Control Schemes for an Industrial Rotary Calciner with a Heat Shield

Ind. Eng. Chem. Res. 1999, 38, 1007-1023

1007

Control Schemes for an Industrial Rotary Calciner with a Heat Shield around the Combustion Zone Selen Ciftci and Nam K. Kim* Department of Chemical Engineering, Michigan Technological University, Houghton, MI, 49931

Soda ash (sodium carbonate) is produced by calcining natural trona ore (sodium sesquicarbonate) in rotary calciners. Shell overheating, the consequent deformation of the calciner shell, and heat loss are frequently encountered problems during this operation. Installation of a concentric, metallic heat shield around the calciner’s combustion zone can help to reduce the shell temperature and recover some of the energy that would otherwise be lost. Another problem often encountered is the deterioration of product quality when the system inputs deviate from their design rates. A mathematical model of the calciner with a heat shield is used to design different control schemes in order to maintain the product quality. Performance of the designed control schemes is demonstrated via computer simulation. Introduction The direct-fired rotary kiln is one of the most important and widely employed high temperature process furnaces in the chemical industry. The large-scale processes and high cost of operation make experimentation on its processes nearly impossible. Therefore, mathematical modeling and computer simulation are powerful tools that can be used to evaluate the process and design its control system. This paper describes a mathematical model of an industrial soda ash calciner which has a heat shield around its combustion zone. The results of steady-state and open-loop dynamic simulations have been published elsewhere.1 Steady state, open-loop dynamics and various control schemes in the absence of the heat shield have also been investigated by Kim et al.2 and Kim and Srivastava.3-5 The present study focuses on the design of different control schemes in the presence of the heat shield. Some important results of the previous studies have also been included. Process Description The general layout of the calciner, for which the model was developed, is given in Figure 1. Both the calciner and the heat shield are constructed from mild steel. The heat shield is installed concentrically around the first 6 m of the kiln. The calciner is utilized for the endothermic decomposition of trona ore (sodium sesquicarbonate) into crude soda ash (sodium carbonate) according to the following reaction:

2(Na2CO3‚NaHCO3‚2H2O) f 3Na2CO3 + CO2 + 5H2O (1) The reaction is first order with respect to the sodium sesquicarbonate concentration and has an activation energy of 33.8 kcal/g‚mol of trona for temperatures lower than 95 °C. At higher temperatures, however, the activation energy becomes 12 kcal/g‚mol of trona. Trona ore is fed to the high end of the kiln and advances

toward the lower discharge end because of the inclination and rotation of the shell. Heat for the reaction is provided by burning a natural gas and air mixture using a single centerline burner. Since the burner is also located at the high end of the kiln, the hot combustion gases move co-currently and in direct contact with the solid. Mathematical Model The mathematical model used for the simulations was derived by Kim and Srivastava2,3 in accordance with the mass and heat balance equations proposed by Manitus et al.6 and Dumont and Belanger.7 The calciner under study is divided into three zones for modeling. In the combustion zone, the first 6 m of the kiln, the calciner shell is left bare to promote full flame development. The solid area available for heat and mass transfer is small because the solid particles slide down instead of showering through the flame. The lifter zone is located between the 6th and 24th m of the kiln. The closely spaced lifting flights of this zone help to shower the solid particles through the gas stream and increase the gassolid contact area. As a result, considerable heat and mass transfer takes place extensively and most of the reaction occurs in this zone. The discharge zone, the last 3 m of the kiln, is left bare to allow dust disengagement from the kiln off-gas. The design of the kiln shows that the distribution of the solid and the dynamics of motion of the solid particles in the bare zones differ from those in the lifter zone. Therefore, some system parameters, such as the retention time, the exposed area for heat and mass transfer, and the heat- and mass-transfer coefficients should be calculated separately for each zone. Also, the presence of the heat shield around the combustion zone (the first bare zone of the kiln) requires additional heat balance equations in comparison to the discharge zone (the second bare zone of the kiln). Mass-Transfer Equations. There are three main groups of equations related to mass transfer within the calciner. These arise from drying of the solids, from the reaction kinetics, and from flow of the solid material and the gas within the kiln.

10.1021/ie980229b CCC: $18.00 © 1999 American Chemical Society Published on Web 01/29/1999

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Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999

Figure 1. General layout of the kiln.

