulated variables chosen, a steady-state model will give the range needed for each variable. One has, however, to add to this a provision

for dynamic control. Regrettably, this is a need rarely satisfied in current practice. Figures 12 and 13 show how increasing the number of control loops increases the reachable space in Yp. While a single control loop (Fair - Trgn) allows stable operation over a wide range of inputs, it is very limited in its ability to adjust Yp. Two or more loops are necessary to allow adjustment of specs such as gasoline yield over a reasonable range. 6. Summary and Conclusions Let us summarize our results in two ways. The first deals with those aspects of partial control which we believe to be of general validity, while the second concerns those results which are of specific interest in the operation and control of FCC’s. Needless to say, our generalizations at this point have been strongly guided by what has been learned from this rather in-depth study of FCC control. These need to be validated and strengthened by studies of other complex systems. 6.1. General Results. One major result of this work is the distinction to be made between effective degrees of freedom and the number of available manipulated variables. It was shown that the former may well be less than the latter due to the fact that two or more manipulated variables may have essentially the same impact on the dominant output variables and the specification vector Yp. In this case the excess of manipulated variables serves, at best, to extend the range of operating space. Another major result is the outline of a procedure for analyzing the way in which design impacts the control of a complex system. There are five main steps required for this analysis. (1) Identification of control system goals. This includes the desired range of product specifications and other process constraints vector Yp; the range over which production rates have to be varied (turn-down ratio); and the range of feed properties that must be accommodated. (2) Generation of model information that adequately characterizes the system. Characterization of the steadystate behavior is of primary interest. Does the system have multiple steady states and input multiplicities? Are there regions in which the steady-state operating points are open-loop unstable? What information is available to determine the range of feasible operating conditions? What output variables can be measured, and of these, which can be predicted with reasonable accuracy using available model information? (3) Determination of effective degrees of freedom. Of the available manipulated variables, which have what impact on Yp and on what time scale? To what extent do subsets of manipulated variables have similar impacts on Yp, thereby reducing the effective degrees of freedom? Which are suitable for control on the various time scales of the process? (4) Determination of the dominant process variables. Which process variables have the strongest correlations with the elements of Yp? (5) Determination of control structures and sufficiency. What dominant process variables and what manipulated variables should be used with respect to the time scale of interest and the operating conditions of interest? If the system is open-loop unstable at the operating conditions of interest, what is the minimum size of the control matrix that will allow stabilization of the system (sufficiency with respect to stability)?


Which choices of control structure give the widest region of stability around the operating point? What is the minimum size of the control matrix that will result in all elements of Yp being maintained within their acceptable bounds (sufficiency with respect to specifications and constraints)? Meeting the goals originally proposed under step 1 for Yp may prove difficult. These goals are determined by market requirements and economics. However, there is no assurance that any economically feasible design for a specific process can meet them. Therefore, a compromise must often be made between the desirable and the achievable. This will require iterating the entire procedure starting with step 1. Some specs may require a different process, and tight specs often require close control of the feed properties. As goals vary between plants even for the same process such as an FCC, so will the design modifications that will be required to meet the goals of each. Environmental considerations have a strong impact on control and must be taken into account in the design. However, even if all specs are totally relaxed, there is a minimum control required to make the process operational and stable. One can then evaluate the potential impact of adding more manipulated variables such as feed temperature, catalyst circulation and heat removal rate by a catalyst cooler, and catalyst activity. Both the ability to handle feeds with different coking rates and the ability to manipulate components of Yp independently were included in the evaluation presented in this paper. For this evaluation understanding the concepts of dominance explained in Arbel et al. (1996) is very important and further illustrated. One also needs to evaluate how different components on Yp are correlated with each other. Some sets of Yp contain items that cannot be controlled independently by each other and some that can. It is also important to evaluate and understand the reachable space for the vector Yp. For the FCC it is shown that by controlling only variables in the unit itself the reachable space for all practical purposes is a surface despite the fact that we have three dominant variables impacting Yp. This is due to the nature of the kinetic equations for existing catalysts. Other catalysts will not have this property, nor will other processes. In a future paper we will discuss what is the main information required to determine this essential property of the process. 6.2. Impact of Design on the Control of FCC’s. Let us now look how these various steps apply to the FCC. Identification of control system goals (step 1) has been discussed in previous papers (see, for instance, Table 2 in Arbel et al., 1996). The Yp vector discussed therein is only a subset of that of commerical interest, but there are enough variables to be illustrative of what is involved. Generation of model information (step 2) has also been discussed at length in that paper. It was shown, for instance, that some process variables such as Trgn can be modeled with much more confidence than, say, ∆T or Tsg. The analysis of steady-state multiplicities was presented in an earlier paper (Arbel et al., 1995b). A detailed analysis for multiplicities and permissible control settings was presented. It was shown that eliminating multiplicities by design is feasible but noneconomic. Determination of the effective degrees of freedom (step 3) showed that for the FCC there are only four in the unit itself. Other variables have a much smaller impact. The number four only applies for fixed feed and

