Improving operability of spouted beds using a simple optimizing control structure

Improving operability of spouted beds using a simple optimizing control structure

N. A. CORRÊA, J. T. FREIRE and R. G. CORRÊA

Chemical Engineering Department, Federal University of São Carlos, Rod. Washington Luiz,

Km 235, 13565-905, São Carlos - SP, Brazil

E-mail: [e-mail]

(Received: July 22, 1999: Accepted: August 30, 1999)

Abstract - In operations using spouted beds, it is of major importance, from an energy consumption point of view, to operate the process as close as possible to the minimum spout flow. At this point, the speed of the gas (for example, warm air in drying operations) is greater than the amount of heat and mass transfer involved, although it only transfers the minimum amount of momentum to maintain the spout. Therefore, by staying close to this minimum flow condition, it is possible to perform a stable operation and to obtain energy savings not only in the heating of the gas but also in its displacement by blowers. In order to improve the operation of such processes, a study is carried out by implementing a simple optimizing control structure on a spouted bed experimental set-up. The air flow is regulated by a frequency inverter, at the speed of blower rotation. A PI controller was used and the set-point for the air flow rate is calculated on-line by a simple and well-known minimization method called Golden Section Search. This set-point is constantly updated with values very close to the actual minimum spout flow rate. To accomplish the calculations and data acquisitions, a microcomputer with an interface and an analog signal conditioner is used .

Keywords: Spouted Beds, Minimum Flow Rate Operation, Optimizing Control, Golden Section Search.

INTRODUCTION

In any process based on spouted beds, energy consumption is high due to the amount of kinetic energy supplied to keep the solid-phase part of the bed moving. Therefore, any way of saving energy that maintains stable operation is highly desirable. Let us take the example of a drying operation for pastes with spouted beds with solid particles. The minimum warm gas flow rate (normally air) for momentum transfer to solid particles is greater than the gas flow rate necessary for the heat and mass transfer which take place in drying (Freire, 1992). The use of a gas flow rate lower than a given minimum value will break the desirable movement of such particles, i.e., the spout.

In order to minimize the energy demand, it is mandatory to operate the process with an air flow rate as close as possible that which still maintains the spout of particulate medium. This flow rate is called minimum spout flow rate,Q_jm. A flow rate lower than the minimum spout flow rate will result in the collapse of the spout movement of the particulate medium. The spouted bed will exhibit a behavior similar to that in a fixed bed operation, which is totally undesirable, mainly in paste drying. In cases like this, the spout movement of the particles is indispensable for increasing the area of heat and mass transfer of the paste and also for dry powder detachment.

Sometimes it is difficult to operate manually the spouted bed at exactly the minimum spout flow rate. Besides the imminence of the collapse of the bed due to any minor disturbance that can extinguish the spout, there is the case where the minimum spout flow rate changes during operation. Therefore, in manual operation, it is a common procedure to set the flow rates lightly higher than the minimum spout flow rate and then monitor the spout for a possible collapse.

The study of control problems in spouted beds is rather reported in the literature. We have found only one paper which deals with the control of a drying process in a mechanically spouted bed dryer (Szentmarjay et al., 1996). Our understanding of the cited paper indicates that the PID control implementation studied was mainly considered to obtain an improvement in the measurement and graphic display of some parameters involved in the process. Control problems, if any, were not addressed. However, Szentmarjay et al. claim that the control strategy implemented in the mechanically spouted bed dryer allowed a stable and economical operation of the dryer, as well as a dried product of good quality. Recently we have initiated a systematic study of the possible control problems of spouted beds in order to propose feasible solutions to improve their operation. We have started from scratch by considering a very simple and well-know control configuration (a multiloop PID scheme) and only looking upon thefluid dynamics and thermal behavior of the spouted bed. Some initial results can be seen in Moreira et al. (1998a,b).

In Moreira et al. (1998a,b), the pressure drop across the bed, DP, is used as a reasonable indication of the fluid dynamics behavior of the spouted bed. In order to monitor for a possible spout collapse, a PI-control pairing DP-VP was implemented between the pressure drop across the bed, DP, and the inlet gas flow rate control valve-stem position, VP. This control strategy was unable to properly correct for disturbances that collapse the spout, especially when in an operating region close to the minimum spout. In this region, the non-linearity is evident since the spouted bed can suddenly become a fixed bed. Besides, if the bed collapses, the PI-control strategy implemented will not be able to reestablish the spout. Such facts will be shown in the following sections. Therefore, a more specific control strategy to deal with this particular behavior of spouted beds is necessary. For this reason, a new control strategy, which takes into account a supervisory control structure, is implemented and tested.