Drying. The free moisture contained within the solid material vaporizes as the solid material is heated up. This occurs in two phases, a constant rate drying and a falling rate drying. Constant rate drying occurs when the moisture content of the solid is greater than the critical moisture content. During this stage, the moisture movement within the solid particles is rapid enough to maintain a saturated condition at the surface, and the rate of drying is controlled by the rate of heat transfer to the evaporating surface. Since the heat of evaporation is provided by hot gas, the constant rate of water removal per unit length of the kiln is given by8

dQh htA(Tg - Tm) )dl Lv

(2)

where Qh is the flow rate of moisture contained within the solids, Lv is the latent heat of the vaporization, ht is the total heat-transfer coefficient, and A is the solid surface exposed per unit length of the kiln. The rate of drying decreases when the moisture content of the solid is less than the critical because the entire evaporating surface can no longer maintain saturation. Controlled primarily by the mechanism of moisture movement within the solid (capillary flow is assumed), the rate of drying during this stage is directly proportional to the free moisture content of the solid and is given by the relation9

dQh ) -KhQh dl

(3)

where Kh is a constant determined at the boundary between the two drying periods. Therefore, eqs 2 and 3 can be equated at this point, and for the known value of critical moisture content, Kh can be calculated. Reaction Kinetics. The reaction is first order; hence, the rate of decomposition is directly proportional to the sesquicarbonate content of the solids.

Kr d (S Q ) ) -Qm Sqe-E/(RTm) dl q m Vm

(4)

where Kr is the frequency factor and Vm is the solid velocity inside the calciner. Solid and Gas Flow Rates. Carbon dioxide and water vapor evolve from the solids as a result of the decomposition reaction. In addition, the drying of the solids should be considered. As a result, the solids’ flow rate, Qm, decreases, and the gas flow rate, Qg, increases down the length of the calciner. The stoichiometry of the reaction dictates that for every 226 units of mass of sodium sequicarbonate decomposed, 67 units of mass of gaseous products are formed. Taking this into consideration,

d 67 d d (Q ) ) (S Q ) + Qh dl m 226 dl q m dl

( )

(5)

and from the law of conservation of mass,

d d (Qg) ) - Qm dl dl

(6)

However, in the combustion zone, the rate of mixing of flame combustion products with the kiln gas has to be considered. Therefore,

d d d (Q ) ) - (Qm) - (Qc) dl g(cz) dl dl

(7)

Heat-Transfer Equations. The heat-transfer process is complex, particularly in a fired kiln in which radiation, convection, and conduction all contribute to the transfer of heat among the gas, kiln wall, and solid charge.10 Three assumptions were made to simplify the heat-transfer equations: (1) all parameters in a given cross section of the calciner are assumed to be constant, (2) conduction is important only in the radial direction, and (3) heat transfer due to conduction and radiation is negligible in the axial direction except radiation from the flame in the combustion section.

Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1009

Figure 2. Heat flows considered in the development of the model.

There are six main heat flow pathways calculated for the entire length of the calciner, namely: Hgm, from the calciner gas to the solid material; Hgw, from the calciner gas to the calciner wall; Hwm, from the calciner wall to the solid material; Hvg, from the evaporated vapor to the calciner gas; Hev, consumed by the evaporation of free moisture; Hre, consumed by the endothermic reaction. Hvg, Hev, and Hre become significant in the lifter zone, where the increased area of contact between the solid material and kiln gas causes drying and an increased rate of reaction. In addition, there are seven more heat flow pathways along the combustion zone that should be considered. Four of these arise from the presence of the heat shield: Hws, from the calciner wall to the heat shield; Hsb, from the heat shield to the infiltrated air; Hwb, from the calciner wall to the infiltrated air; Hso, from the heat shield to the ambient air. The other three flows are involved with the flame in the combustion zone. The flame is assumed to be cylindrical in shape, having a length of 6 m and a diameter equal to half the diameter of the kiln. It is further assumed that combustion is complete as soon as the fuel air mixture leaves the burner. Adiabatic combustion temperature is thus achieved at the burner exit. The combustion products then lose heat by virtue of convection and radiation to the kiln wall and gas as they move down the length of the combustion zone. The heat flows associated with the flame are Hfg, from the

flame to the calciner gas; Hfm, from the flame to the solid material; Hfw, from the flame to the calciner wall. After the combustion zone, the rest of the kiln is exposed to the surrounding air. Therefore, for the rest of the kiln Hwo (heat flow from the calciner wall to the ambient air) should be considered instead of the heat flow pathways related to the heat shield. The above-mentioned heat flows are shown in Figure 2. The direction of each form of heat flow is indicated via arrows. However, heat flows Hvg, Hre, and Hev cannot be assigned any direction. These flows are represented by circles in order to distinguish them from the other fluxes.5 Following the order of explanation given above, all of the heat flow equations used for simulations are presented here:

bare zones: Hgm ) hmL2(Tg - Tm) + σL2emeg(Tg4 - Tm4)

(8a)

Hgw ) hgL3(Tg - Tw) + σL3eweg(Tg4 - Tw4) (9a) Hwm ) hwL1(Tw - Tm) + σL2ew(1 - eg)em(Tw4 - Tm4) (10a)

1010


lifter zones: Hgm ) UA(Tg - Tm)

(8b)

Hgw ) hgL3′(Tg - Tw) + σL3′eweg(Tg4 - Tw4)

(9b)

Hwm ) hwL1′(Tw - Tm) Hvg ) -

495-530 K 435-465 K 340-370 K 85-93%

(12)

soda ash content of the solids at

simulation

actual plant data

d (S Q ∆H) dl q m

(13)