catalyst properties. Feed properties and catalyst properties can change during operation and be treated as perturbations. However, in an FCC both can be used as manipulated inputs. In fact, they are very important inputs in process optimization. As Yp has a large dimension, we have to realize that our ability to change it in the unit itself is limited. With four manipulated variables we have exact control on all dominant variables affecting Yp and unit operation, but this is still partial control on the entire Yp vector. One can successfully operate with fewer manipulated variables. In fact in partial combustion one dominant control loop (Fair - Trgn) is enough to control and stabilize the unit over a wide range of feed properties and catalyst activities. The only other way to widen the accessible space is to modify either feed or catalyst properties. In an FCC it is possible to modify the relative cracking rate matrix by either modifying the catalyst or using modifiers, and the approach of the paper could be applied to evaluate the impact of such modifications. Not all processes have this option. In fixed beds catalysts cannot be changed on-line and require a shutdown for change. The range of potential modification of the reaction matrix may also be more limited for the processes. An extensive study of the dominant process variables (step 4) was given in the previous paper (Arbel et al., 1996). This is explored further in this paper. One of the most important points is that in partial combustion Tris and Trgn are the most important dominant variables while in complete combustion Trgn is replaced by excess O2. It was further shown that, in partial combustion, partial control of the unit itself can be achieved using only Trgn (in conjunction with Fair as the manipulated variable). Control structures and sufficiency (step 5) have been evaluated in detail in this paper. The effect of environmental considerations was illustrated through the requirement to control CO emissions. This can be done in two ways. One is to use promoters to achieve full CO combustion. The other is to provide a CO boiler. The first option requires that air rate must be adjusted to meet the maximum permissible CO emissions, which means controlling excess oxygen at some minimum level. Under such conditions air rate does not impact the dominant process variables. There are other environmental constraints that impact FCC operation, and a similar methodology can be used for them. The effects of adding additional manipulated variables by providing a feed preheater or catalyst cooler were explored. It was shown that a feed preheater does not increase the effective degrees of freedom but merely the range over which the unit can be operated. A catalyst cooler does provide an additional degree of freedom in complete combustion and allows one to process feeds with a wider range of coking characteristics. We want to point out that we have not tried to give an exhaustive analysis of the FCC. There are other design modifications in current practice, such as staged feed injection and recycle of unconverted feed, that are part of the ability to control Yp. The methodology of the paper should be useful for such modification as well as for a large number of nonlinear processes that have similar properties and an Yp of large dimension. In conclusion, let us return to the general problem of partial control. We can, at this point, see no way to


define a rigorous algorithmic approach, but this is a feature of almost all design procedures for complex systems such as chemical reactors, entire processes, and the like. We have similar problems in both reactor selection and scaleup as well as separation system synthesis. Systematic approaches can be outlined; generalized algorithmic techniques can be developed which will provide guidance; but in the end many of the key design decisions will have to be made based on criteria which are not wholy quantitative. Engineering judgment will always be necessary. This should be kept in mind when developing methodologies for both process and control system design. We hope that this paper will stimulate research along these lines. Acknowledgment This work was supported by the Division of Basic Energy Sciences of the Department of Energy under Grant No. DE-FG02-91-ER14221. The authors want to acknowledge their gratitude for this support. We also express our thanks to Coleman Brosilow and Manfred Morari for their many valuable comments on earlier drafts of this paper. Nomenclature ∆T ) temperature drop from the stack gas to the regenerator dense bed (Tsg - Trgn) [°F] A ) relative catalyst activity air/oil ) air flowrate to feed flowrate ratio (FairMWair/Ffeed) [lb of air/lb of feed] cat/oil ) catalyst flowrate to feed flowrate ratio (Fcat/Ffeed) [lb of cat/lb of feed] CCR ) Conradson carbon residue Conv. ) conversion [wt %] Crgc ) coke on regenerated catalyst [wt %] DMC ) dynamic matrix control E/RT ) activation energy term in the cracking rate equations Fair ) air flowrate to the regenerator [mol/s] Fcat ) catalyst circulation rate [lb/s] Fcool ) catalyst circulation rate through the catalyst cooler [lb/s] Ffeed ) oil feed flowrate [lb/s] Gcd ) primary control structure of partial control Gs ) slow control structure of partial control HFO ) heavy fuel oil LFO ) light fuel oil O2,sg ) oxygen in stack gas [mol %] Tcool ) cooled catalyst temperature [°F] Tfeed ) oil feed temperature [°F] Tmix ) temperature at the riser bottom after feed and catalyst mix [°F] Trgn ) regenerator dense bed temperature [°F] Tris ) riser top temperature [°F] Tsg ) stack gas temperature [°F] Ucd ) vector of frequently (fast) manipulated variables Ucs ) vector of nonfrequently (slow) manipulated variables Xpt ) relative CO combustion rate-level of promoter Ycd ) vector of outputs controlled by the primary control structure Ycd,sp ) vector of set points for the variables controlled by the primary control structure