The idea of this new control strategy is quite simple. From time to time, the control algorithm identifies, on site, the gas flow rate Q_max (equivalent to DP_max) and a sufficient gas flow rate to establish the spout, Q_j (equivalent to a DP_j). The actual minimum spouted flow rate, Q_jm, must lie in between, since it corresponds to the minimum pressure drop across the spouted bed (DP_jm), where the spout still exists. With the Golden Section Search method (Press et al., 1989), it is possible to establish a flow rate as close as possible to the minimum spout flow rate. This flow rate is then the actual set-point of the PI-controller for the flow rate control loop. This minimization method has the advantage of only considering comparisons of measured pressure drop values across the spouted bed that makes the method fast and then suitable to be including in the control algorithm. To achieve implementation of this control algorithm and also minimize the energy demands of spouted beds, we have to modify the PI-control pairing from DP-VP to Q - w and change the control valve to a frequency inverter actuator.

This paper is organized as follows. In the next section, the fluid dynamics behavior of spouted beds is outlined and the control problem associated with this particular behavior is presented. Then, we describe an attempt to solve the control problem mentioned above with a classic PI-control structure. A new control strategy is proposed and the Golden Section Search method is incorporated into it. The experimental set-up is described and the paper ends after a discussion of and conclusions about some closed-loop runs of the new control strategy.

The Spouted Bed and the Control Problem

The spouted bed is a system that is capable of performing certain useful cyclic operations on solid particles with a high degree of mixture between a fluid and these particles. For that reason, it is already used in several industrial applications such as drying of grains, paste-like material, suspension, solids coating and many others applications (Mathur & Epstein, 1974). Several tests have already indicated the viability of using spouted beds as a dryer in the dehydration of fruit pulp, bovine blood, egg, yeast, tomato puree, banana puree, aluminium hydroxide, beans, corn, soy beans, etc. The most common configuration of a spouted bed consists of a circular cylinder with a diverging conical base filled with a given amount of particles. The cone vertex is truncated to form a nozzle (inlet hole) through which a fluid enters (generally warm air in drying processes) at a considerably high flow rate to facilitate a characteristic movement of the particles, the spout. These particles, impelled by the fluid, pass through the spout channel and decelerate forming a fountain. Then, they drop to the side into the annulus area (between the spout and the vessel wall). The annulus forms a very dense packing of particles, which show a slow descending movement. The particles move downwards and encounter the spout to establish a cyclical movement. Depending on the process, the particle can be grains, seeds or inert particles with different shapes such as spheres, pellets, bullets and many others. Spherical inert particles, with d_p=0.36 cm, are used in our experimental set-up. There is also another configuration based on an entirely conical vessel. This work uses the first configuration. The spouted bed can operate continuously or in batches. In this work, we make use of the first type of operation.

The characteristic fluid dynamics behavior of a spouted bed is best described with reference to a plot of pressure drop across the bed versus the superficial velocity or the gas flow rate in the spouted bed, Q. This behavior, shown in Figure 1, is obtained by gradually increasing the fluid flow rate up to Q_j (path of increasing flow rate) and by gradually decreasing Q down to the initial fixed bed condition (path of decreasing flow rate), where the spout no longer exists. See Mathur & Epstein (1974) for a complete description of this hysteresis loop in the fluid dynamics behavior of spouted beds.

Figure 1
: Pressure drop across the system – gas flow rate curve for our experimental set-up, which includes a cyclone at the output gas. Inert spherical glass particles: d_p = 0.36 cm, D_c = 15 cm, D_i = 3.5cm, q = 60^o and H = 23.5cm.

An Important Operational Constraint: The Control Problem

As we can see in Figure 1, the minimum pressure drop across the bed, DP_jm, also has a correspondent value in path of the increasing flow rate. If some control configuration is designed based on keeping track of the pressure drop across de bed, DP_j, close to DP_jm, it may not succeed. After some disturbance in the direction of the decreasing flow rate, this control loop would seek the value of DP_jm on path the increasing flow rate as its actual reference value and move the spouted bed into fixed bed operation mode. This situation is undesirable and is a serious operational constraint in spouted bed processes. In the next section, we discuss an implementation of an unsuited control structure to overcome this constraint. Therefore, one important control problem in the operation of spouted beds is to maintain the spout despite input disturbances.