5 m from the feed end 12 m from the feed end 17 m from the feed end

63.94% 80.78% 86.88%

62-67% 74-79% 80-87%

Hws ) σFwsπD(Tw4 - Ts4)

(14)

Hsb ) hsπDs(Ts - Tb)

(15)

Hwb ) hbπD(Tw - Tb)

(16)

Table 2. Comparison of Simulation and Actual Soda Ash Contents

temperature. Qb is the mass flow rate of the infiltrated air, and Mw and Ms are the per unit length masses of the calciner wall and the heat shield, respectively. Heat Shield

4

Hfg ) σπDfefeg(Tf4 - Tg4) + hfπDf(Tf - Tg) d (Q C T ) (18) dl c c f Hfm ) σL2ef(1 - eg)emFfm(Tf4 - Tm4)

(19)

Hfw ) σπDfef(1 - eg)ewFfw(Tf4 - Tw4)

(20)

Hwo ) hoπD(Tw - To) + σπDw(Tw4 - To4) (21) Taking these flows into consideration, the heat balance equations for the calciner can be written as

( ) ( )

QgCg dTg dTg ) - QgCg + Hfg + Hvg - Hgm - Hgw Vg dt dl (22)

QmCm dTm dTm ) - QmCm + Hgm + Hwm + Hfm Vm dt dl Hev - Hre (23)

( ) ( )

QcCc dTf dTf ) -QcCc - Hfw - Hfm - Hfg (24) Vg dt dl QbCb dTb dTb ) - QbCb + Hwb + Hsb Vb dt dl

dTw ) Hfw + Hgw - Hwm - Hwb - Hws dt

(25) (26a)

dTw ) Hfw + Hgw - Hwm - Hwo dt

(26b)

dTs ) Hws - Hsb - Hso dt

(27)

MsCs

actual plant data

502.84 K 466.25 K 361.01 K 88.80%

d (Q L ) dl h v

Hso ) hsoπDs(Ts - To) + σπDses(Ts - To ) (17)

MwCw

simulation

(11)

4

MwCw

calciner gas temp solid spill temp calciner shell temp soda ash content of the product

d (Q C T ) dl m v m

Hev ) Hre ) -

(10b)

Table 1. Comparison of Simulation and Actual Plant Data, at the Discharge End

where Cg, Cm, Cb, Cw, and Cs are the specific heats and Tg, Tm, Tb, Tw, and Ts are the temperatures of the calciner gas, solids, infiltrated (bulk) air, calciner wall, and heat shield, respectively. Cc is the specific heat of the flame combustion products and Tf is the flame

Before we continue with the design of the control systems, the heat shield should be commented on briefly. The heat shield is utilized in order to avoid shell overheating, which is an inevitable problem in the operation of the calciner, because of the flame in the combustion zone. The design of the heat shield has been discussed in detail by Kim et al.11 and Kim and Srivastava.5 Steady-state and open-loop dynamics temperature profiles for the shield have been simulated, and the effectiveness of the shield in lowering the shell temperature below the critical temperature (672 K) of mild steel12 has been verified, as have been its energysaving benefits.1 To give the reader an idea about the credibility of the steady-state simulations, the results obtained are compared to the available plant data in Tables 1 and 2. Also, temperature profiles along the combustion zone are presented in Figure 3a to give the reader an idea about the effect of the heat shield. Finally, Figure 3b is included to prove, in the presence of the heat shield, energy can be saved without sacrificing product quality. PID Control Systems for the Calciner The steady state and dynamics of the calciner have been successfully simulated using the model described above.1 This study aims to employ this model to design control schemes improving the product quality of the calciner. Three PID (proportional integral derivative) feedback control schemes are presented in this paper. The performance of each scheme is tested with respect to step disturbances in the ore feed rate ((20 tph) (tph ) tons per hour) and the sodium sesquicarbonate content of the feed ((5%). Typical steady-state operating conditions for the calciner are given in Table 3. The natural gas flow rate to the burner is the manipulated variable for all of the schemes presented. The control objective is to keep the unreacted sesquicarbonate content of the product close to its steady-state value of 0.016%. The Ziegler-Nichols tuning method13 is used to calculate the controller settings which are given in Table 4. The response of the calciner wall and the heat shield is reported at 3 m from the feed end because this point was noted to be the hottest area of the kiln shell for steady-state computations with the heat shield.1 The manipulated variable, natural gas rate, is monitored at


Figure 3. (a) Temperature profiles along the combustion zone. (b) Soda ash conversion profiles along the calciner. (The conversion remains the same at a lower natural gas flow rate in the presence of the heat shield.) Table 3. Typical Operating Conditions for the Calciner Trona ore feed rate, ton/h natural gas rate, ton/h combustion (primary) air rate, ton/h

200 4.2 92.4

Trona Ore Feed Composition, mass % sodium sesquicarbonate free moisture insolubles