Yg ) gasoline yield [wt %] Yp ) vector of process outputs Ypj,max ) upper limit on component j in the vector of process outputs Ypj,min ) lower limit on component j in the vector of process outputs Ypj ) component j in the vector of process outputs Ywg ) wet gas yield [wt %] z ) relative coking rate

Literature Cited Arbel, A.; Huang, Z.; Rinard, I. H.; Shinnar, R.; Sapre, A. V. Dynamics and Control of Fluidized Catalytic Crackers. 1. Modeling of the Current Generation of FCC’s. Ind. Eng. Chem. Res. 1995a, 34, 1228. Arbel, A.; Rinard, I. H.; Shinnar, R.; Sapre, A. V. Dynamics and Control of Fluidized Catalytic Crackers. 2. Multiple Steady States and Instabilities. Ind. Eng. Chem. Res. 1995b, 34, 3014. Arbel, A.; Rinard, I. H.; Shinnar, R. Dynamics and Control of Fluidized Catalytic Crackers. 3. Designing the Control System: Choice of Manipulated and Measured Variables for Partial Control. Ind. Eng. Chem. Res. 1996, 35, 2215. Avidan, A. FCC is Far from Being a Mature Technology. Oil Gas J. 1992, OGJ Special, 59. Avidan, A.; Shinnar, R. Development of Catalytic Cracking Technology. A Lesson in Chemical Reactor Design. Ind. Eng. Chem. Res. 1990, 29, 931. Avidan, A.; Edwards, M.; Owen, H. Innovative Improvements Highlight FCC’s Past and Future. Oil Gas J. 1990, 88 (2), 33. Balchen, G. J.; Mumme, K. I. Process Control Structure and Application; Van Nostrand Reinhold: New York, 1988. Cutler, C. R.; Ramaker, B. L. Dynamic Matrix ControlsA Computer Control Algorithm. Proceedings of the Automatic Control Conference, San Francisco, CA, 1980; Paper WP5-B. Fisher, W. R.; Doherty, M. F.; Douglas, J. M. The Interface Between Design and Control. 1,2,3. Ind. Eng. Chem. Res. 1988, 27, 597. Grace Davison. Guide to Fluid Catalytic Cracking Part I; W. R. Grace @ Co.sConn.: 1993. Huq, I.; Morari, M. Design and Operational Modifications to Model IV FCCUs to Improve Dynamic Performance. AIChE J. 1995, 4, 1481. Meadowcroft, T. A.; Stephanopoulos, G.; Brosilow, C. The Modular Multivariable Controller: I: Steady-State properties. AIChE J. 1992, 38, 1254. Morari, M.; Arkun, Y.; Stephanopolous, G. Studies in the Synthesis of Control Structure for Chemical Processes, Parts I, II, and III. AIChE J. 1982, 28, 60. Perkins, J. D., Ed. IFAC Workshop: Intereactions Between Process Design and Process Control; Pergamon Press: New York, 1992. Price, R. M.; Georgakis, C. Plantwide Regulatory Control Design Procedure Using Tiered Framework. Ind. Eng. Chem. Res. 1993, 32, 2693. Silverstein, J.; Shinnar, R. The Effect of Design on the Stability and Control of Fixed Bed Catalytic Reactors with Heat Feedback 1. Concepts. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 241. Zafiriou, E., Ed. IFAC Workshop on Integration of Process Design & Control: IPCD ‘94; Pergamon Press: New York, 1994.

Received for review June 19, 1996 Revised manuscript received October 23, 1996 Accepted October 28, 1996X IE960356C

X Abstract published in Advance ACS Abstracts, December 15, 1996.

Dynamics and Control of Fluidized Catalytic Crackers. 4. The Impact of

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