An Attempt to Solve the Control Problem with a Classic PI-Control Structure

In Moreira et al. (1998a), the implementation and testing of a multiloop PI controller in a spouted bed are performed. Based on the fluid dynamics and thermal behavior of the system, around the minimum spouted bed fluid flow rate, a transfer function matrix is identified for control purposes. This transfer function matrix relates the pressure drop across the spouted bed (DP) and the exit fluid temperature (T_e) to the inlet fluid flow rate control valve-stem position (VP) and the electrical power supplied to the inlet fluid heat exchanger (POW). The elements of this 2X2 transfer function matrix are identified as a first-order with time delay transfer function. The control pairings are DP-VP and T_e - POW. The performance of the control system is tested for set-point tracking, disturbance rejection and interaction between the control loops around a previously defined control design operating region. In all cases the control system presents a good performance. A weak interaction is observed for a set-point step change in loop DP-VP. In fact, POW has almost no impact on DP. However, when we drastically decreased the gas flow rate, Q, below Q_jm, the control loop DP-VP was unable to properly control DP without extinguishing the spout (Figure 2). In Figure 2, the operating point is moved to the path of the increasing flow rate (Figure 1), since the control loop DP-VP can not distinguish between the (VP) from the path of the increasing flow rate and that from the path of the decreasing flow rate. The first DP is 'selected' and the gas flow rate is reduced.

Figure 2
: Closed-loop performance of the multiloop PI-control DP - VP and T_e - POW, after a drastic disturbance in Q below Q_jm, when the loop DP - VP was not able to maintain the spout and shift the operating region into the path of the increasing flow rate (data from Moreira, 1997).

The same problem was observed even when a multiloop tuning method was implemented (Moreira et al., 1998b). The multiloop tuning method was used to deal with the minimization of loop interaction and therefore it was not supposed to overcome the end of the spout.

Another important observation obtained from Moreira et al. (1998a,b) was concerning the closed-loop dynamics of both loops DP-VP and T_e - POW, where the former is much faster than the latter.

All these facts led us to think of a different control strategy to improve the operation of spouted beds and solve the control problem studied here. First, control of the faster behavior of the fluid dynamics of the spouted bed will be built into a single SISO control loop configuration. And the quality of the product – dry material as in a drying operation – will be controlled by a different and ‘independent’ control structure. Second, the minimization of energy costs and the stable operation of the spouted bed will be achieved by pairing Q with the blower's motor frequency, w, instead of DP with VP. This new pairing will be included in an optimizing control strategy where a minimization search is implemented to establish a suitable gas flow rate as the set-point for the PI-control pairing Q - w.

Optimizing Control Strategy

The on-line, recursively updated, implementation of set-points in control systems is denominated Optimizing or Supervisory Control, where optimization algorithms are employed to maximize profits or to minimize costs. In our case, we are interested in the decrease in energy demands in spouted beds, specially the minimization of energy used in gas displacement by blowers, without losing the main operational characteristic of spouted beds: the spout.

In this work, the objective function to be minimized is the spouted bed pressure drop across the bed, DP, by a suitable choice of a fluid flow rate, Q, with the constraint that the spout extinction should be avoided. That is

min DP

Q

subject to (1)

DP ³ DP_jm

There are several optimization algorithms in the literature and one of the simplest was used: the Golden Section Search method (Press et al., 1989).

The applied control strategy can be visualized in the diagram in Figure 3.

Figure 3
: Block diagram of the optimizing control strategy.

It is important to point out that the optimizing control proposed modifies the spouted bed operation during the procedure for the calculation of the minimum. All intermediary set-points for the PI-control loop, Q_sp, are implemented until a suitable value (minimum) is obtained. Someone can argue that this is an inconvenient procedure. However, if you consider the difficulty of obtaining good models to predict the minimum spout flow rate, Q_jm, the methodology proposed here seems to be fine. Besides, this PI-control loop Q - w is fast enough so as to not affect the dynamics of the other loops. The steps implemented in the optimizing control algorithm are now presented.

Application of the One-dimensional Golden Section Search Method

The Golden Section Search method consists of surrounding the minimum of a function with three points starting from a < b < c such that f(a) < f(b)and f(b)< f(c). A new point X is introduced into this interval such that a < x < b or b < x < c. If, for example, b < x < c, f(x) is calculated. For f(b)< f(x) , the new triplet surrounding the minimum is given by a < b < x. When f(b) > f(x), the new triplet becomes b < x < c. This procedure is repeated until the distance between the points in the triplet is below a given tolerance.

For the recursive calculations, the localization of a x point inside the initial search interval a < b < c, is given at a fractional distance starting from the medium point b in the largest interval [a,b] or [b,c]. This distance is 38.197% of the selected interval and is denominated Golden Section (Press et al., 1989).