90.83 0.72 8.45

Combustion and Infiltrated Air Composition O2 N2 H2O Trona ore feed temp, K combustion air temp, K infiltrated air temp, K ambient air temp, K

22.93 76.77 0.72 280 280 280 280

the feed end. The variations in calciner gas and product temperatures, and concentration, are presented at the discharge end. The profile of the controlled variable is presented above the profile of the manipulated variable for comparison. Controlled Variable: Sodium Sesquicarbonate Content of the Product. The closed-loop system response, when the unreacted sesquicarbonate content of the product is the direct controlled variable, is

Table 4. PID Controller Settings controlled variable

Tg (K)

Sq (%)

Tm (K)

Kc τ1 τD

50.0 [(kg/h)/K] 2.778 × 10-3 h-1 6.944 × 10-4 h-1

2647.0 [(kg/h)/%] 216.70 × 10-3 h-1 541.70 × 10-4 h-1

19.1 [(kg/h)/K] 208.33 × 10-3 h-1 520.83 × 10-4 h-1

displayed in Figures 4, parts a and b, and 5 parts a and b. It can be seen from the graphs that this scheme has several shortcomings, such as long dead and settling times and high initial deviations from the steady-state values. Moreover, the unreacted sodium sesquicarbonate content of the product is the direct controlled variable of this control scheme, which makes on-line solid composition analysis necessary. Although sophisticated on-line analyzers are available, their industrial application is undermined by their high cost.5 All system variables exhibit a somewhat large dead time, which is nearly the retention time of the solids in the calciner. The controller is unable to take any corrective action before the first batch of the solids subjected to disturbance reaches the spill end of the calciner. This large dead time causes a long settling time, and also large initial deviations from the steadystate values, especially for a +20 tph disturbance in the

1012


(a)

(b)

Figure 4. (a) PID control on the sodium sesquicarbonate content of the product: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); at 3 m from the feed end. (b) PID control on the sodium sesquicarbonate content of the product: Closed-loop response of the system to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

feed ore rate. Increasing the sodium sesquicarbonate content of the feed and increasing the feed rate both increase the amount of reactants entering the calciner. Therefore, more energy should be supplied into the system in both cases. However, increasing the feed rate means that more insolubles are entering the system along with the reactants, and that they also should be heated up to the reaction temperature. Thus, positive (negative) disturbances in the feed rate need more (less) energy supplements in comparison to the disturbances in the sodium sesquicarbonate content of the feed. From the heat balance equations, it is evident that the calciner wall temperature is dependent on heat transfer from the flame in the combustion zone of the

calciner. This can easily be observed in the simulation results. The large deviation peak in the natural gas rate (for a +20 tph disturbance in the feed rate) is also reflected in the calciner shell temperature. An increased (reduced) natural gas burning rate results in a raised (lowered) shell temperature. A warmer (cooler) shell in turn radiates more (less) heat to the heat shield, thereby raising (decreasing) the shield temperature. Although it is not possible to utilize this scheme easily, it is still beneficial to have these simulation results to have a criteria about the near-ideal fulfillment of the control objective. Controlled Variable: Kiln Off-Gas Temperature. In trona industries, control of product quality is usually


(a)

(b)

Figure 5. (a) PID control on the sodium sesquicarbonate content of the product: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); at 3 m from the feed end. (b) PID control on the sodium sesquicarbonate content of the product: Closed-loop response of the system to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

maintained by controlling the kiln off-gas temperature at a desired steady-state value. Taking the off-gas temperature as the controlled variable has two advantages: (1) The kiln gas has a much smaller retention time in comparison to the solid; hence, there is less dead time observed in the response of the system. (2) The gas temperature may easily be measured on-line with the help of thermocouples. Figures 6 parts a and b, and 7, parts a and b, present the closed-loop response of the system with kiln off-gas temperature control. Owing to the large velocity of the kiln gas, the dead time observed in both controlled and manipulated variables is rather short in comparison to the previous control scheme. Product temperature and sodium sesquicarbonate concentration, however, exhibit a larger dead time as a result of the large retention time of the solids in the kiln. Calciner shell and heat shield tem-

peratures rise (decline) from their steady-state values, depending on the manipulations made in the natural gas rate. The kiln off-gas temperature is kept at its steady-state value for all disturbances. Nevertheless, this scheme fails to control the sodium sesquicarbonate concentration of the product satisfactorily. Positive disturbances result in undercalcination, whereas overcalcination is observed for negative disturbances. Trona industries solve this problem by adjusting the setpoint of the kiln off-gas temperature to retain the unreacted sodium sesquicarbonate content of the product at its steadystate value. This makes the control scheme depend on the judgment and experience of the operator. Controlled Variable: Product Temperature. Figures 8, parts a and b, and 9, parts a and b, display the closed-loop response of the system with the product

1014


(a)

(b)

Figure 6. (a) PID control on the off-gas temperature: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); at 3 m from the feed end. (b) PID control on the off-gas temperature: Closed-loop response of the system to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

temperature as the controlled variable. Looking at the concentration profiles, it can be concluded that this scheme is successful in eliminating the problem of overand undercalcination. Because of the large retention time of solids in the calciner, this scheme does exhibit a large dead time, as in the case of the product sodium sesquicarbonate content control scheme. However, the product temperature control scheme is advantageous in that the product temperature can be easily measured on-line with the help of thermocouples. Because of the low controller gain used for this design, the variations in the manipulated variable are not as large as the variations in the product sesquicarbonate content control scheme. The calciner wall and heat shield temperatures rise (decline) from their steady-

state values, depending on the manipulations of the natural gas flow rate. Feedforward Control Scheme Feedback control schemes must be able to detect a deviation in one (or more) of the system outputs from a certain setpoint in order to feed this error signal back into the controller. Only then can the controller change the manipulated variable. However, the controller does not use any information about the source and size of the disturbance. In contrast, a feedforward control scheme is based on detecting a disturbance as soon as it hits the system. In this case, the manipulated variable


(a)

(b)

Figure 7. (a) PID control on the off-gas temperature: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); at 3 m from the feed end. (b) PID control on the off-gas temperature: Closed-loop response of the system to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

can be adjusted to keep the output variables constant. Feedforward controllers can be especially effective for slow-moving systems which contain large dead times. To be able to implement feedforward control, we must know how the disturbance and manipulated variable are related to the controlled variable. To establish these relationships, we used the process reaction curve method. Step disturbances were introduced in the principal system inputs Sq(in), Qm(in), and Qh(in), which can be potential disturbances, and also in the manipulated variable, natural gas rate (Ngas). Open-loop responses of the controlled variable (Sq(out), sodium sesquicarbonate content of the product) were simulated for each disturbance.1 These profiles were approximated by firstorder transfer functions with dead time.

For a first-order-with-dead-time model the parameters are determined by the graphical calculations. With X(s) denoting the input and Y(s) denoting the output, the form of the model is given as:14 -t s Y(s) Kpe d ) X(s) τps + 1

(28)

Both X(s) and Y(s) are deviation variables. The graphical calculations are shown in Figure 10. The magnitude of the input change, δ, the magnitude of the steady-state change in the input, ∆, and the times at which the output reaches 28 and 63% of its final value are determined from the graph.

1016


(a)

(b)

Figure 8. (a) PID control on the product temperature: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); at 3 m from the feed end. (b) PID control on the product temperature: Closed-loop response of the system to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

The model parameters are calculated as14

Kp ) ∆/δ τp ) 1.5(t63% - t28%) td ) t63% - τ A sample calculation using the process reaction curve in Figure 10 is carried out in the Appendix. The result of this calculation provides the second entry of Table 5. Figure 11 compares the actual open-loop simulation result and this first-order-with-dead-time approxima-

tion. Table 5 shows the transfer functions relating the controlled variable Sq(out) to potential system disturbances and the manipulated variable Ngas. All the transfer functions given in Table 5 are obtained using the method described above. Figure 12 shows a simple feedforward block diagram. The load disturbance D(s) enters the process through the GD(s) process transfer function. The same disturbance is also fed into a feedforward control device that has a transfer function GF(s). The feedforward controller detects changes in the load D(s) and makes changes in the manipulated variable Ngas(s). Thus, the transfer function of a feedforward controller is a relationship between the manipulated variable and


(a)

(b)

Figure 9. (a) PID control on the product temperature: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); at 3 m from the feed end. (b) PID control on the product temperature: Closed-loop response of the system to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

a disturbance variable.

GF(s) )

expressed as

Ngas(s) D(s)

)

GD(s)

GM(s) )

GM(s)

Following the example given above for the transfer function relating the controlled variable Sq(out) and the disturbance Qm(in), GD(s) is given as

GD(s) )

Sq(out) Qm(in)

-2

)

-0.43s

(5.72 × 10 )e 0.044s + 1

and from the last entry of Table 5 we can see GM(s) is

Sq(out) Ngas

)

(6.943 × 10-4)e-0.187s 0.163s + 1

Taking the ratio [-GD(s)/GM(s)] the feedforward controller transfer function GF(s) becomes

GF(s) ) -

(

)(

(5.72 × 10-2)e-0.43s 0.163s + 1 0.044s + 1 (6.943 × 10-4)e-0.187s

)

Details on the digital implementation of feedforward control is given by Marlin.14 The closed-loop profiles of the calciner with feedforward control are shown in Figures 13, parts a and b,

1018


Figure 10. Process reaction curve.

Figure 11. Approximation of the open-loop sytstem response by a first-order transfer function with dead time. Disturbance: +20 tph in the ore feed rate.


Figure 12. Block diagram of feedforward control.