In this work, the initial search interval corresponding to a < b < c is given by

(2)

where Q_j is the gas flow rate value at the point where the bed begins to spout (path of the increasing flow rate). k is a weight value between 0 and 1. k=1 was adopted.

Eq. (2) indicates that Q_jm must lie between the value for a gas flow rate where the particles start to move from a resting condition and another gas flow rate value lower than the one that corresponds to the maximum pressure drop across the bed.

The algorithm should identify Q_max and Q_j. These values are obtained in a start-up procedure by increasing the gas flow rate gradually and introducing the measured DP values into the optimization routine. Then, the minimization procedure seeks the smallest gas flow rate inside the search interval and implements it as an effective set-point in the PI controller. If the spout is extinguished, the algorithm tries to reestablish it using minimization routine for a given number of attempts. If it does not succeed, the operational conditions have probably been changed due to batch operation and/or input disturbances (variations in paste feed, temperature or bed load, for example), and the optimization routine starts again to determine the new values for Q_max and Q_j. All these steps are represented in the block diagram in Figure 4.

Figure 4
: Block diagram of the optimization procedure.

RESULTS AND DISCUSSION

Early in this paper, we presented Figure 1, which shows the characteristic curve of our spouted bed. It is important to point out the positions of Q_max, Q_j and Q_jm on this curve for future analysis.

Figures 6, 7 and 8 show tests of the control system with the optimizing PI-control structure and the classic PI-control, which is the one not seeking the optimum Q value.

Figure 5:
Experimental set-up scheme.

Figure 6
: Closed-loop behavior of DP during start-up and optimizing control (first one-third part); disturbance in Q and optimizing control (second one-third part) and disturbance in Q without optimizing control (third one-third part).

Figure 7:
Closed-loop behavior of Q_sp (set-point) during start-up and optimizing control (first one-third part); disturbance in Q and optimizing control (second one-third part) and disturbance in Q without optimizing control (third one-third part).

Figure 8:
Closed-loop behavior of w (manipulated variable) during start-up and optimizing control (first one-third part); disturbance in Q and optimizing control (second one-third part) and disturbance in Q without optimizing control (third one-third part).

The first one-third of Figure 6 shows the control system behavior during start-up, where the positions of Q_max and Q_j are identified by the optimization routine (Figure 4). Q_max corresponds to the highest value of DP (DP_max) in this first one-third of Figure 6, while Q_j corresponds to the first DP after DP_max, as indicated in the first one-third of Figure 6 and also in Figure 1. From the definition of the initial optimization search interval, the optimization routine establishes the set-point at Q_sp=1.05 m³/min, as shown in the first one-third of Figure 7. At t =500 s, a disturbance is applied, thereby decreasing the air flow rate. The drawer valve in the air line (Figure 5) is used for this disturbance and the spout is extinguished (an abrupt decrease in DP, as shown in the second one-third of Figure 6). In a similar way, as described in the start-up procedure, new positions are identified for Q_max and Q_j and a new set-point is established at Q_sp=1.05 m³/min (second one-third of Figure 7). A difference of 0.05 m³/min is observed between the two set-points (first and second one-third of Figure 7). This difference is due to packing. At the start-up, the particles are more packed (they form a denser medium) than when the spout is extinguished. Therefore, the bed of particles needs a higher flow rate to 'break' the particulate medium and promote the spout. Hence, Q_max and Q_j show larger values than those referring to the particulate medium already 'broken' once. The fluctuations observed in DP (Figure 6) are due to the regulatory PI-control actions.

Third one-third of the Figure 6 presents the performance of PI-control without supervisory mode (optimizing control), with the set-point equal to Q_sp=1.05 m³/min (second one-third of Figure 7). After returning the drawer valve to the initial position established in the start-up procedure, which is verified by a decrease in w at 800 s (Figure 8), the spout is once again extinguished at 1000 s.

It is observed that pressure increased as expected (Figure 6). At this operating point, with Q_sp=1.05 m³/min, there are two values for DP: one in the path of increasing flow rate (fixed bed: no spout) and another in the path of the decreasing flow rate (Figure 1). The PI-control, without the supervisory mode, could not reestablish the spout, since the operation is being performed at a DP in the path of the increasing flow rate and achieved after the end of the spout. Only the optimizing control will be able to, automatically, spout the particles again.

With this optimizing control strategy, it was possible to operate close to the minimum spout condition. During the disturbance test, the set-point was established at Q_sp=1.05 m³/min (only 5% larger than the minimum spout flow rate). If the minimization search interval is reduced, with k < 1 (Eq. 2), it would be possible to obtain a Q_sp closer to Q_jm. So, why not try the minimum spout flow rate itself? The answer is: instability. At this operating point, the spout will suffer several collapses and reestablishments with excessive action in the final control element (frequency inverter and blower). This will result in an apparently unnecessary effort.