(a)

(b)

Figure 13. (a) Feedforward control scheme: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); at 3 m from the feed end. (b) Feedforward control scheme: Closed-loop response of the system to step changes of (5% in the sodium sesquicarbonate content of the feed ore (from the steady-state value of 90.83%); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

and 14, parts a and b. This final scheme provides very effective control for the system, considering the shorter dead time elapsed and the smaller initial deviation in

the controlled variable compared to previous schemes. The control objective has been met successfully for feed rate disturbances, although there is an error of 20% in

1020


(a)

(b)

Figure 14. (a) Feedforward control scheme: Closed-loop response of the calciner wall and heat shield temperatures to step changes of (20 tph in the feed rate (from the steady-state value of 200 tph); at 3 m from the feed end. (b) Feedforward control scheme: Closed-loop response of the system to step changes of (20 tph in the ore feed rate (from the steady-state value of 200 tph); natural gas flow rate at the feed end, rest of the system variables at the discharge end.

the controlled variable in the case of a -5% step disturbance in the sesquicarbonate content of the feed ore. Simulation results for the positive disturbances introduced in both system inputs show that the initial response of the manipulated variable is higher than its final settling value. This is the reason for the overcalcination tendency of the product within the first 50 min after the disturbance. The opposite holds true for negative disturbances, and the product sesquicarbonate content initially rises from its steady-state value. Once again the calciner wall and heat shield temperatures exhibit their dependency on the natural gas-burning rate. By comparing overall efficiency of the controllers presented in this study, one can see the advantages of feedforward control over feedback control. In theory,

perfect control can be achieved using a feedforward controller, although the perfect model also has to be known. In this study the first-order approximations used are reasonably close to the actual open-loop simulation results, though not perfect. Thus, some deviations from the steady state are observed in closedloop simulations. Another shortcoming of feedforward control is that the disturbance must be detected. If the disturbance cannot be measured, feedforward control cannot be used. This is one reason why feedforward control for throughput changes is commonly used, whereas feedforward control for feed composition disturbances is occasionally used. The former requires a flow-measurement device, which is usually available. The latter requires a composition analyzer, which may or may not be available.15 In this study one of the

Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1021 Table 5. Transfer Functions Relating the Controlled Output to the Potential Disturbances and the Manipulated Variable Sq(out) Sq(in)

(2.64 × 10-2)e-0.408s 0.0833s + 1

[5.0%]a

Qm(in)

[20 tph]a

(5.72 × 10-2)e-0.43s 0.044s + 1

Qh(in)

[0.5%]a

(5.44 × 10-2)e-0.392s 0.0917s + 1

Ngas

-

[-200 kg/h]a

(6.943 × 10-4)e-0.187s 0.163s + 1

a The values in the brackets are the step disturbances used to derive the transfer functions.

Table 6. Summary of System Parameters’ Values for the Controllers Implementeda contoller

disturbance

Sq (%)

Tm (K)

Twall (K)

Tg (K)

FBC on Sq

-5% Sq +5% Sq -20 tph Qm +20 tph Qm

0.0159 0.0158 0.0159 0.0158

464.82 467.56 463.61 468.52

606.34 613.93 599.91 619.84

497.79 507.46 489.86 516.94

FBC on Tg


0.0066 0.0327 0.0012 0.1075

469.91 462.82 476.90 454.48

607.47 612.l92 602.35 616.81

502.88 502.88 502.88 502.88

FBC on Tm


0.0124 0.0194 0.0100 0.0223

466.30 466.30 466.29 466.30

606.62 613.66 599.83 619.35

499.27 506.23 492.50 514.70

FFCn


0.0125 0.0159 0.0180 0.0185

466.24 467.54 462.82 467.52

606.59 613.93 598.93 619.63

499.22 507.43 489.16 515.93

a After 5 h of simulation is completed; all system parameter values are given at the feed end, except Twall which is given at 3 m.

disturbances introduced to the system is the sesquicarbonate content of the feed ore whose detection would require a costly on-line analyzer. Conclusion This study involves mathematical modeling of an industrial calciner which has a heat shield around its combustion zone. A model developed in previous studies has been used to design four control schemes. The performance of those control schemes was evaluated with respect to positive and negative disturbances in two principal system inputs. A summary of system parameters’ values after 5 h of simulation time is given in Table 6. The simulation results reveal that PID feedback schemes based on controlling the product temperature and sodium sesquicarbonate concentration exhibit large dead times. These large dead times result in large initial deviations from steady state and long settling times. If the kiln off-gas temperature is used as the controlled variable, the problem of large dead time is eliminated. However, the sodium sesquicarbonate concentration of the product cannot be controlled satisfactorily in this way. Another way of eliminating the large dead time is to employ a feedforward controller. A first-order input-output model of the calciner was

derived which was used to design a feedforward scheme. This feedforward control scheme was especially successful in handling disturbances in the feed ore rate. Nevertheless, the implementation of the feedforward scheme for disturbances in the sodium sesquicarbonate content of the feed ore would require an on-line feed ore composition analysis, which can be costly. The large retention time of the solids in the calciner is the main problem which hinders the development of efficient control schemes. Developing a dead time compensator and a cascade control scheme for the calciner will be the objective of continuing research. Acknowledgment The authors wish to acknowledge the Graduate School of Michigan Technological University for financial support provided during this study. Nomenclature A ) area of the solids exposed to the gas, per unit length of the calciner, m2/m Cb, Cc, Cg, Cm, Cs, Cv, Cw ) specific heat of the infiltrated air, flame combustion products, calciner gas, solids, heat shield, vapors, and the calciner wall, kcal/(kg‚K) D ) diameter of the kiln, m Df ) diameter of the flame, m Ds ) diameter of the heat shield, m D(s) ) disturbance to the system E ) activation energy for trona decomposition, kcal/g‚mol of trona ef, eg, em, es, ew ) emissivity of the flame, kiln gas, solid material, heat shield, and kiln wall Ffm, Ffw, Fws ) form factor for radiative heat transfer between the flame and solid, flame and wall, and wall and shield g ) acceleration due to gravity, m/s2 GD(s), GF(s), GM(s) ) transfer functions defined in the text hb, hf, hg, hm, ho, hw ) heat-transfer coefficients of infiltrated air, flame, kiln gas, solid material, ambient air, and kiln wall hs, hso ) convective heat-transfer coefficient for heat transfer between the heat shield and infiltrated air and the heat shield and ambient air, kcal/h‚m2‚K Hev, Hfg, Hfm, Hfw, Hgm, Hgw, Hre, Hvg, Hsb, Hso,Hwb, Hwm, Hws, Hwo ) heat flows defined in the text, kcal/(h‚m) Kh ) proportionality constant used in drying equation, m-1 Kp ) process gain Kr ) frequency factor in the reaction rate expressions, h-1 l ) length, m L1 ) arc length of kiln circumference in contact with the solid material (in the bare zones), m L2 ) segment of the solid material open to heat exchange with the kiln gas, m L3 ) arc length of kiln circumference not in contact with the solid (in the bare zones), m L1′ ) equivalent of L1 in the lifter zone, m L3′ ) equivalent of L3 in the lifter zone, m Lv ) latent heat of evaporation of water, kcal/kg Ms ) mass per unit length of the shield, kg/m Mw ) mass per unit length of the calciner wall, kg/m Ngas ) natural gas (burning) rate, kg/h

1022


Qb, Qc, Qg, Qg(cz), Qh, Qm ) flow rate of the infiltrated air, flame combustion products, calciner gas (in the last 21 m of the kiln), calciner gas (in the combustion zone of the kiln), free moisture within the solid, and the solids, kg/h Qh(in) ) free moisture within the feed ore, mass % Qm(in) ) feed ore rate, tph Sq, Sq(in), Sq(out) ) sodium sesquicarbonate content of the solids inside the kiln at any given time, of the feed ore, and of the product, mass % t ) time, h td ) dead time t28%, t63% ) times at which the system output reaches 28% and 63% of its final value (for the process reaction curve) Tam, Tb, Tf, Tg, Tm, Ts, Tw ) temperature of the ambient, infiltrated air, flame, calciner gas, solids, heat shield, and calciner wall, K U ) combined heat-transfer coefficient for convective and radiative heat flow between solids and gas in the lifter zone, kcal/(h‚m2‚K) Vb ) velocity of the infiltrated air, m/h Vg ) velocity of the calciner gas, m/h Vm ) solids velocity through the calciner, m/h

(d) Heat capacities are as follows:

Cb ) 0.77(0.249 + 2.62 × 10-5Tb) + 0.23(0.228 + 2.6 × 10-5Tb) Cc ) 0.737(0.249 + 2.62 × 10-5Tf) + 0.066(0.228 + 2.6 × 10-5Tf) + 0.1096(0.2406 + 3.96 × 10-5Tf) + 0.0861(0.431 + 1.44 × 10-4Tf) Cg ) (MN2(0.249 + 2.62 × 10-5Tg) + MO2(0.228 + 2.6 × 10-5Tf) + MCO2(0.2406 + 3.96 × 10-5Tf) + MH2O(0.431 + 1.44 × 10-4Tf))/(MN2 + MO2 + MCO2 + M H 2O ) where MN2, MO2, MCO2 and MH2O are the mass flow rates of nitrogen, oxygen, carbon dioxide, and water vapor in the kiln gas calculated by the stoichiometry of the natural gas combustion:

Cv ) (8.22 + 1.5 × 10-6Tg + 1.34 × 10-6Tg2)/18 (e) Sample transfer function calculation for feedforward control from Figure 10:

Greek Symbols σ ) Stefan constant, τp ) process time constant

kcal/h‚m2‚K4

∆ ) (1.16 - 0.016)% ) 1.144% δ ) 20 tph

Appendix

Kp ) (1.144%)/20 tph ) 5.72 × 10-2 (%/tph)