Finally, the savings made in blower energy demands is analyzed. The real advantage of acting directly on the blower's electric motor, using a frequency inverter, is the modulation of electric energy in accordance with the required flow rate. If a control valve is used, electric energy expenses will be excessive, since the blower will continually supply the same amount of air, while consuming more energy than that necessary to establish the spout. For example, during this experiment, the energy demanded by the blower was approximately 0.8 kWh after 1160 s of total running time, much smaller than 1.8 kWh, the value when a control valve is used during the same period of time. In addition, the blower is operated below its maximum capacity, which prolongs its operational life.

CONCLUSIONS

We may conclude that the optimizing control strategy, using the simple Golden Section Search method of minimization, is fast and works fine in the control of the fluid dynamics of a spouted bed.

Although shifting the operation back and forth, in order to search for the optimum set-point of the fluid flow rate is inconvenient, the capacity of the control system to reestablish the spout is robust and makes this strategy a good option when one wishes to operate very close to the minimum spout. PI-control (without the supervisory mode) can not achieve this performance.

An energy savings is evident and should be explored in more detail in the future.

ACKNOWLEDGEMENTS

The authors would like to express their gratitude for the financial support provided by PRONEX/FINEP (under grant 142849/97-9) and CNPq.

NOMENCLATURE

a,b,c,x arbitrary variables

D_c circular cylinder diameter (cm)

D_i gas inlet diameter (cm)

d_p particle diameter (cm)

e error: Q_sp - Q (m³/min)

f arbitrary function

H bed height (cm)

H_c circular cylinder height (cm)

i iterative index

k weight value used to modify the minimization interval, 0 to 1(dimensionless)

POW electrical power supplied to the inlet fluid heat exchanger (kW)

Q gas flow rate (m³/min)

Q_j gas flow rate with spout (m³/min)

Q_jm minimum spout flow rate (m³/min)

Q_max gas flow rate at maximum pressure drop across the spouted bed (m³/min)

Q_sp set-point for the PI-control loop Q - w (m³/min)

t time (min)

T_e fluid temperature at the exit (^oC)

VP inlet gas flow rate control valve-stem position, 0 to 1 (dimensionless)

Greek Letters

DP pressure drop across bed (mmHg)

DP_j pressure drop across bed with spout (mmHg)

DP_jm pressure drop at minimum spout flow rate (mmHg)

DP_jmax maximum pressure drop across the spouted bed (mmHg)

q angle of the cone vertex (^o)

w the blower's motor frequency (Hz)

Abbreviations

PC-AT486 Personal computer

PI Proportional-Integral control mode

PID Proportional-Integral-Derivative control mode

• Freire, J.T., Drying of Pastes in Spouted Beds. In: Freire, J.T. & Sartori, D.J.M.. Special Topics in Drying. Vol. 1, Chap. 2, p.42-85, EDUFSCar, Săo Carlos, Brazil (1992) (in portuguese).
• Mathur, K.E. and Epstein, N., Spouted Beds. Academic Press, New York, USA (1974).
• Moreira, E. A., Multiloop Control of a Spouted Bed. M.Sc. Thesis, PPG/DEQ/UFSCar, Săo Carlos, Brazil (1997) (in portuguese).
• Moreira, E. A., Corręa, N. A., Freire, J. T. and Corręa, R. G., "Implementation and Test of a Multiloop PID Controller in a Spouted Bed". Proceedings of the 11th International Drying Symposium - IDS'98, Halkidiki, Greece, August 19-22, Vol. A, p.557-564 (1998a).
• Moreira, E. A., Corręa, N. A., Kwong, W. H., Freire, J. T. and Corręa, R. G., "Comparison and Implementation of Two Multiloop PID Controller Tuning Methods Applied to a Spouted Bed". Proceedings of the Latin-America Congress on Heat and Mass Transfer - LATCYM'98, Salta, Argentina, October 5-8, Vol. I, p.222-227 (1998b).
• Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical Recipes - The Art of Scientific Computing. Cambridge University Press, Cambridge, UK (1989).
• Szentmarjay, T., Szalay, A., Pallai, E., Bencze, T. and Vass, J., Control of Drying Process in Mechanically Spouted Bed Dryer. Drying Technology, Vol. 14, No. 3 and 4, p.501-512 (1996).

Publication Dates

• Publication in this collection
  01 Mar 2000
• Date of issue
  Dec 1999

History

• Received
  22 July 1999
• Accepted
  30 Aug 1999