(a) The coefficients used in the simulation have the following values: A ) 98.05 m2/m, Cm ) 0.271 kcal/(kg‚ K), Cs ) 0.120 kcal/(kg‚K), Cw ) 0.120 kcal/(kg‚K), D ) 5.0 m, Df ) 2.5 m, Ds ) 5.1016 m, E ) 33.8 kcal/g‚mol of trona (T < 95 °C), and E ) 12 kcal/g‚mol of trona (T > 95 °C), ef ) 0.19, eg ) 0.1, em ) 0.5, es ) 0.8, ew )0.3, Ffm ) 0.3, Ffw ) 0.3, hf ) 2.0, hg ) 2.5, hm ) 4.0, hw ) 30.0, Kr ) 1.9 × 107 h-1, L1 ) 1.31 m, L2 ) 1.33 m, L3 ) 14.40 m, L1′ ) 1.03 m, L3′ ) 14.68 m, Lv ) 540.0 kcal/ kg, Ms ) 2500.0 kg/m, Mw ) 6000.0 kg/m, U ) 50 kcal (h‚m2‚K), Vb ) 17775.93 m/h, Vg ) 10 000 m/h, Vm ) 36.4 m/h. (b) Convective heat-transfer coefficients ho and hso were estimated by the correlation

( ) ( )

cpµa hL ) 0.036 Ka Ka

0.333

LVaFa µa

( ) ( 0.333

τp ) 26.72 min 3

t63% ) td + τp ) 28.46 min Solving for td and τp from the above equations results in

td ) 25.84 min ) 0.43 h τp ) 2.62 min ) 0.044 h With those values the transfer function relating Sq(out) and Qm(in) becomes

0.8

Sq(out) Qm(in)

where Ka, µa, Fa, and Va are the thermal conductivity, viscosity, density, and velocity of the ambient air. L is the kiln length under consideration. (c) Convective heat-transfer coefficients hb and hs were estimated by the correlation

hDe cpµa ) 0.023 Κa Ka

t28% ) td +

)

DeVaFa µa

0.8

where Ka, µa, Fa, and Va are the thermal conductivity, viscosity, density, and velocity of the ambient air. De is the equivalent diameter of the annular passage between the shield and the kiln.

)

5.72 × 10-2e-0.43s 0.044s + 1

Literature Cited (1) Ciftci, S.; Kim, N. K. Simulation and Control of an Industrial Rotary Calciner with a Heat Shield around the Combustion Zone. Trans. Inst. Chem. Eng. 1996, 74, 901. (2) Kim, N. K.; Srivastava, R.; Lyon, J. Simulation of an Industrial Calciner with Trona Ore Decomposition. Ind. Eng. Chem. Res. 1988, 27, 1194. (3) Kim, N. K.; Srivastava, R. Simulation and Control of an Industrial Calciner. Ind. Eng. Chem. Res. 1990, 29, 71. (4) Kim, N. K.; Srivastava, R. Computer Simulation of an Industrial Calciner with an Improved Control Scheme. Ind. Eng. Chem. Res. 1991, 30, 594. (5) Kim, N. K.; Srivastava, R. Design of a Heat Shield and Advanced Control Systems for a Rotary Calciner. Chem. Eng. Commun. 1993, 122, 171.

Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1023 (6) Manitus, A.; Kurcyvsz, E.; Kawecki W. Mathematical Model of the Aluminum Oxide Rotary Kiln. Ind. Eng. Chem. Process Des. Dev. 1974, 13, 841. (7) Dumont, G.; Belanger, P. R. Steady State Study of a Titanium Dioxide Rotary Kiln. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 107. (8) Coulson, J. M.; Richardson, J. F. Unit Operations; Pergamon Press Ltd: Oxford, England, 1978. (9) Geankoplis, C. J. Transport Processes and Unit Operations; Prentice Hall: Englewood Cliffs, NJ, 1993. (10) Tscheng, S. H.; Watkinson, A. P. Convective Heat Transfer in a Rotary Kiln. Can. J. Chem. Eng. 1979, 57, 433. (11) Kim, N. K.; Lyon J. E.; Suryanarayana, N. V. Heat Shields for High-Temperature Kilns. Ind. Eng. Chem. Process. Des. Dev. 1986, 25, 843.

(12) Clarke, L.; Davidson, R. Manual for Process Engineering Calculations; McGraw-Hill: New York, 1962. (13) Stephanopoulos, G. Chemical Process Control; Prentice Hall Inc.: Englewood Cliffs, NJ, 1984. (14) Marlin, T. E. Process Control; McGraw-Hill: New York, 1995. (15) Luyben, W. L. Process Modeling, Simulation and Control for Chemical Engineers; McGraw-Hill: New York, 1990.

Received for review April 13, 1998 Revised manuscript received November 24, 1998 Accepted November 29, 1998 IE980229B

Control Schemes for an Industrial Rotary Calciner with a Heat Shield

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